document_title: Diffusion

question_text: where does diffusion take place in our body

question_tokens: where does diffusion take place in our body

text: Diffusion

text: Diffusion vs. bulk flow[edit]

text: An example of a situation in which bulk motion and diffusion can be differentiated is the mechanism by which oxygen enters the body during external respiration known as breathing. The lungs are located in the thoracic cavity, which expands as the first step in external respiration. This expansion leads to an increase in volume of the alveoli in the lungs, which causes a decrease in pressure in the alveoli. This creates a pressure gradient between the air outside the body at relatively high pressure and the alveoli at relatively low pressure. The air moves down the pressure gradient through the airways of the lungs and into the alveoli until the pressure of the air and that in the alveoli are equal i.e. the movement of air by bulk flow stops once there is no longer a pressure gradient.

text: The air arriving in the alveoli has a higher concentration of oxygen than the “stale” air in the alveoli. The increase in oxygen concentration creates a concentration gradient for oxygen between the air in the alveoli and the blood in the capillaries that surround the alveoli. Oxygen then moves by diffusion, down the concentration gradient, into the blood. The other consequence of the air arriving in alveoli is that the concentration of carbon dioxide in the alveoli decreases. This creates a concentration gradient for carbon dioxide to diffuse from the blood into the alveoli, as fresh air has a very low concentration of carbon dioxide compared to the blood in the body.

text: The pumping action of the heart then transports the blood around the body. As the left ventricle of the heart contracts, the volume decreases, which increases the pressure in the ventricle. This creates a pressure gradient between the heart and the capillaries, and blood moves through blood vessels by bulk flow down the pressure gradient. As the thoracic cavity contracts during expiration, the volume of the alveoli decreases and creates a pressure gradient between the alveoli and the air outside the body, and air moves by bulk flow down the pressure gradient.

text: Diffusion in the context of different disciplines[edit]

text: The concept of diffusion is widely used in: physics (particle diffusion), chemistry, biology, sociology, economics, and finance (diffusion of people, ideas and of price values). However, in each case, the object (e.g., atom, idea, etc.) that is undergoing diffusion is “spreading out” from a point or location at which there is a higher concentration of that object.

text: There are two ways to introduce the notion of diffusion: either a phenomenological approach starting with Fick's laws of diffusion and their mathematical consequences, or a physical and atomistic one, by considering the random walk of the diffusing particles.[2]

text: In the phenomenological approach, diffusion is the movement of a substance from a region of high concentration to a region of low concentration without bulk motion. According to Fick's laws, the diffusion flux is proportional to the negative gradient of concentrations. It goes from regions of higher concentration to regions of lower concentration. Some time later, various generalizations of Fick's laws were developed in the frame of thermodynamics and non-equilibrium thermodynamics.[3]

text: From the atomistic point of view, diffusion is considered as a result of the random walk of the diffusing particles. In molecular diffusion, the moving molecules are self-propelled by thermal energy. Random walk of small particles in suspension in a fluid was discovered in 1827 by Robert Brown. The theory of the Brownian motion and the atomistic backgrounds of diffusion were developed by Albert Einstein.[4] The concept of diffusion is typically applied to any subject matter involving random walks in ensembles of individuals.

text: Biologists often use the terms "net movement" or "net diffusion" to describe the movement of ions or molecules by diffusion. For example, oxygen can diffuse through cell membranes so long as there is a higher concentration of oxygen outside the cell. However, because the movement of molecules is random, occasionally oxygen molecules move out of the cell (against the concentration gradient). Because there are more oxygen molecules outside the cell, the probability that oxygen molecules will enter the cell is higher than the probability that oxygen molecules will leave the cell. Therefore, the "net" movement of oxygen molecules (the difference between the number of molecules either entering or leaving the cell) is into the cell. In other words, there is a net movement of oxygen molecules down the concentration gradient.

text: History of diffusion in physics[edit]

text: In the scope of time, diffusion in solids was used long before the theory of diffusion was created. For example, Pliny the Elder had previously described the cementation process, which produces steel from the element iron (Fe) through carbon diffusion. Another example is well known for many centuries, the diffusion of colours of stained glass or earthenware and Chinese ceramics.

text: In modern science, the first systematic experimental study of diffusion was performed by Thomas Graham. He studied diffusion in gases, and the main phenomenon was described by him in 1831–1833:[5]

text: "...gases of different nature, when brought into contact, do not arrange themselves according to their density, the heaviest undermost, and the lighter uppermost, but they spontaneously diffuse, mutually and equally, through each other, and so remain in the intimate state of mixture for any length of time.”

text: The measurements of Graham contributed to James Clerk Maxwell deriving, in 1867, the coefficient of diffusion for CO2 in air. The error rate is less than 5%.

text: In 1855, Adolf Fick, the 26-year-old anatomy demonstrator from Zürich, proposed his law of diffusion. He used Graham's research, stating his goal as "the development of a fundamental law, for the operation of diffusion in a single element of space". He asserted a deep analogy between diffusion and conduction of heat or electricity, creating a formalism that is similar to Fourier's law for heat conduction (1822) and Ohm's law for electric current (1827).

text: Robert Boyle demonstrated diffusion in solids in the 17th century[6] by penetration of Zinc into a copper coin. Nevertheless, diffusion in solids was not systematically studied until the second part of the 19th century. William Chandler Roberts-Austen, the well-known British metallurgist, and former assistant of Thomas Graham, studied systematically solid state diffusion on the example of gold in lead in 1896. :[7]

text: "... My long connection with Graham's researches made it almost a duty to attempt to extend his work on liquid diffusion to metals."

text: In 1858, Rudolf Clausius introduced the concept of the mean free path. In the same year, James Clerk Maxwell developed the first atomistic theory of transport processes in gases. The modern atomistic theory of diffusion and Brownian motion was developed by Albert Einstein, Marian Smoluchowski and Jean-Baptiste Perrin. Ludwig Boltzmann, in the development of the atomistic backgrounds of the macroscopic transport processes, introduced the Boltzmann equation, which has served mathematics and physics with a source of transport process ideas and concerns for more than 140 years.[8]

text: In 1920–1921 George de Hevesy measured self-diffusion using radioisotopes. He studied self-diffusion of radioactive isotopes of lead in liquid and solid lead.

text: Yakov Frenkel (sometimes, Jakov/Jacov Frenkel) proposed, and elaborated in 1926, the idea of diffusion in crystals through local defects (vacancies and interstitial atoms). He concluded, the diffusion process in condensed matter is an ensemble of elementary jumps and quasichemical interactions of particles and defects. He introduced several mechanisms of diffusion and found rate constants from experimental data.

text: Some time later, Carl Wagner and Walter H. Schottky developed Frenkel's ideas about mechanisms of diffusion further. Presently, it is universally recognized that atomic defects are necessary to mediate diffusion in crystals.[7]

text: Henry Eyring, with co-authors, applied his theory of absolute reaction rates to Frenkel's quasichemical model of diffusion.[9] The analogy between reaction kinetics and diffusion leads to various nonlinear versions of Fick's law.[10]

text: Basic models of diffusion[edit]

text: Diffusion flux[edit]

text:
Each model of diffusion expresses the diffusion flux through concentrations, densities and their derivatives. Flux is a vector

J

{\displaystyle \mathbf {J} }

. The transfer of a physical quantity

N

{\displaystyle N}

 through a small area

Δ
S

{\displaystyle \Delta S}

 with normal

ν

{\displaystyle \nu }

 per time

Δ
t

{\displaystyle \Delta t}

 is

text:
where

(

J

,
ν
)

{\displaystyle (\mathbf {J} ,\nu )}

 is the inner product and

o
(
⋯
)

{\displaystyle o(\cdots )}

 is the little-o notation. If we use the notation of vector area

Δ

S

=
ν

Δ
S

{\displaystyle \Delta \mathbf {S} =\nu \,\Delta S}

 then

text:
The dimension of the diffusion flux is [flux] = [quantity]/([time]·[area]). The diffusing physical quantity

N

{\displaystyle N}

 may be the number of particles, mass, energy, electric charge, or any other scalar extensive quantity. For its density,

n

{\displaystyle n}

, the diffusion equation has the form

text:
where

W

{\displaystyle W}

 is intensity of any local source of this quantity (the rate of a chemical reaction, for example). For the diffusion equation, the no-flux boundary conditions can be formulated as

(

J

(
x
)
,
ν
(
x
)
)
=
0

{\displaystyle (\mathbf {J} (x),\nu (x))=0}

 on the boundary, where

ν

{\displaystyle \nu }

 is the normal to the boundary at point

x

{\displaystyle x}

.

text: Fick's law and equations[edit]

text: Fick's first law: the diffusion flux is proportional to the negative of the concentration gradient:

text: The corresponding diffusion equation (Fick's second law) is

text:
where

Δ

{\displaystyle \Delta }

 is the Laplace operator,

text: Onsager's equations for multicomponent diffusion and thermodiffusion[edit]

text:
Fick's law describes diffusion of an admixture in a medium. The concentration of this admixture should be small and the gradient of this concentration should be also small. The driving force of diffusion in Fick's law is the antigradient of concentration,

−
∇
n

{\displaystyle -\nabla n}

.

text: In 1931, Lars Onsager[11] included the multicomponent transport processes in the general context of linear non-equilibrium thermodynamics. For multi-component transport,

text:
where

J

i

{\displaystyle \mathbf {J} _{i}}

 is the flux of the ith physical quantity (component) and

X

j

{\displaystyle X_{j}}

 is the jth thermodynamic force.

text: The thermodynamic forces for the transport processes were introduced by Onsager as the space gradients of the derivatives of the entropy density s (he used the term "force" in quotation marks or "driving force"):

text:
where

n

i

{\displaystyle n_{i}}

 are the "thermodynamic coordinates". For the heat and mass transfer one can take

n

0

=
u

{\displaystyle n_{0}=u}

 (the density of internal energy) and

n

i

{\displaystyle n_{i}}

 is the concentration of the ith component. The corresponding driving forces are the space vectors

text:
where T is the absolute temperature and

μ

i

{\displaystyle \mu _{i}}

 is the chemical potential of the ith component. It should be stressed that the separate diffusion equations describe the mixing or mass transport without bulk motion. Therefore, the terms with variation of the total pressure are neglected. It is possible for diffusion of small admixtures and for small gradients.

text: For the linear Onsager equations, we must take the thermodynamic forces in the linear approximation near equilibrium:

text:
where the derivatives of s are calculated at equilibrium n*. The matrix of the kinetic coefficients

L

i
j

{\displaystyle L_{ij}}

 should be symmetric (Onsager reciprocal relations) and positive definite (for the entropy growth).

text: The transport equations are

text:
Here, all the indexes i, j, k = 0, 1, 2, ... are related to the internal energy (0) and various components. The expression in the square brackets is the matrix

D

i
k

{\displaystyle D_{ik}}

of the diffusion (i,k > 0), thermodiffusion (i > 0, k = 0 or k > 0, i = 0) and thermal conductivity (i = k = 0) coefficients.

text:
Under isothermal conditions T = constant. The relevant thermodynamic potential is the free energy (or the free entropy). The thermodynamic driving forces for the isothermal diffusion are antigradients of chemical potentials,

−
(
1

/

T
)

∇

μ

j

{\displaystyle -(1/T)\,\nabla \mu _{j}}

, and the matrix of diffusion coefficients is

text: (i,k > 0).

text:
There is intrinsic arbitrariness in the definition of the thermodynamic forces and kinetic coefficients because they are not measurable separately and only their combinations

∑

j

L

i
j

X

j

{\displaystyle \sum _{j}L_{ij}X_{j}}

 can be measured. For example, in the original work of Onsager[11] the thermodynamic forces include additional multiplier T, whereas in the Course of Theoretical Physics[12] this multiplier is omitted but the sign of the thermodynamic forces is opposite. All these changes are supplemented by the corresponding changes in the coefficients and do not affect the measurable quantities.

text: Nondiagonal diffusion must be nonlinear[edit]

text: The formalism of linear irreversible thermodynamics (Onsager) generates the systems of linear diffusion equations in the form

text:
If the matrix of diffusion coefficients is diagonal, then this system of equations is just a collection of decoupled Fick's equations for various components. Assume that diffusion is non-diagonal, for example,

D

12

≠
0

{\displaystyle D_{12}\neq 0}

, and consider the state with

c

2

=
⋯
=

c

n

=
0

{\displaystyle c_{2}=\cdots =c_{n}=0}

. At this state,

∂

c

2

/

∂
t
=

D

12

Δ

c

1

{\displaystyle \partial c_{2}/\partial t=D_{12}\,\Delta c_{1}}

. If

D

12

Δ

c

1

(
x
)
<
0

{\displaystyle D_{12}\,\Delta c_{1}(x)<0}

 at some points, then

c

2

(
x
)

{\displaystyle c_{2}(x)}

 becomes negative at these points in a short time. Therefore, linear non-diagonal diffusion does not preserve positivity of concentrations. Non-diagonal equations of multicomponent diffusion must be non-linear.[10]

text: Einstein's mobility and Teorell formula[edit]

text: The Einstein relation (kinetic theory) connects the diffusion coefficient and the mobility (the ratio of the particle's terminal drift velocity to an applied force)[13]

text: where D is the diffusion constant, μ is the "mobility", kB is Boltzmann's constant, T is the absolute temperature.

text:
Below, to combine in the same formula the chemical potential μ and the mobility, we use for mobility the notation

m

{\displaystyle {\mathfrak {m}}}

.

text: The mobility—based approach was further applied by T. Teorell.[14] In 1935, he studied the diffusion of ions through a membrane. He formulated the essence of his approach in the formula:

text: This is the so-called Teorell formula. The term "gram-ion" ("gram-particle") is used for a quantity of a substance that contains Avogadro's number of ions (particles). The common modern term is mole.

text: The force under isothermal conditions consists of two parts:

text:
Diffusion force caused by concentration gradient:

−
R
T

1
n

∇
n
=
−
R
T

∇
(
ln

(
n

/

n

eq

)
)

{\displaystyle -RT{\frac {1}{n}}\,\nabla n=-RT\,\nabla (\ln(n/n^{\text{eq}}))}

.
Electrostatic force caused by electric potential gradient:

q

∇
φ

{\displaystyle q\,\nabla \varphi }

.

tag: ol

text: Here R is the gas constant, T is the absolute temperature, n is the concentration, the equilibrium concentration is marked by a superscript "eq", q is the charge and φ is the electric potential.

text: The simple but crucial difference between the Teorell formula and the Onsager laws is the concentration factor in the Teorell expression for the flux. In the Einstein–Teorell approach, If for the finite force the concentration tends to zero then the flux also tends to zero, whereas the Onsager equations violate this simple and physically obvious rule.

text: The general formulation of the Teorell formula for non-perfect systems under isothermal conditions is[10]

text:
where μ is the chemical potential, μ0 is the standard value of the chemical potential. The expression

a
=
exp

(

μ
−

μ

0

R
T

)

{\displaystyle a=\exp \left({\frac {\mu -\mu _{0}}{RT}}\right)}

 is the so-called activity. It measures the "effective concentration" of a species in a non-ideal mixture. In this notation, the Teorell formula for the flux has a very simple form[10]

text:
The standard derivation of the activity includes a normalization factor and for small concentrations

a
=
n

/

n

⊖

+
o
(
n

/

n

⊖

)

{\displaystyle a=n/n^{\ominus }+o(n/n^{\ominus })}

, where

n

⊖

{\displaystyle n^{\ominus }}

 is the standard concentration. Therefore, this formula for the flux describes the flux of the normalized dimensionless quantity

n

/

n

⊖

{\displaystyle n/n^{\ominus }}

:

text: Teorell formula for multicomponent diffusion[edit]

text: The Teorell formula with combination of Onsager's definition of the diffusion force gives

text:
where

m

i

{\displaystyle {\mathfrak {m_{i}}}}

 is the mobility of the ith component,

a

i

{\displaystyle a_{i}}

 is its activity,

L

i
j

{\displaystyle L_{ij}}

 is the matrix of the coefficients,

X

j

{\displaystyle X_{j}}

 is the thermodynamic diffusion force,

X

j

=
−
∇

μ

j

T

{\displaystyle X_{j}=-\nabla {\frac {\mu _{j}}{T}}}

. For the isothermal perfect systems,

X

j

=
−
R

∇

n

j

n

j

{\displaystyle X_{j}=-R{\frac {\nabla n_{j}}{n_{j}}}}

. Therefore, the Einstein–Teorell approach gives the following multicomponent generalization of the Fick's law for multicomponent diffusion:

text:
where

D

i
j

{\displaystyle D_{ij}}

 is the matrix of coefficients. The Chapman–Enskog formulas for diffusion in gases include exactly the same terms. Earlier, such terms were introduced in the Maxwell–Stefan diffusion equation.

text: Jumps on the surface and in solids[edit]

text: Diffusion of reagents on the surface of a catalyst may play an important role in heterogeneous catalysis. The model of diffusion in the ideal monolayer is based on the jumps of the reagents on the nearest free places. This model was used for CO on Pt oxidation under low gas pressure.

text:
The system includes several reagents

A

1

,

A

2

,
…
,

A

m

{\displaystyle A_{1},A_{2},\ldots ,A_{m}}

 on the surface. Their surface concentrations are

c

1

,

c

2

,
…
,

c

m

.

{\displaystyle c_{1},c_{2},\ldots ,c_{m}.}

 The surface is a lattice of the adsorption places. Each reagent molecule fills a place on the surface. Some of the places are free. The concentration of the free places is

z
=

c

0

{\displaystyle z=c_{0}}

. The sum of all

c

i

{\displaystyle c_{i}}

 (including free places) is constant, the density of adsorption places b.

text:
The jump model gives for the diffusion flux of

A

i

{\displaystyle A_{i}}

 (i = 1, ..., n):

text: The corresponding diffusion equation is:[10]

text:
Due to the conservation law,

z
=
b
−

∑

i
=
1

n

c

i

,

{\displaystyle z=b-\sum _{i=1}^{n}c_{i}\,,}

 and we have the system of m diffusion equations. For one component we get Fick's law and linear equations because

(
b
−
c
)

∇
c
−
c

∇
(
b
−
c
)
=
b

∇
c

{\displaystyle (b-c)\,\nabla c-c\,\nabla (b-c)=b\,\nabla c}

. For two and more components the equations are nonlinear.

text: If all particles can exchange their positions with their closest neighbours then a simple generalization gives

text:
where

D

i
j

=

D

j
i

≥
0

{\displaystyle D_{ij}=D_{ji}\geq 0}

 is a symmetric matrix of coefficients that characterize the intensities of jumps. The free places (vacancies) should be considered as special "particles" with concentration

c

0

{\displaystyle c_{0}}

.

text: Various versions of these jump models are also suitable for simple diffusion mechanisms in solids.

text: Diffusion in porous media[edit]

text: For diffusion in porous media the basic equations are:[15]

text: where D is the diffusion coefficient, n is the concentration, m > 0 (usually m > 1, the case m = 1 corresponds to Fick's law).

text: For diffusion of gases in porous media this equation is the formalisation of Darcy's law: the velocity of a gas in the porous media is

text:
where k is the permeability of the medium, μ is the viscosity and p is the pressure. The flux J = nv and for

p
∼

n

γ

{\displaystyle p\sim n^{\gamma }}

 Darcy's law gives the equation of diffusion in porous media with m = γ + 1.

text: For underground water infiltration the Boussinesq approximation gives the same equation with m = 2.

text: For plasma with the high level of radiation the Zeldovich–Raizer equation gives m > 4 for the heat transfer.

text: Diffusion in physics[edit]

text: Elementary theory of diffusion coefficient in gases[edit]

text:
The diffusion coefficient

D

{\displaystyle D}

 is the coefficient in the Fick's first law

J
=
−
D

∂
n

/

∂
x

{\displaystyle J=-D\,\partial n/\partial x}

, where J is the diffusion flux (amount of substance) per unit area per unit time, n (for ideal mixtures) is the concentration, x is the position [length].

text: Let us consider two gases with molecules of the same diameter d and mass m (self-diffusion). In this case, the elementary mean free path theory of diffusion gives for the diffusion coefficient

text:
where kB is the Boltzmann constant, T is the temperature, P is the pressure,

ℓ

{\displaystyle \ell }

 is the mean free path, and vT is the mean thermal speed:

text: We can see that the diffusion coefficient in the mean free path approximation grows with T as T3/2 and decreases with P as 1/P. If we use for P the ideal gas law P = RnT with the total concentration n, then we can see that for given concentration n the diffusion coefficient grows with T as T1/2 and for given temperature it decreases with the total concentration as 1/n.

text: For two different gases, A and B, with molecular masses mA, mB and molecular diameters dA, dB, the mean free path estimate of the diffusion coefficient of A in B and B in A is:

text: The theory of diffusion in gases based on Boltzmann's equation[edit]

text:
In Boltzmann's kinetics of the mixture of gases, each gas has its own distribution function,

f

i

(
x
,
c
,
t
)

{\displaystyle f_{i}(x,c,t)}

, where t is the time moment, x is position and c is velocity of molecule of the ith component of the mixture. Each component has its mean velocity

C

i

(
x
,
t
)
=

1

n

i

∫

c

c
f
(
x
,
c
,
t
)

d
c

{\displaystyle C_{i}(x,t)={\frac {1}{n_{i}}}\int _{c}cf(x,c,t)\,dc}

. If the velocities

C

i

(
x
,
t
)

{\displaystyle C_{i}(x,t)}

 do not coincide then there exists diffusion.

text: In the Chapman–Enskog approximation, all the distribution functions are expressed through the densities of the conserved quantities:[8]

text:
individual concentrations of particles,

n

i

(
x
,
t
)
=

∫

c

f

i

(
x
,
c
,
t
)

d
c

{\displaystyle n_{i}(x,t)=\int _{c}f_{i}(x,c,t)\,dc}

 (particles per volume),
density of momentum

∑

i

m

i

n

i

C

i

(
x
,
t
)

{\displaystyle \sum _{i}m_{i}n_{i}C_{i}(x,t)}

 (mi is the ith particle mass),
density of kinetic energy

text: The kinetic temperature T and pressure P are defined in 3D space as

text:
where

n
=

∑

i

n

i

{\displaystyle n=\sum _{i}n_{i}}

 is the total density.

text:
For two gases, the difference between velocities,

C

1

−

C

2

{\displaystyle C_{1}-C_{2}}

 is given by the expression:[8]

text:
where

F

i

{\displaystyle F_{i}}

 is the force applied to the molecules of the ith component and

k

T

{\displaystyle k_{T}}

 is the thermodiffusion ratio.

text: The coefficient D12 is positive. This is the diffusion coefficient. Four terms in the formula for C1-C2 describe four main effects in the diffusion of gases:

text:
∇

(

n

1

n

)

{\displaystyle \nabla \,\left({\frac {n_{1}}{n}}\right)}

 describes the flux of the first component from the areas with the high ratio n1/n to the areas with lower values of this ratio (and, analogously the flux of the second component from high n2/n to low n2/n because n2/n = 1 – n1/n);

n

1

n

2

(

m

2

−

m

1

)

n
(

m

1

n

1

+

m

2

n

2

)

∇
P

{\displaystyle {\frac {n_{1}n_{2}(m_{2}-m_{1})}{n(m_{1}n_{1}+m_{2}n_{2})}}\nabla P}

 describes the flux of the heavier molecules to the areas with higher pressure and the lighter molecules to the areas with lower pressure, this is barodiffusion;

m

1

n

1

m

2

n

2

P
(

m

1

n

1

+

m

2

n

2

)

(

F

1

−

F

2

)

{\displaystyle {\frac {m_{1}n_{1}m_{2}n_{2}}{P(m_{1}n_{1}+m_{2}n_{2})}}(F_{1}-F_{2})}

 describes diffusion caused by the difference of the forces applied to molecules of different types. For example, in the Earth's gravitational field, the heavier molecules should go down, or in electric field the charged molecules should move, until this effect is not equilibrated by the sum of other terms. This effect should not be confused with barodiffusion caused by the pressure gradient.

k

T

1
T

∇
T

{\displaystyle k_{T}{\frac {1}{T}}\nabla T}

 describes thermodiffusion, the diffusion flux caused by the temperature gradient.

text: All these effects are called diffusion because they describe the differences between velocities of different components in the mixture. Therefore, these effects cannot be described as a bulk transport and differ from advection or convection.

text: In the first approximation,[8]

text:
D

12

=

3

2
n
(

d

1

+

d

2

)

2

[

k
T
(

m

1

+

m

2

)

2
π

m

1

m

2

]

1

/

2

{\displaystyle D_{12}={\frac {3}{2n(d_{1}+d_{2})^{2}}}\left[{\frac {kT(m_{1}+m_{2})}{2\pi m_{1}m_{2}}}\right]^{1/2}}

 for rigid spheres;

D

12

=

3

8
n

A

1

(

ν

)
Γ
(
3
−

2

ν
−
1

)

[

k
T
(

m

1

+

m

2

)

2
π

m

1

m

2

]

1

/

2

(

2
k
T

κ

12

)

2

ν
−
1

{\displaystyle D_{12}={\frac {3}{8nA_{1}({\nu })\Gamma (3-{\frac {2}{\nu -1}})}}\left[{\frac {kT(m_{1}+m_{2})}{2\pi m_{1}m_{2}}}\right]^{1/2}\left({\frac {2kT}{\kappa _{12}}}\right)^{\frac {2}{\nu -1}}}

 for repulsing force

κ

12

r

−
ν

.

{\displaystyle \kappa _{12}r^{-\nu }.}

text:
The number

A

1

(

ν

)

{\displaystyle A_{1}({\nu })}

 is defined by quadratures (formulas (3.7), (3.9), Ch. 10 of the classical Chapman and Cowling book[8])

text: We can see that the dependence on T for the rigid spheres is the same as for the simple mean free path theory but for the power repulsion laws the exponent is different. Dependence on a total concentration n for a given temperature has always the same character, 1/n.

text: In applications to gas dynamics, the diffusion flux and the bulk flow should be joined in one system of transport equations. The bulk flow describes the mass transfer. Its velocity V is the mass average velocity. It is defined through the momentum density and the mass concentrations:

text:
where

ρ

i

=

m

i

n

i

{\displaystyle \rho _{i}=m_{i}n_{i}}

 is the mass concentration of the ith species,

ρ
=

∑

i

ρ

i

{\displaystyle \rho =\sum _{i}\rho _{i}}

 is the mass density.

text:
By definition, the diffusion velocity of the ith component is

v

i

=

C

i

−
V

{\displaystyle v_{i}=C_{i}-V}

,

∑

i

ρ

i

v

i

=
0

{\displaystyle \sum _{i}\rho _{i}v_{i}=0}

. The mass transfer of the ith component is described by the continuity equation

text:
where

W

i

{\displaystyle W_{i}}

 is the net mass production rate in chemical reactions,

∑

i

W

i

=
0

{\displaystyle \sum _{i}W_{i}=0}

.

text:
In these equations, the term

∇
(

ρ

i

V
)

{\displaystyle \nabla (\rho _{i}V)}

 describes advection of the ith component and the term

∇
(

ρ

i

v

i

)

{\displaystyle \nabla (\rho _{i}v_{i})}

 represents diffusion of this component.

text: In 1948, Wendell H. Furry proposed to use the form of the diffusion rates found in kinetic theory as a framework for the new phenomenological approach to diffusion in gases. This approach was developed further by F.A. Williams and S.H. Lam.[16] For the diffusion velocities in multicomponent gases (N components) they used

text:
Here,

D

i
j

{\displaystyle D_{ij}}

 is the diffusion coefficient matrix,

D

i

(
T
)

{\displaystyle D_{i}^{(T)}}

 is the thermal diffusion coefficient,

f

i

{\displaystyle f_{i}}

 is the body force per unite mass acting on the ith species,

X

i

=

P

i

/

P

{\displaystyle X_{i}=P_{i}/P}

 is the partial pressure fraction of the ith species (and

P

i

{\displaystyle P_{i}}

 is the partial pressure),

Y

i

=

ρ

i

/

ρ

{\displaystyle Y_{i}=\rho _{i}/\rho }

 is the mass fraction of the ith species, and

∑

i

X

i

=

∑

i

Y

i

=
1.

{\displaystyle \sum _{i}X_{i}=\sum _{i}Y_{i}=1.}

text: Diffusion of electrons in solids[edit]

text: When the density of electrons in solids is not in equilibrium, diffusion of electrons occurs. For example, when a bias is applied to two ends of a chunk of semiconductor, or a light shines on one end (see right figure), electron diffuse from high density regions (center) to low density regions (two ends), forming a gradient of electron density. This process generates current, referred to as diffusion current.

text: Diffusion current can also be described by Fick's first law

text: where J is the diffusion current density (amount of substance) per unit area per unit time, n (for ideal mixtures) is the electron density, x is the position [length].

text: Diffusion in geophysics[edit]

text: Analytical and numerical models that solve the diffusion equation for different initial and boundary conditions have been popular for studying a wide variety of changes to the Earth's surface. Diffusion has been used extensively in erosion studies of hillslope retreat, bluff erosion, fault scarp degradation, wave-cut terrace/shoreline retreat, alluvial channel incision, coastal shelf retreat, and delta progradation[17]. Although the Earth's surface is not literally diffusing in many of these cases, the process of diffusion effectively mimics the holistic changes that occur over decades to millennia. Diffusion models may also be used to solve inverse boundary value problems in which some information about the depositional environment is known from paleoenvironmental reconstruction and the diffusion equation is used to figure out the sediment influx and time series of landform changes[18].

text: Random walk (random motion)[edit]

text: One common misconception is that individual atoms, ions or molecules move randomly, which they do not. In the animation on the right, the ion on in the left panel has a “random” motion, but this motion is not random as it is the result of “collisions” with other ions. As such, the movement of a single atom, ion, or molecule within a mixture just appears random when viewed in isolation. The movement of a substance within a mixture by “random walk” is governed by the kinetic energy within the system that can be affected by changes in concentration, pressure or temperature.

text: Separation of diffusion from convection in gases[edit]

text: While Brownian motion of multi-molecular mesoscopic particles (like pollen grains studied by Brown) is observable under an optical microscope, molecular diffusion can only be probed in carefully controlled experimental conditions. Since Graham experiments, it is well known that avoiding of convection is necessary and this may be a non-trivial task.

text: Under normal conditions, molecular diffusion dominates only on length scales between nanometer and millimeter. On larger length scales, transport in liquids and gases is normally due to another transport phenomenon, convection, and to study diffusion on the larger scale, special efforts are needed.

text: Therefore, some often cited examples of diffusion are wrong: If cologne is sprayed in one place, it can soon be smelled in the entire room, but a simple calculation shows that this can't be due to diffusion. Convective motion persists in the room because the temperature [inhomogeneity]. If ink is dropped in water, one usually observes an inhomogeneous evolution of the spatial distribution, which clearly indicates convection (caused, in particular, by this dropping).[citation needed]

text: In contrast, heat conduction through solid media is an everyday occurrence (e.g. a metal spoon partly immersed in a hot liquid). This explains why the diffusion of heat was explained mathematically before the diffusion of mass.

text: Other types of diffusion[edit]

text:
Anisotropic diffusion, also known as the Perona–Malik equation, enhances high gradients
Anomalous diffusion,[19] in porous medium
Atomic diffusion, in solids
Eddy diffusion, in coarse-grained description of turbulent flow
Effusion of a gas through small holes
Electronic diffusion, resulting in an electric current called the diffusion current
Facilitated diffusion, present in some organisms
Gaseous diffusion, used for isotope separation
Heat equation, diffusion of thermal energy
Itō diffusion, mathematisation of Brownian motion, continuous stochastic process.
Knudsen diffusion of gas in long pores with frequent wall collisions
Levy flights and walks
Momentum diffusion ex. the diffusion of the hydrodynamic velocity field
Photon diffusion
Plasma diffusion
Random walk,[20] model for diffusion
Reverse diffusion, against the concentration gradient, in phase separation
Rotational diffusion, random reorientations of molecules
Surface diffusion, diffusion of adparticles on a surface
Turbulent diffusion, transport of mass, heat, or momentum within a turbulent fluid


document_title: Legal drinking age

question_text: what is the minimum drinking age in ireland

root

text: Legal drinking age

text: Africa[edit]

text: The most common minimum age to purchase alcohol in Africa is 18. Although it varies from the lowest age limit in Ethiopia being only 15 years, Zimbabwe with a minimum purchase age of 16 years, Gambia with a age limit of 17 years and Uganda where the minimum legal purchase age is 18 but minors aged 16 or 17 may consume a glass of beer, wine or cider with a meal at a restaurant. Cameroon and Egypt are the only countries in Africa with a minimum purchase age of 21 years. However Algeria, Angola (except Luando Province), Central African Republic, Comoros, Equatorial Guinea, Gabon, Guinea-Bissau, Morocco, Togo, Tunisia and the Western Sahara have no laws on the book restricting the sale of alcohol to minors. In Libya, Somalia and Sudan the sale, production and consumption of alcohol is completely prohibited.

tag: p

text:
Country
State/Region/Province
De jure
Notes

Drinking age
Purchase age

 Algeria
None[3]

 Angola

None[3]
There is no national legislation prohibiting the sale of alcohol to minors.

Luanda Province:
18[4]
Legislation in Luanda Province:
It is illegal to sell alcoholic beverages to anyone under the age of 18. It is also illegal for minors to buy and consume alcohol.[4]

 Botswana
None[5]
18[5]
It is illegal for any person with a liquor license to sell or supply alcoholic beverages to minors under the age of 18 years. Because the law only applies to licensees it is not illegal for minors to buy, consume or possess alcoholic beverages.

 Burundi
None[6]
18 (None if accompanied by parent or legal guardian)[6]
It is illegal for any person with a liquor license to sell or supply alcoholic beverages to unaccompanied minors under the age of 18 years.

 Cameroon
21/18 (if accompanied by a person 21 years of age or older)[7]
It is illegal for any person with a liquor license, to sell or supply alcoholic beverages to anyone under 18 years of age. The law permits adults from the ages 18 to 21 to consume, purchase and buy alcoholic beverages if accompanied by a person 21 years of age or older. Anyone over the age of 21 years may buy or consume alcohol unaccompanied.

 Cape Verde
None[8]
18[8]
It is illegal for any person to sell or supply alcoholic beverages to minors under the age of 18 years.

 Central African Republic
None[3]

 Comoros
None[3]

 Egypt
21[3]

 Equatorial Guinea
None[3]

 Eritrea
None[9]
18[9]
It is illegal for any person to sell or serve alcoholic beverages to minors under the age of 18 years.

 Ethiopia
None[10]
15[10]
It is illegal for any person to sell, offer, serve or allow to serve alcoholic beverages "in substantial quantities" to any infant or young person. The criminal code defines a young person as any person under the age of 15 years. But the Criminal Code states: "Whoever endangers the health of another, intentionally and unscrupulously, by administering or serving, or by causing or permitting to be administered or served, to minors (defined as anyone under the age of 18 years) (...) alcoholic beverages or spirituous liquors of such kind or in such quantity as to make their injurious effect certain or probable, is punishable with simple imprisonment not exceeding one year, and fine."

 Gabon
None[3]

 Gambia
None[11][3]
17[11][3]
It is illegal to sell, serve or supply alcoholic beverages to child or young person. A "young person" is defined as anyone under the age of 17 by the Children and Young Persons Act, 1949 Section 2.

 Ghana
18[12]

 Guinea-Bissau
None[3]

 Kenya
None[13]
18[13]
It is illegal to sell, serve or supply alcoholic beverages to anyone under the age of 18 years.

 Lesotho
18[14]
It is illegal to sell, serve or supply any alcoholic beverage to a minor under the age of 18 years. It is also illegal for minors to consume, buy or attempt to buy alcohol.

 Liberia
None
18[3]
It is illegal to sell, serve or supply alcoholic beverages to anyone under the age of 18 years.

 Libya
Illegal[15]
Previously Article 498 of the Libyan Penal Code prohibted the sale of alcoholic beverages to juveniles under the age of 16 years.[3]

 Malawi
None
18[16]
It is illegal to sell, serve or supply alcoholic beverages to anyone under the age of 18 years.

 Mauritius
None
18[17]
It is illegal to sell, serve or supply alcoholic beverages to anyone under the age of 18 years.

 Morocco
None[3]

 Mozambique
18[18]

 Namibia
None
18[19]
It is illegal to sell, serve or supply alcoholic beverages to anyone under the age of 18 years.

 Niger
18[3]

 Nigeria
18[3]

 Republic of the Congo
None
18[20]

 Rwanda
18[3]

 Senegal
18[21]

 Seychelles
18[3]

 Somalia
Illegal[22]

 South Africa
18
The parent, adult guardian of a minor or a person responsible for administering a religious sacrament, may on occasion supply to that minor a moderate quantity of liquor to be consumed by the minor in the presence and under the supervision of that parent, guardian or other person.[23]

 South Sudan
18[3]

 Sudan
Illegal[24]

 Swaziland
18[3]

 Tanzania
None
18[25]

 Togo
None[3]

 Tunisia
None[3]

 Uganda
None[26]
18
16 (wine, beer, porter, cider, perry or native liquor with meal)[26]
It is illegal for any licensee to sell, serve or supply alcoholic beverages to anyone under the age of 18 years. The law provides a exception for anyone who is 16 or 17 years of age, and consumes a fermented alcoholic drink with a meal, in a part of a licensed premises that serves meals and is not a bar.

 Western Sahara
None[3]

 Zambia
18[27]
It is illegal for any person with a liquor license, to sell, serve or supply alcoholic beverages to anyone under 18 years of age. Before the Liquor Licensing Act was enacted in 2011, the minimum age to sell, serve and supply alcoholic beverages was 14 years.[28]

 Zimbabwe
None[29]
16 [29]
It is illegal for any person to sell, lend, give, supply, deliver or offer alcoholic beverages to any child under the age of 16 years, except upon production of a written order signed by the parent or guardian of the child known to such person. The police has the duty to seize any alcoholice beverage in the possession of a child under the age of 16 years without a written consent of the parents or legal guardian.

tag: table

text: Americas[edit]

text: The minimum age to purchase and consume varies, but the most common age is 18 years. However in North America the age limits varies between 18 and 21 years of age. Throughout the United States the minimum legal age to purchase any alcoholic beverage from a shop, supermarket, liquor store, bar, club or any other licensed premises is 21 years of age. In Canada each province can decide which minimum age limit is to be set to buy or consume alcohol. Most provinces have a minimum age of 19 years, while Alberta, Manitoba and Quebec have set a minimum age of 18 years. In South America all countries have set a minimum purchase age of 18 years, except for Guyana where minors aged 16 or 17 may consume a glass of beer, wine or cider in a restaurant provided they buy a meal, and Paraguay the only country with a minimum legal purchase and drinking age of 20 years.

text:
Country
State/Region/Province
De jure
hideNotes

Drinking age
Purchase age

 Anguilla
None[30]
18 [30]
It is illegal to sell or serve alcoholic drinks to anyone under the age of 18 years. Violating the regulation is punished with a $9.600 fine.

 Antigua and Barbuda
None
16[31]
The sale and distribution of alcohol to a person under 16 years of age is illegal.

 Argentina
18[32]

 Bahamas
18[33]
It is illegal for any adult to sell, serve or supply any alcoholic beverage to a child (defined as anyone under the age of 18 years). The law provides a exception to treat a illness in urgent cases or upon order by a medical doctor.

 Barbados
None
16[34]
It is illegal to sell or serve any alcoholic beverage to anyone under the age of 16 years. The President of the Barbados Road Safety Association is trying to raise the drinking age to 18 years due to the fact that the law is often violated.[34]

 Belize
18[35]
Drinking age is rarely enforced. IDs are almost never requested.

 Bermuda
18[36]
It is illegal to sell or serve any alcoholic beverage to a child under the age of 18 years.

 Bolivia
None[37]
18 [37]
It is illegal to sell or serve alcoholic beverages to minors under the age of 18 years. Every sold alcoholic beverage has to have a warning message on the bottle or container reading: “VENTA PROHIBIDA A MENORES DE 18 AÑOS DE EDAD” (Sale prohibited to (anyone) under 18 years of age) and “EL CONSUMO EXCESIVO DE ALCOHOL ES DAÑINO PARA LA SALUD” (Excessive alcohol consumption is harmful to (ones) health).

 Brazil
None[38]
18 [38]
It is illegal to sell, serve or supply any alcoholic beverage to a person under 18 years of age. The presidential law enacted on March 17 2015 made any violation of the law a criminal offence. Any adult person selling, serving, giving or supplying alcoholic beverages to a minor is punished with imprisonment of 2 to 4 years, a fine of R$ 3.000 to R$ 10.000 and a ban to operate any business selling or serving alcohol.

 British Virgin Islands
16[35]
It is illegal to sell or to supply alcohol to anyone under the age of 16.

 Canada
 Alberta
 Manitoba
 Quebec
18[39][40][41]
In Alberta no person may give or sell or permit any person to give or sell liquor to a minor in licensed premises.[39] In Manitoba a person must not give, sell or otherwise supply liquor to a minor. the law provides exceptions for a doctor, dentist, pharmacist or other health care professional for medical purposes; for sacramental purposes and by the parent, guardian, spouse or common-law partner, if it is given or supplied in a residence.[40] In Quebec the law probits the sale of alcoholic beverages to a minor under the age of 18 years.[41]

 Ontario
 Saskatchewan
 British Columbia
 Newfoundland and Labrador
 Nova Scotia
 New Brunswick
 Prince Edward Island
 Northwest Territories
 Yukon
 Nunavut
19

 Cayman Islands
18[42]
It is prohibited to sell, serve or supply alcoholic beverages to anyone under the age of 18 years. It is also illegal for any minor to buy, attempt to buy or consume alcoholic beverages. Violation of the lawis punished with a fine of five thousand dollars, and the court may, if the offence was committed by the licensee, order that the licensee shall forfeit his licence and that no licence may be issued to that person for a period not exceeding ten years from the date of his conviction.

 Chile
18[43]
The minimum age is 18 to enter an enclosure that sells alcoholic beverages. Selling alcohol to a minor may incur a fine. One must provide identification upon request. Residents of Chile over the age of 18 must carry their Chilean identification card issued by the Civil Registry and Identification Service at all times.[44]

 Colombia
None
18[45]
The law prohibits the sale of alcohol to a minor (anyone under the age of 18 years). It is not illegal for minors to buy, attempt to buy or consume alcohol.[45]

 Costa Rica
None
18[46]
The law prohibits the sale of alcohol to a minor (anyone under the age of 18 years). Selling alcohol to a minor will be punished with a fine equivalent to ten basic salaries. Whoever permits minors to maintain in any establishment which main purpose is to sell alcoholic beverages, will be sanctioned with a fine equivalent to five salaries. It is not illegal for minors to buy, attempt to buy or consume alcohol.[46]

 Cuba
None
16[47]
The penal code prohibits any adult to induce any young person under the age of 16 years, to habitually consume alcoholic beverages. However this means that defacto anyone selling, serving or supplying alcohol should check if the buyer has attained the age of 16 years. In most cases this law is not strictly enforced.[47][48]

 Dominican Republic
None
18[49]

 Ecuador
None
18[50]
It is illegal to sell alcohol beverages to a minor under the age of 18 years of age. The law obligates establishments to place a visible notice at the point of sale and to check identification to enforce the law. However it is not illegal for minors to buy, attempt to buy or consume alcohol.[50]

 El Salvador
None
18[51]
It is strictly prohibited to sell or serve alcoholic beverages to a minor under the age of 18 years. Violation of the law is punished with ¢ 25,000.00 and if convicted once more the license will be suspended for a period of six months. It is legal for minors to buy, attempt to buy and consume alcohol.[51]

 Falkland Islands
18[52]
It is illegal for any adult to sell, give or provide alcohol to a minor under the age of 18 years in any public place or licensed premises. Parents may permit their children to consume alcohol on private premises. Minors consuming alcohol in public are committing a criminal offence. The law provides exceptions for the consumption of alcohol by minors for prescription of or at the direction of a government medical officer or in the course of the administration of Holy Communion according to the rites of any Christian denomination.[52]

 Grenada
18[53]
It is illegal to sell, serve or supply any alcoholic drink to a minor under 18 years of age. Minors under 18 years are prohibited by law, to consume alcoholic beverages in public.[53]

 Guatemala
18[54]
It is illegal to sell, serve or supply any alcoholic drink to a minor under 18 years of age. Minors under 18 years are prohibited by law, to consume alcoholic beverages in public.[54]

 Guyana
18/16 for beer, wine and cider with meal[55]
It is illegal to sell or serve alcool to a person under 18 years of age. The law provides a exception for minors aged 16 and 17, if they consume a glass of beer, wine oder cider with a meal in a restaurant. Otherwise attempting to buy alcohol or buying alcohol as a minor is a offence.[55]

 Haiti
None
18[56]
It is illegal to sell or serve alcohol to minors from May 17 2017. Vendors are required to check identification.

 Honduras
18[43]

 Jamaica
None
18[57]
It is illegal to sell or serve any alcoholic beverage to a child (which is defined as anyone under the age of 18 years).[57]

 Mexico
18[43]
The minimum age to buy and consume alcoholic beverages is regulated by each state of Mexico. But all states have set a minimum age of 18 years, and in no state it is illegal for minors to buy and consume alcohol.

 Nicaragua
None
14 (restaurant)
18 (bars, clubs, markets, supermarkets, sports and recreation centers)[58]
The law from 1980 prohibits the sale of alcoholic beverages to minors under the age of 18 years. Ever point of sale or establishment serving alcohol, is required to post a notice stating that the sale of alcohol to minors under 18 years of age is illegal. However the law permits children as young as 14 to purchase and consume alcohol in a restaurant without further restrictions.[58]

 Panama
None
18[59]

 Paraguay
20[60]
According to Art. 1° of the law to "ban on the sale of alcoholic beverages to minors", it is illegal to serve or sell alcohol or to allow the consumption by minors under 20 years of age. Furthermore, under Art 2° all public establishments selling alcohol must display a clearly legible notice in the sales area with the following text: "ESTA PROHIBIDA LA VENTA DE BEBIDAS ALCOHÓLICAS A MENORES DE VEINTE AÑOS DE EDAD" (It is illegal (prohibited) to sell alcoholic beverages to minors under 20 years of age)

 Peru
None
18[61]

 Puerto Rico
18

 Saint Vincent and the Grenadines
16[62]

 Trinidad and Tobago
None
18[63]
It is illegal to sell, serve or supply alcoholiv beverages to child under the age of 18 years. It is also illegal for an adult to send a child to buy alcohol on behalf. It is not illegal for children to buy or consume alcohol.[63]

 Turks and Caicos Islands
None
18[64]
It is illegal to serve or sell liquor to a young person under the age of eighteen years. Minors under the age of sixteen years may not present in a licensed premises mainly serving and selling alcoholic beverages.[64]

 United States
(50 states and integral territories)
Varies by jurisdiction[43]
21[43]
The National Minimum Drinking Age Act of 1984 withholds revenue from states that allow the purchase of alcohol by anyone under the age of 21. Prior to the effective date of that Act, the drinking age varied from state to state. Some states do not allow those under the legal drinking age to be present in liquor stores or in bars (usually, the difference between a bar and a restaurant is that food is served only in the latter). Contrary to popular belief, since the act went into law, only a few states prohibit minors and young adults from consuming alcohol in private settings. As of January 1, 2010, 15 states and the District of Columbia ban underage consumption outright, 17 states do not ban underage consumption, and the remaining 18 states have family member or location exceptions to their underage consumption laws.
Federal law explicitly provides for religious exceptions. As of 2005, 31 states have family member or location exceptions to their underage possession laws. However, non-alcoholic beer in many (but not all) states, such as Idaho, Texas, and Maryland, is considered legal for those under the age of 21.[65]
By a judge's ruling, South Carolina appears to allow the possession and consumption of alcohol by adults 18 to 20 years of age, but a circuit court judge has said otherwise.[66]
The states of Washington and Wisconsin allows the consumption of alcohol in the presence of parents.
Some U.S. states have legislation that make providing to and possession of alcohol by persons under twenty-one a gross misdemeanor with a potential penalty of a $5,000 fine or up to year in jail.[67]
See also: Minor in Possession and List of alcohol laws of the United States

 United States Virgin Islands
18[68]

 Uruguay
None
18[69]
Only selling alcohol to minors under the age of 18 is prohibited, consumption and purchase by minors is not illegal.

 Venezuela
None
18[70]
Only selling alcohol to minors under the age of 18 is prohibited, consumption and purchase by minors is not illegal.[70]

text: Asia[edit]

text:
Country
State/Region/Province
De jure
Notes

Drinking age
Purchase age

 Afghanistan
Illegal[71]

 Bangladesh
(Illegal for Muslims.)[72]
Alcohol will be sold to foreigners in certain locations, albeit clandestinely.[citation needed]

 Bhutan
18[73]

 Brunei
17 with restrictions, unless Muslim[43]
Non-Muslims over 17 years of age are allowed to import alcohol not to exceed maximum total volume 2 liters of liquor and 12 cans of beer at 330 ml for personal use, once in 48 hours. This alcohol must be “stored and consumed at the place of residence of the importer” and is “not to be given, transferred or sold to another person.”.[43]

 Cambodia
None[74]

 China
18[43]
Introduced in January 2006.[75]

 Hong Kong
18[76]
The regulation is only applicable to restaurants, bars and clubs, where a liquor license is required. Private drinking is also not regulated.[citation needed]

 India
18–25 (varies by jurisdiction)[43]

Main article: Alcohol laws of India
Consumption of alcohol is illegal in the states of Bihar, Gujarat and Nagaland.[77]

 Indonesia
21[78]

 Iran
Illegal [43]
There is a ban on alcohol, but religious minorities may purchase small amounts from shops owned by the same religious minority.[79]

 Iraq
Illegal[80]

 Israel
None
18[43]
Israel law prohibits selling or serving alcohol to minors, but it does not prohibit minors to drink, although the police may confiscate alcoholic drinks consumed by minors in public.[citation needed]

 Japan
20[43]

 Jordan
18[81]

 Kazakhstan
21[82]

 Kuwait
Illegal[83]

 Kyrgyzstan
18[43]

 Lebanon
18[43]
Often unenforced and according to a global school health study, 40% of minors over 13 drink alcohol and up to 25% buy it from stores.[84]

 Macau
None[85]

 Malaysia
21
Increased from 18 to 21 in December 2017.[86]

 Maldives
Illegal except for tourists, 18[citation needed]
Sale of alcohol is limited to tourist resorts. It is illegal to sell alcohol to local Maldivians[87]

 Mongolia
18[88]

 Myanmar
None
18[89]

   Nepal
18
The legal age for consumption of alcohol in Nepal is 18. However, there are exceptions to underage consumption for purposes of religious ceremonies.[citation needed]

 North Korea
18[90]

 Oman
21
Residents need personal liquor licenses to consume alcohol in their private residences.[91][92]

 Pakistan
Illegal (18 for non-Muslims) [43]
Non-Muslim citizens may possess alcohol to be used in accordance with religious ceremonies[43]

 Palestinian Authority
16[citation needed]
Legal in most cities.[citation needed]

 Philippines
18[93]

 Qatar
Illegal[citation needed]
Muslims are allowed to purchase alcohol, but generally not allowed to consume. Non Muslims are allowed to purchase, and consume alcohol. The only legal distributor of alcohol in the country is the Qatar Distribution Company located in Doha.[citation needed]

 Saudi Arabia
Illegal
Drinking or possessing alcohol is illegal in the Kingdom of Saudi Arabia. Persons who drink or possess alcohol are subject to arrest and trial. Punishments range from heavy fines, lengthy prison terms and whippings.[citation needed]

 Singapore
None (Private places, sometimes with permission from parents/guardian)
18 (Public places e.g. bars and restaurants)
18[43]
For convenience stores, those who pretend to be 18 years and above in a "Challenge 18" scheme will be downgraded to "Challenge 21" scheme, and after which the licences will be revoked once they pretend to be 18 years and above if it is on "Challenge 21".[citation needed]. It is illegal to purchase alcohol in Singapore or consume in a nightclub/allow entry to the nightclub under 18. Home and private drinking of alcohol is allowed, although the safest age could be 6. Parents can try a sip of alcohol at any age.[citation needed]

 South Korea
None
19[94]
The age limit for alcohol is after January 1 of the year one's age turns to 19.[95]

 Sri Lanka
21[43]

 Syria
18[citation needed]

 Taiwan
18[96]

It is illegal for anyone under the age of 18 to consume alcohol.[97]
Parents, guardians, and others taking care of people under 18 shall prohibit underage drinking,[98] or risk administrative fines of 10000 to 50000 new Taiwan dollars when the situations are serious.[99]
One shall not supply alcohol to anyone under the age of 18.[100] A violator shall be administratively fined 3000 to 15000 New Taiwan Dollars.[101]

 Tajikistan
18[43]

 Thailand
20[102]
The Alcoholic Beverage Control Act of 2008 increased the drinking age in Thailand from 18 to 20, private drinking is not regulated in private locations.[102][103]

 Turkmenistan
18[43]

 United Arab Emirates
18–21 (varies by jurisdiction).[104]
Expatriate non-Muslim residents may request a liquor permit to purchase alcoholic beverages, but it is illegal for such holders to provide drinks to others.[105]
The legal age for drinking alcohol is 18 in Abu Dhabi (although a Ministry of Tourism by-law allows hotels to serve alcohol only to those over 21), and 21 in Dubai and the Northern Emirates (except Sharjah, where drinking alcohol is illegal).[104]
It is a punishable offence to drink, or to be under the influence of alcohol, in public.[104]

 Uzbekistan
None
20[43]

 Vietnam
18[43]

 Yemen
Illegal[citation needed]
Exception is in Aden Region where it's legal for 21 and up[citation needed]

text: Europe[edit]

text: Most countries within Europe have set 18 as the minimum age to purchase alcohol. Although Austria, Belgium, Cyprus, Denmark, Germany, Gibraltar, Liechtenstein, Luxembourg, Malta, Serbia and Switzerland (except Ticino) maintain a minimum purchase age below 18 years permitting minors either full or limited access to alcohol. In 2005[106], 2007[107] and recently in 2015[108] the European Union has failed to enact a law forcing member states to raise their purchase age to 18 years. But in the past years several European countries have raised their drinking/purchase age or enacted laws restricting the access to alcohol for minors:

text:
In 2002 the autonomous communities Madrid,[109] Valencia[110] and Catalonia[111] raised their minimum purchase age to 18 years. Previous to 2002 Valencia and Madrid had a minimum purchase age of 16 years, and in Catalonia minors aged 16 or 17 could purchase alcohol up to 23% ABV on and off premises.
In 2004 Denmark[112] raised its off premises purchase age from 15 to 16 years.
In November 2005 Switzerland passed its "Food and Commodities Regulation"[113] (German: Lebensmittel- und Gebrauchsgegenständeverordnung), introducing a ban on alcohol sales to anyone under the age of 16, although the 1980 passed "Alcohol Law"[114] (German: Alkoholgesetz) already required a minimum age of 18 years for the retail sale of distilled spirits. Therefore, it is illegal to sell fermented alcohol (e.g. beer, wine, sparkling wine or cider) to anyone under the age of 16, and any distilled alcoholic beverages to anyone under the age of 18 years. Further the canton of Ticino introduced a contonal law in 1989 banning all alcohol sales to anyone under the age of 18 years.[115]
In 2006 the autonomous communitie Castile and León[116] raised its minimum purchase age from 16 to 18 years.
In late 2006, Gibraltar[117] lawmakers passed the "Children and Young Persons (Alcohol, Tobacco and Gaming) Act 2006", which raised the minimum purchase age from 16 to 18 years. But the new law made an exception: minors aged 16 or 17 can purchase and consume on premises beer, wine or cider under 15% ABV or pre-packed containers of an alcoholic strength not exceeding 5.5% ABV (e.g. alcopops).
In 2009 France[118] raised its minimum purchase age to 18 years, and fines were increased for selling or serving alcohol to a minor (up to 7,500 €). Previous to 2009 the minimum age to purchase any alcohol from off licensed premises was 16 years. In order to purchase alcohol on premises the minimum age was 16 years for low alcoholic beverages such as wine, beer, cider, perry, mead, crème de cassis and juices from fermented fruits or vegetables that contain 1.2 to 3° alcohol, natural sweet wines from controlled cultivation – to purchase or be served stronger alcoholic drinks one had to be 18 years of age.
In October 2009, the government of Malta[119] passed a new law raising its drinking and purchase age from 16 to 17 years.
In 2010 the autonomous community of Galicia raised its minimum purchase age from 16 to 18 years.[120]
In 2011 Denmark[121] passed a new law, raising the minimum age for off-premises sale of alcohol >16.5% ABV to 18 years of age. The age to purchase alcohol <16.5% ABV remaines at 16.
Italy raised its minimum purchase age from 16 to 18 in 2012. Previously Italy did not have a purchase age for off-premises sales, and the minimum age of 16 years for on premises sales was barely enforced. [122]
In 2013 the government of Portugal restricted alcohol sales to young people: distilled spirits can not be sold to anyone under the age of 18, and other alcohol (e.g. beer, wine or cider) can't be sold to anyone under the age of 16. Previously the minimum age for all kinds of alcoholic beverages was 16 years.[123]
As of 1 January 2014, the minimum legal purchase and consumption age was raised from 16 to 18 in the Netherlands. Previously young people over the age of 16 could purchase and consume alcohol <15% ABV, and adults aged 18 and over could purchase alcohol over 15% ABV.[124]
As of March 2015, the autonomous community of Asturias raised its drinking age from 16 to 18 years. Asturias was Spain's last community with a drinking age of 16 years. The new law brings the drinking age into line with the rest of Spain.[125]
As of 1 January 2018, Lithuania raised its minimum drinking age from 18 to 20 years[126]

tag: ul

text:
Country
State/Region/Province
De jure
Notes

Drinking age
Purchase age

 Albania
18[43]

 Andorra
18[127]

 Armenia
None[128]
18[128]
There are no laws mandating alcohol vendors to ID potential underage drinkers. ID checks are very rarely, if ever, carried out[128]

 Austria
 Burgenland
 Lower Austria
 Vienna
16
[129]

 Carinthia
 Upper Austria
 Salzburg
 Styria
 Tyrol
 Vorarlberg
16 (beer, wine and cider)
18 (distilled beverages)
Carinthia also requires adolescents to maintain a blood alcohol level below 0.05%.[129]

 Azerbaijan
None[130]
18[130]
It is illegal to sell or serve alcohol to a minor under 18 years of age.[130]

 Belarus
None[131]
18[131]
The law prohibits the sale of alcohol to anyone under the age of 18 years. However, the law is rarely enforced.[131]

 Belgium
None[132]
16 (beer, wine and cider)
18 (spirits)[132]
Since 10 January 2010, it is illegal to "sell, serve, or offer" any form of distilled alcohol to those under the age of 18 or any alcoholic drink to those under 16. So fermented drinks like beer or wine are permitted above 16.[132] Previously, it was illegal to sell alcoholic drinks to under-16s, but accompanying adults could buy drinks for them.

 Bosnia and Herzegovina
None[133]
18[133]
Selling alcohol to a minor under the age of 18 years is a offence. The law does not prohibit minors from buying, attempting to buy or consuming alcohol.[133]

 Bulgaria
None[134]
18[134]
By law, it is illegal to serve or sell alcohol to any child under the age of 18. There is no restrictions for minors consuming alcohol.[134]

 Croatia
None[135]
18[135]
It is prohibited to sell or serve alcohol to anyone under 18 years of age. There is no minimum age to buy or consume alcohol by law.[135]

 Cyprus
None[136]
17[136]
It is illegal to sell or serve alcohol to anyone under the age of 17 years. There is no minimum age to buy, attempt to buy or consume alcohol in public.[136]

 Czech Republic
None
18[137]
It is illegal to provide alcohol to minors[138] (punishable by fine or up to 1[139] or 2[140] year(s) imprisonment). Consumption itself is not prohibited by law.[141]

 Denmark
None
16 (<16.5% ABV)
18 (≥16.5% ABV)
While there is no age requirement for drinking alcohol in Denmark, there are laws that prevent minors from buying alcohol:

In order to buy alcohol above 1.2% and below 16.5% ABV in stores, one must be 16 years of age.
In order to buy alcohol above 16.5% ABV in stores, one must be 18 years of age.[142]

By tradition, youths are privately allowed to drink alcohol after their confirmation.[143] If a shop or bar fails to ask for an ID card and is identified having sold alcohol to an underage, it is subject to fine. A national ID card, obtained in the local town hall, can serve as age verification.[144] This card is rarely used though since a passport or drivers license is more commonly used.[145]
Both the legal drinking and purchasing age in the Faroe Islands is 18.[citation needed]

 Estonia
18[146]
It is illegal to sell, serve or supply alcoholic beverages to anyone under the age of 18 years. Alcohol found in possession of any child can be confiscated by the police.

 Finland
18 (possession and purchase of 1.2–22% ABV)
20 (for possession and purchase of 23–80% ABV)
18 (for all in bars, clubs and restaurants)[147]
All major grocery chains have implemented a policy to ask for ID if the customer looks under 30.[148] Stores may refuse to sell alcohol if the customer is accompanied by a minor, or if proxy purchasing is suspected. Purchasing alcohol on behalf of a minor is a criminal offence.[147][149]
Police may search minors in public places and confiscate or destroy any alcoholic beverages in their possession. Incidents are reported to the legal guardian and social authorities, who may intervene with child welfare procedures. In addition, those aged 15 or above are subject to a fine.[150]
In private, offering alcohol to a minor is considered a criminal offence if it results in drunkenness and the act can be deemed reprehensible as a whole, considering the minor's age, degree of maturity and other circumstances.[147]

 France
None
18
France has no explicitly stated consumption age,[151] but selling alcohol to a minor (under 18) is illegal[152] and can be fined 7500 euros.[151] This age was raised from 16 to 18 in 2009.[153][154]

 Georgia
None[155]
18[155]
By Georgian law, the sale of alcoholic beverages to anyone under the age of 18 years is prohibited.[155]

 Germany
14(beer, wine and cider if accompanied)
16 (beer, wine and cider)
18 (spirits and aliments containing spirits above negligible amounts)[156]
It is illegal to sell, serve or supply fermented alcoholic beverages (beer, wine, cider and sparkling wine) to anyone under 16 years of age. However this age limit drops down to 14 if a minor is accompanied by his parent or legal guardian. It is generally illegal to serve, sell or supply any beverage containing spirits and aliments containing spirits above negligible amounts, to anyone under the age of 18 years. Violation of the "Protection of Young Persons Act" can be fined up to 50.000€.
See also: Alcohol laws in Germany

 Gibraltar
None[157]
18
16(beer, wine and cider)[157]
It is illegal to sell alcoholic drinks to anyone under the age of 18, other than the following two exceptions. The minimum age to be served in licensed premises is 16 if:[157]

The alcoholic beverage is beer, wine or cider below 15% ABV, or
The alcoholic beverage is served in a bottle, or a pre-packaged container below 5.5% ABV.

 Greece
None[158]
18[158]
In 2008, the consumption of alcoholic beverages was prohibited for minors in public. However, the law does not apply to private events or private premises.[158]

 Hungary
18[43]

 Iceland
None
20[159]
Possession or consumption of alcohol by minors is not an offence, but supplying them with alcohol is.

 Ireland
None (on private residence with permission from parents or guardians)[160]
18[160]
It is illegal for minors to buy alcohol or for a third party to attempt to buy it for minors. It is illegal to purchase alcohol for anybody under the age of consent without permission from their guardians.[161]

 Italy
None [162]
18[163][162]
In 2012 the then Health Minister Renato Balduzzi proposed to raise the age to 18.[162] Selling alcohol to those under the age of 18 in shops carries a fine between €250 and €1000. Serving alcoholic beverages to those under the age of 16 is a criminal offense and is punished with prison up to one year, if the individual is 16 or 17 it will be treated as an offense that is fined between €250 and €1000 (Legge n. 189/2013).

 Kosovo
None[citation needed]

 Latvia
None[164]
18[164]
It is illegal to sell or serve alcoholic beverages to any minor under the age of 18 years. There is no minimum age to consume or possess alcohol.[164]

 Liechtenstein
16 beer, wine and cider
18 spirits and spirit-based beverages[165]
Wine, beer and ciders as well as some other party drinks sometimes without spirits may be purchased by the age of 16. Spirits as well as alcopops may be sold only to people at least 18.[165]

 Lithuania
20[126]
It is illegal to sell, serve or supply alcoholic beverages to anyone under the age of 20 years. Persons under the age of 20 are prohibited from consuming alcoholic beverages or from possessing them. The minimum age was raised from 18 to 20 since 2018.[126]

 Luxembourg
None [166]
16[166]
It is illegal to sell or serve alcoholic beverages >1.2% ABV to any person under the age of 16 years. Violation is fined €251 to €1.000.[166]

 Macedonia
18[167]
Must show an ID card upon request. In certain smaller places, such as family-owned convenience stores and street kiosks, there is little to no enforcement on how old or young somebody purchases alcohol. There is little to no enforcement for drinking privately, but drinking in bars may require an ID.

 Malta
17[168]
Must provide identification upon request.

 Moldova
None[169]
18[169]
It is illegal to sell, or serve alcoholic beverages to anyone under the age of 18 years. It is not illegal for minors to buy, attempt to buy or consume alcohol. The minimum purchase age was raised from 16 to 18 in 2012.[170][169]

 Montenegro
18[citation needed]

 Netherlands
18
The legal age for purchasing and consumption of alcoholic beverages was raised from 16 to 18 since 2014. Alcohol is commonly available upon parental permission. Selling alcoholic beverages to people under 18 is illegal, buying alcoholic beverages for someone else under the age of 18 is also illegal.[citation needed]

 Norway
None[171]
18 (<22%)
20 (≥22% ABV)[43]
Selling alcohol to or buying alcohol for minors is illegal. Minors are defined as under 18 for beer and wine, under 20 for drinks that contain 22% ABV or more. Minors who buy alcohol are not held criminally responsible; instead, the crime lies with those who sold it or obtained it for them.
Alcohol with more than 60% ABV is generally not sold in Norway, although exceptions may be made by the government for specific products.[172]
Alcohol possessed by minors may be confiscated as evidence. Drinking in public is prohibited, though this is rarely enforced in recreational areas.[173]

 Poland
None[174]
18[174]
Article 15 of The Act on Upbringing in Sobriety and Counteracting Alcoholism[175] clearly states that buyers or persons being served must be at least 18 and prove it with ID if they look like they may not be at least that age. There is no mention of consumption age in this or any other act in Poland. Drinking in public places, with the exception of designated drinking zones, is illegal regardless of age.

 Portugal
None[176]
18[176]

 Romania
None
18[177]
According to law 61/1991 updated in 2008, paragraphs 21-25, it is illegal to serve or sell alcohol to minors.

 Russia
None
18[178]
There is no law or regulation in Russia that prohibits minors from consuming alcohol, but selling alcohol to minors is prohibited by federal and additional regional laws.

 San Marino
16[179]

 Serbia
None
16[180]

 Slovakia
18[181]

 Slovenia
None
18[182]
There is no law regulating the possession and consumption, but it is illegal to sell or offer alcohol of any kind to minors.

 Spain
18
Asturias was the last autonomous community in Spain where the drinking age was increased to 18 (previously 16) on 1 May 2015.[183]

 Sweden

None

None (less than 2.25% ABV)
18 (bars and restaurants)
18 (2.25%–3.5% ABV in food shops)
20 (Systembolaget shops)[184],

See also: Alcohol in Sweden
Many clubs choose to have higher age limits than 18, commonly 20 or 23. It is legal to drink below 18, but it is illegal to sell, lend or give alcohol to someone under that age and the police can seize alcohol from them, apart from being served alcohol supervised in private "in moderation". It is legal to serve an underage person alcohol in a private place.[185] The reason for lower limit in bars than in Systembolaget shops is that bartenders have a legal responsibility for how drunk a guest gets.

  Switzerland
  Switzerland (federal law)
None
(See notes)
16 (fermented alcoholic drinks with less than 15% ABV and natural wines with less than 18% ABV)[186]
18 (spirits) [187]
Whoever offers or supplies alcoholic beverages to a child under the age of 16 years in an amount which is harmful to one's health is punished with imprisonment up to 3 years or a fine.[188] Whoever sells or supplies spirits to a person under the age of 18 years is punished with a fine up to 10.000 CHF.[189]

 Ticino
18
The canton Ticino prohibits selling and consumption of any type of alcohol by minors under the age of 18. Some shops and supermarkets may not sell alcohol to minors under the age of 18.[190]

 Turkey
18[43]

See also: Alcohol laws of Turkey

 Ukraine
18[43]

 United Kingdom
 England
 Wales
18[191]
16 (beer, wine or cider with meal)[191]
5 (private)[192]
None (under medical supervision, or in an emergency)[192]
Legislation in  England and  Wales:

It is illegal to sell, serve, offer or consume alcoholic beverages on licensed premises under the age of 18, other than the following two exceptions:[191]

Minors aged 16 or 17 may consume wine, beer or cider on licensed premises when ordered with a meal, and accompanied by an adult.[191]
It is legal to sell liqueur confectionery to someone of any age.

It is illegal to permit minors under the age of 5 to consume alcoholic beverages unless under medical supervision or in an emergency.[192]
Persons over 17 are entitled to their own duty free allowance, which includes alcohol. [193]

 Scotland
18
16 (beer, wine or cider on licensed premises with meal)[194]
None (private)
Legislation in  Scotland:

It is illegal to sell, serve, offer or consume alcoholic beverages in public under the age of 18, other than the following two exceptions:[195]

Minors aged 16 or 17 may consume wine, beer or cider on licensed premises when ordered with a meal.[195]
It is legal to sell liqueur confectionery to someone of any age.

Persons over 17 are entitled to their own duty free allowance, which includes alcohol. [193]

 Northern Ireland
18
Legislation in Northern Ireland:
It is illegal to sell, serve, offer or consume alcoholic beverages in public under the age of 18.

 United Kingdom
Challenge 21 and Challenge 25 (applies to all of the  United Kingdom)
Under the BBPA's Challenge 21 and Challenge 25 schemes, customers attempting to buy alcoholic beverages are asked to prove their age if in the retailer's opinion they look under 21[196] (or optionally 25) even though the law states they must be a minimum of 18. Many supermarket and off-licence chains display Challenge 21 (or Challenge 25) notices stating that they will not serve persons who look under 21 (or 25) without ID.

text: Oceania[edit]

text:
Country
State/Region/Province
De jure
Notes

Drinking age
Purchase age

 American Samoa
21[197]

 Australia
18[43][198]

Main article: Alcohol laws of Australia
Varies by state. Some states restrict possession and consumption to over 18, all states restrict purchasing to over 18. In some states, minors may consume alcohol in a private residence with parental permission.[199]

 Fiji
18[200]
The drinking age was 21 from 2006 to 2009 but was lowered to 18 in 2009.[200]

 Guam
21[201]

 Micronesia, Federated States of
18[202]

 New Zealand
None
18[203]
Minimum age applies for beverages with 1.15% ABV or over; no restrictions on beverages less than 1.15% ABV.[204]
Persons under 18 may drink outside private residences or private functions if accompanied by their parent or legal guardian. Alcohol may be supplied to minors only by, or with express consent from, their parent or legal guardian.[205]

 Northern Mariana Islands
21[206]

 Palau
21[207]
It is illegal to sell or serve any alcoholic beverage to a person under 21 years of age. Minors may access a bar or licensed premises only if accompanied by a parent or legal guardian. Minors buying, consuming or attempting to buy alcohol are commiting a offence. The law provides a exception for the consumption of alcohol by minors as part of a religiously recognized ceremony.[207]

 Papua New Guinea
18[208]
It is illegal for a minor to purchase, consume or attempt to purchase alcoholic beverages. Any licence holder has to ensure that the customer who he sells or serves alcohol to, is at least 18 years of age. Violation of this law is fined.[208]

 Samoa
21[209]
Selling or serving alcohol to a person under the age of twenty-one years is punished with three hundred dollars or imprisonment for nine months or both, a fine and imprisonment.[210]

 Solomon Islands
None[210]
21[210]
Selling or serving alcohol to a person under the age of twenty-one years old is punished with a three hundred dollar fine or imprisonment for nine months or both, a fine and imprisonment.[210]

 Tokelau
18[211]

 Tonga
18[212]
Selling, serving or supplying alcohol to a minor is illegal. It is also illegal for minors to buy, attempt to buy or consume alcohol in any public place and any violation of this law is fined up to $1,000.[212]

 Vanuatu
18[213]
It is unlawful to sell, serve or supply alcohol to any person under the age of 18 years. Violation of the law is fined up to VT 25,000 or by a term of imprisonment not exceeding 3 months, or by both, fine and imprisonment. Any minor under the age of 18 years, being found in possession or consumption of alcohol is fined up to VT 10,000.[213]


document_title: Ottoman Egypt

question_text: when did the ottoman empire take over egypt

text: Ottoman Egypt

text: Ottoman Egypt covers two main periods of the history of Egypt from the 16th through early 20th centuries, when under the rule of or allied to the Ottoman Empire that was based in (present day) Turkey.

text: Egypt Eyalet[edit]

text: The Egypt Eyalet (1517–1867) was established when the Egypt region came under the direct rule of the Ottoman Empire with their 1517 victory over the Mamluk Sultanate. The interruption of the Napoleon's French campaign in Egypt and Syria (1798–1801) allowed Muhammad Ali's seizure of power from Ottoman Hurshid Pasha, and the founding of the Muhammad Ali dynasty.

text: Khedivate of Egypt[edit]

text: The Khedivate of Egypt (1867–1914) was an autonomous tributary state of the Ottoman Empire. Muhammad Ali's self-appointed status as a viceroyalty or Khedive was officially acknowledged in 1867, though by then Egypt was subject to the influence of France and especially the United Kingdom, who completed the Suez Canal in 1869.


document_title: Football helmet

question_text: when did the nfl switch from leather helmets

text: Football helmet

text: History[edit]

text: Invention[edit]

text: One of the first instances of football headgear dates to 1896 when Lafayette College halfback George "Rose" Barclay began to use straps and earpieces to protect his ears. It is not certain who invented the football helmet. Many sources give credit for the creation of the helmet to James Naismith, while other sources credit U.S. Naval Academy Midshipman Joseph M. Reeves (later to become the "Father of Carrier Aviation"), who had a protective device for his head made out of mole skin to allow him to play in the 1893 Army-Navy game. Reeves had been advised by a Navy doctor that another kick to his head would result in "instant insanity" or even death, so he commissioned an Annapolis shoemaker to make him a helmet out of leather.[1] Later, helmets were made of padded leather and resembled aviators' helmets or modern day scrum caps. At least in professional football, they were optional. Some National Football League players, notably Hall-of-Famer Bill Hewitt, played all or most of their careers without a helmet.

text: Early years[edit]

text: One innovation from the early 1900s period was hardened leather. 1917 marked the first time helmets were raised above the head in an attempt to direct blows away from the top of the head.[clarification needed] Ear flaps also had their downfall during this period as they had little ventilation and made it difficult for players to hear. The 1920s marked the first time that helmets were widely used in the sport of football. These helmets were made of leather and had some padding on the inside, but the padding was insufficient and provided little protection. In addition, they lacked face masks. As a result, injuries were very common. Early helmets also absorbed a lot of heat, making them very uncomfortable to wear.

text: In 1939, the Riddell Company of Chicago, Illinois started manufacturing plastic helmets because it felt that plastic helmets would be safer than those made of leather. Plastic was found to be more effective because it held its shape when full collision contact occurred on a play. These helmets were also much more comfortable and had more padding to cushion the head in an impact. Included with the plastic helmet came plastic face mask, which allowed the helmet to protect the entire head. By the mid-1940s, helmets were required in the NFL. They were still made of leather, but with improved manufacturing techniques had assumed their more familiar spherical shape. The NFL initially allowed either plastic or leather helmets, but in 1948 the league outlawed the plastic helmet, considering the hard-plastic material to be an injury risk. The NFL repealed this rule in 1949, and by 1950, the plastic helmet had become universal in that league.[2]

text: Introduction of advanced materials[edit]

text: By the 1950s, the introduction of polymers ended the leather helmet era. The last leather helmet manufacturer, MacGregor, ceased production of leather helmets in the mid-1960s. The NFL also recommended face masks for players in 1955,[3] reducing the number of broken noses and teeth, but also necessitating new rules prohibiting opposing players from grabbing the face mask. By varying accounts, either Pat Studstill or Garo Yepremian was the last to forgo the facemask; among non-kickers, Tommy McDonald was the last to do so.

text: Modern helmet components[edit]

text: Inflatable padding[edit]

text: According to Andrew Tucker, football helmets adequately protected players from catastrophic brain injuries, but helmet manufacturers were motivated to design helmets that decrease the risk of concussions. Vin Ferrara,[4] a former Harvard quarterback, accidentally discovered a new way to cushion football helmets. One night, Ferrara was looking for an aspirin when he saw a squirt bottle in his medicine cabinet. As he pumped it and then punched it, he realized that the bottle withstood the blows of different forces. Ferrara immediately came up with the idea to encase football helmets with a number of inflatable pockets in order to cushion the blows a football player receives and reduce concussions.

text: More recently, in 2003 Schutt sports introduced their football helmets which contained TPU, or thermoplastic urethane. They would argue that this helps cushion the head more than any other helmet in the market. Schutt also believes that TPU makes the helmet less prone to mold and easier overall to clean and keep sanitary.[5]

text: Visors[edit]

text: A more recent addition to the football helmet is the visor or eye shield, which is affixed to the face mask to protect players from glare or eye injuries, such as pokes. It is believed that the first player to use a protective visor Mark Mullaney of the NFL's Minnesota Vikings in 1984, in order to protect a healing eye injury. Top manufacturers of visors are Nike, Oakley, and Under Armour, with Leader being the first to come out with a visor/shield for former Chicago Bears quarterback Jim McMahon (who needed the visor because of a childhood eye injury).[citation needed] While Mullaney and McMahon's visors were tinted, most of the earlier visors were clear or smoked, but they are now offered in a variety of styles ranging from blue, gold, black, rainbow, silver, or amber. High-school and pee-wee leagues prohibit all but clear visors. This rule was enacted so that training staff and coaches can easily view a player's face and eyes in the case of a serious injury, to discern if the player is conscious.[citation needed] The NCAA banned the use of tinted visors for the same reason, and the NFL has followed suit as well. However, players with eye problems may still obtain special permission to wear tinted visors, some notable examples being LaDainian Tomlinson and Chris Canty.[6]

text: Sensors[edit]

text: Helmet shock data loggers and shock detectors  monitor impacts a player receives, such as the force and direction of the impact. If the force recorded by the sensors is over 100 Gs, it signals a possible concussion.{[7]} Some players will experience up to 2,000 of these potential concussion blows each season.This data is then analyzed by doctors.  New rules have been implemented[vague] which instruct that any player who has a particularly high reading of force needs to be taken off the field and examined before they can play another down.

text: Headsets[edit]

text: Two Ohio inventors devised a headset for Cleveland Browns coach Paul Brown so he could radio plays to his quarterback. It was banned shortly after its first use in 1956. The NFL approved use of headsets for all NFL teams in 1994.[8]

text: NFL rules state that all helmets equipped with headsets must have a visible green dot on the back.  A few times in 2006, the holder on the field goal attempt was told to pull up and throw or run at the last second because of a change the coaches saw on the field. According to the NFL, this gave teams an "unfair advantage." The new rules let each team know who is wearing a headset and hearing the plays being called.[citation needed]

text: One-bar face masks[edit]

text: The one-bar face mask was once common but its use has been supplanted in professional and amateur sport. For example, it has been illegal in the National Football League since 2004, but a grandfather clause allowed players who wore the mask prior to 2004 to continue to do so for the remainder of their careers.  No current professional player currently wears such a face mask; the last player to do so was Scott Player, who last played professionally in 2009.

text: Typically, by the mid-1980s only placekickers and punters in professional football in Canada and the United States wore the one-bar face mask, a notable exception being quarterback Joe Theismann.

text: The one-bar had two different variations.  The standard one-bar was made from nylon or other hard plastic and was bolted to both side of the helmet just in front of the earholes.  There was a "snub" version that did not extend as far out in front of the helmet as the standard.

text: Face masks for football helmets today are multibar.  The multibar facemasks are typically constructed out of metal, such as titanium, stainless steel, or most commonly carbon steel. Each facemask is coated with Polyarmor G17, a powder coating that is resistant to impact and corrosion.  The Polyarmor is a thermoplastic coating used on a number of surfaces. While some organizations purchase new face masks every season, others have their equipment reconditioned.

text: Recent designs[edit]

text: In 2002, American football equipment manufacturer Riddell released a new design of helmet called the Revolution.[9] The newer design was released in response to a study on concussions. In addition, Riddell has recently come out with a new design of helmets, the Riddell Speed Flex. This helmet came out in 2014.[10] This new helmet uses elements of Riddell's older helmets, the 360 and the Revolution, such as Side Impact Protection and All Points Quick Release face mask attachment system.[11]

text: In 2007, Schutt Sports announced the arrival of a next generation helmet, the Schutt ION 4D. This next generation design was in response to the demand for a safer football helmet.  The design includes an integrated face guard. This new face guard design features shock absorbing "Energy Wedges" that reduce the force of impacts to the face guard. College teams wearing the helmet include Air Force, Penn State and Virginia.[12] Schutt has also distinguished between their varsity helmets and youth helmets. The varsity helmets from Schutt are made with polycarbonate, which is a very strong polymer designed to take bigger hits. The Schutt youth helmets however; are made from ABS, which is a lighter material, meant for kids who do not take as powerful of hits.[5]

text: Recently, a brand new type of helmet has come into play. Vicis is a new company that is producing helmets that have a softer outer layer. The softer layer absorbs more energy from impacts. In addition, the inside of the helmet also has a foam like substance which absorbs energy and improves comfort.[13]

text: Safety research and testing[edit]

text: NOCSAE certification[edit]

text:
Rules in place for NFL, NCAA, and high school football require that all helmets be certified by the National Operating Committee on Standards for Athletic Equipment.[14][15][16]
Reliance on NOCSAE certification has been criticized on numerous grounds, including that organization's control by equipment manufacturers causes a conflict of interest, testing data that focuses on skull fractures instead of concussions, and failure to take into account new research.[14][17][18]

text: The most common NOCSAE test is the  drop test. This test uses a 13-pound dummy head full of sensors and a gelatin material. The head and helmet is dropped from a height of 60 at one of the six NOCSAE specified locations on the helmet. These locations include the front, rear, left side, right side, right boss, and left boss. The sensors in the dummy head measure the amount of force that the head experiences. The NOCSAE has certain regulations such as the peak severity index can never  more than1200 SI. If a helmet fails to meet these requirements, they do not pass the NOCSAE drop test.[19][20]

text: Current research[edit]

text: There has been significant study/research regarding head injuries in football, as well as football helmet design in recent years.  Kevin Guskiewicz, a professor at The University of North Carolina and a MacArthur Fellow, has for many years been researching concussions in football of all age groups.[21]  He has been equipping UNC football helmets with accelerometers to measure impacts and concussions.   Also, the NFL has awarded over $1.6 million in sports medical research, almost $1 million of which has been toward concussion prevention.[22] All this concussion prevention research has led football helmet manufacturers to develop safer products.  A joint effort between Virginia Tech and Wake Forest has been testing current football helmets and giving them yearly ratings since 2011.  On a scale out of 5 stars, only one helmet was awarded a 5 in 2011. In 2012, two additional helmet designs were awarded 5 stars.[23][24]

text: Controversies revolving around football helmets always regard their ability to decrease head/brain injury rates, including concussions. However, recent research has begun to assess the tests specifically employed to create the safest football equipment. In 2015, David Camarillo at Stanford conducted a study that suggested football helmet tests did not account for the delay between injury-causing brain movement and stress impact.[25]

text: Other research[edit]

text: Neuroscientists  at Ohio State University launched baseballs from air cannons at football helmets in order to simulate a kick or blow to the head such as a tackle. It was found that the helmets could withstand 2,500 Newtons or about 562 pounds of force.

text: Vijay Gupta, a professor at UCLA, has done research and produced a special polymer that if added as a layer on the inside of football helmets can produce up to a 25% decrease in the g-forces a player would experience.[26]  This reduction of forces would produce a similar amount of reduction of the probability of a player suffering a concussion from the same hits.

text: Logo display[edit]

text: National Football League[edit]

text:
In 1948, the Los Angeles Rams were the first NFL team to put logos on their helmets; the basic "ram's horn" logo on the helmet has remained mostly the same, except for color, ever since. As of 2018
the Cleveland Browns are the last remaining NFL teams not using any form of primary logo on its helmets. The Pittsburgh Steelers are the only NFL team that puts its logo on only one side of the helmet (the right side),[why?] while the Cincinnati Bengals, after using a wordmark for a helmet logo into the 1980s, use a striping pattern instead of a logo.