This article is about coefficient of molecular diffusion of mass. For other uses, see Diffusivity.
Diffusivity, mass diffusivity or diffusion coefficient is a proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration of the species (or the driving force for diffusion). Diffusivity is encountered in Fick's law and numerous other equations of physical chemistry.
The diffusivity is generally prescribed for a given pair of species and pairwise for a multi-species system. The higher the diffusivity (of one substance with respect to another), the faster they diffuse into each other. Typically, a compound's diffusion coefficient is ~10,000× as great in air as in water. Carbon dioxide in air has a diffusion coefficient of 16 mm2/s, and in water its diffusion coefficient is 0.0016 mm2/s.[1][2]
Diffusivity has dimensions of length2 / time, or m2/s in SI units and cm2/s in CGS units.
An approximate dependence of the diffusion coefficient on temperature in liquids can often be found using Stokes–Einstein equation, which predicts that
where
D is the diffusion coefficient,
T1 and T2 are the corresponding absolute temperatures,
The dependence of the diffusion coefficient on temperature for gases can be expressed using Chapman–Enskog theory (predictions accurate on average to about 8%):[3]
1 and 2 index the two kinds of molecules present in the gaseous mixture,
T is the absolute temperature (K),
M is the molar mass (g/mol),
p is the pressure (atm),
is the average collision diameter (the values are tabulated[5] page 545) (Å),
Ω is a temperature-dependent collision integral (the values are tabulated[5] but usually of order 1) (dimensionless).
Pressure dependence of the diffusion coefficient
For self-diffusion in gases at two different pressures (but the same temperature), the following empirical equation has been suggested:[3]
where
D is the diffusion coefficient,
ρ is the gas mass density,
P1 and P2 are the corresponding pressures.
Population dynamics: dependence of the diffusion coefficient on fitness
In population dynamics, kinesis is the change of the diffusion coefficient in response to the change of conditions. In models of purposeful kinesis, diffusion coefficient depends on fitness (or reproduction coefficient) r:
where is constant and r depends on population densities and abiotic characteristics of the living conditions. This dependence is a formalisation of the simple rule: Animals stay longer in good conditions and leave quicker bad conditions (the "Let well enough alone" model).
Effective diffusivity in porous media
The effective diffusion coefficient describes diffusion through the pore space of porous media.[6] It is macroscopic in nature, because it is not individual pores but the entire pore space that needs to be considered. The effective diffusion coefficient for transport through the pores, De, is estimated as follows:
where
D is the diffusion coefficient in gas or liquid filling the pores,
εt is the porosity available for the transport (dimensionless),
The transport-available porosity equals the total porosity less the pores which, due to their size, are not accessible to the diffusing particles, and less dead-end and blind pores (i.e., pores without being connected to the rest of the pore system). The constrictivity describes the slowing down of diffusion by increasing the viscosity in narrow pores as a result of greater proximity to the average pore wall. It is a function of pore diameter and the size of the diffusing particles.
Example values
Gases at 1 atm., solutes in liquid at infinite dilution. Legend: (s) – solid; (l) – liquid; (g) – gas; (dis) – dissolved.
^ abcdefCussler, E. L. (1997). Diffusion: Mass Transfer in Fluid Systems (2nd ed.). New York: Cambridge University Press. ISBN0-521-45078-0.
^ Welty, James R.; Wicks, Charles E.; Wilson, Robert E.; Rorrer, Gregory (2001). Fundamentals of Momentum, Heat, and Mass Transfer. Wiley. ISBN978-0-470-12868-8.
^ abHirschfelder, J.; Curtiss, C. F.; Bird, R. B. (1954). Molecular Theory of Gases and Liquids. New York: Wiley. ISBN0-471-40065-3.
^Grathwohl, P. (1998). Diffusion in natural porous media: Contaminant transport, sorption / desorption and dissolution kinetics. Kluwer Academic. ISBN0-7923-8102-5.
January 12, 2023
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This article is about coefficient of molecular diffusion of mass For other uses see Diffusivity Diffusivity mass diffusivity or diffusion coefficient is a proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration of the species or the driving force for diffusion Diffusivity is encountered in Fick s law and numerous other equations of physical chemistry The diffusivity is generally prescribed for a given pair of species and pairwise for a multi species system The higher the diffusivity of one substance with respect to another the faster they diffuse into each other Typically a compound s diffusion coefficient is 10 000 as great in air as in water Carbon dioxide in air has a diffusion coefficient of 16 mm2 s and in water its diffusion coefficient is 0 0016 mm2 s 1 2 Diffusivity has dimensions of length2 time or m2 s in SI units and cm2 s in CGS units Contents 1 Temperature dependence of the diffusion coefficient 1 1 Solids 1 2 Liquids 1 3 Gases 2 Pressure dependence of the diffusion coefficient 3 Population dynamics dependence of the diffusion coefficient on fitness 4 Effective diffusivity in porous media 5 Example values 6 See also 7 ReferencesTemperature dependence of the diffusion coefficient EditSolids Edit The diffusion coefficient in solids at different temperatures is generally found to be well predicted by the Arrhenius equation D D 0 exp E A R T displaystyle D D 0 exp left frac E text A RT right where D is the diffusion coefficient in m2 s D0 is the maximal diffusion coefficient at infinite temperature in m2 s EA is the activation energy for diffusion in J mol T is the absolute temperature in K R 8 31446 J mol K is the universal gas constant Liquids Edit An approximate dependence of the diffusion coefficient on temperature in liquids can often be found using Stokes Einstein equation which predicts thatD T 1 D T 2 T 1 T 2 m T 2 m T 1 displaystyle frac D T 1 D T 2 frac T 1 T 2 frac mu T 2 mu T 1 where D is the diffusion coefficient T1 and T2 are the corresponding absolute temperatures m is the dynamic viscosity of the solvent Gases Edit The dependence of the diffusion coefficient on temperature for gases can be expressed using Chapman Enskog theory predictions accurate on average to about 8 3 D A T 3 2 p s 12 2 W 1 M 1 1 M 2 displaystyle D frac AT frac 3 2 p sigma 12 2 Omega sqrt frac 1 M 1 frac 1 M 2 where D is the diffusion coefficient cm2 s 3 4 A is an empirical coefficient equal to 1 859 10 3 a t m A 2 c m 2 K 3 2 s g m o l textstyle 1 859 times 10 3 mathrm frac atm cdot mathrm AA 2 cdot cm 2 K 3 2 cdot s sqrt frac g mol 1 and 2 index the two kinds of molecules present in the gaseous mixture T is the absolute temperature K M is the molar mass g mol p is the pressure atm s 12 1 2 s 1 s 2 textstyle sigma 12 frac 1 2 sigma 1 sigma 2 is the average collision diameter the values are tabulated 5 page 545 A W is a temperature dependent collision integral the values are tabulated 5 but usually of order 1 dimensionless Pressure dependence of the diffusion coefficient EditFor self diffusion in gases at two different pressures but the same temperature the following empirical equation has been suggested 3 D P 1 D P 2 r P 2 r P 1 displaystyle frac D P1 D P2 frac rho P2 rho P1 where D is the diffusion coefficient r is the gas mass density P1 and P2 are the corresponding pressures Population dynamics dependence of the diffusion coefficient on fitness EditIn population dynamics kinesis is the change of the diffusion coefficient in response to the change of conditions In models of purposeful kinesis diffusion coefficient depends on fitness or reproduction coefficient r D D 0 e a r displaystyle D D 0 e alpha r where D 0 displaystyle D 0 is constant and r depends on population densities and abiotic characteristics of the living conditions This dependence is a formalisation of the simple rule Animals stay longer in good conditions and leave quicker bad conditions the Let well enough alone model Effective diffusivity in porous media EditThe effective diffusion coefficient describes diffusion through the pore space of porous media 6 It is macroscopic in nature because it is not individual pores but the entire pore space that needs to be considered The effective diffusion coefficient for transport through the pores De is estimated as follows D e D e t d t displaystyle D text e frac D varepsilon t delta tau where D is the diffusion coefficient in gas or liquid filling the pores et is the porosity available for the transport dimensionless d is the constrictivity dimensionless t is the tortuosity dimensionless The transport available porosity equals the total porosity less the pores which due to their size are not accessible to the diffusing particles and less dead end and blind pores i e pores without being connected to the rest of the pore system The constrictivity describes the slowing down of diffusion by increasing the viscosity in narrow pores as a result of greater proximity to the average pore wall It is a function of pore diameter and the size of the diffusing particles Example values EditGases at 1 atm solutes in liquid at infinite dilution Legend s solid l liquid g gas dis dissolved Values of diffusion coefficients gas 3 Species pair Temperature C D cm2 s Solute SolventWater g Air g 25 0 260Oxygen g Air g 25 0 176Values of diffusion coefficients liquid 3 Species pair Temperature C D cm2 s Solute SolventAcetone dis Water l 25 1 16 10 5Air dis Water l 25 2 00 10 5Ammonia dis Water l 12 citation needed 1 64 10 5Argon dis Water l 25 2 00 10 5Benzene dis Water l 25 1 02 10 5Bromine dis Water l 25 1 18 10 5Carbon monoxide dis Water l 25 2 03 10 5Carbon dioxide dis Water l 25 1 92 10 5Chlorine dis Water l 25 1 25 10 5Ethane dis Water l 25 1 20 10 5Ethanol dis Water l 25 0 84 10 5Ethylene dis Water l 25 1 87 10 5Helium dis Water l 25 6 28 10 5Hydrogen dis Water l 25 4 50 10 5Hydrogen sulfide dis Water l 25 1 41 10 5Methane dis Water l 25 1 49 10 5Methanol dis Water l 25 0 84 10 5Nitrogen dis Water l 25 1 88 10 5Nitric oxide dis Water l 25 2 60 10 5Oxygen dis Water l 25 2 10 10 5Propane dis Water l 25 0 97 10 5Water l Acetone l 25 4 56 10 5Water l Ethyl alcohol l 25 1 24 10 5Water l Ethyl acetate l 25 3 20 10 5Values of diffusion coefficients solid 3 Species pair Temperature C D cm2 s Solute SolventHydrogen Iron s 10 1 66 10 9Hydrogen Iron s 100 124 10 9Aluminium Copper s 20 1 3 10 30See also EditAtomic diffusion Effective diffusion coefficient Lattice diffusion coefficient Knudsen diffusionReferences Edit CRC Press Online CRC Handbook of Chemistry and Physics Section 6 91st Edition Diffusion a b c d e f Cussler E L 1997 Diffusion Mass Transfer in Fluid Systems 2nd ed New York Cambridge University Press ISBN 0 521 45078 0 Welty James R Wicks Charles E Wilson Robert E Rorrer Gregory 2001 Fundamentals of Momentum Heat and Mass Transfer Wiley ISBN 978 0 470 12868 8 a b Hirschfelder J Curtiss C F Bird R B 1954 Molecular Theory of Gases and Liquids New York Wiley ISBN 0 471 40065 3 Grathwohl P 1998 Diffusion in natural porous media Contaminant transport sorption desorption and dissolution kinetics Kluwer Academic ISBN 0 7923 8102 5 Retrieved from https en wikipedia org w index php title Mass diffusivity amp oldid 1111456993, wikipedia, wiki, book, books, library,
