Diffusivity, mass diffusivity or diffusioncoefficient is a proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration of the species. 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, 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. Diffusivity has an SI unit of m2/s. In CGS units it is given in cm2/s.
Temperature dependence of the diffusion coefficient
Solids
The diffusion coefficient in solids at different temperatures is generally found to be well predicted by the Arrhenius equation: where
Liquids
An approximate dependence of the diffusion coefficient on temperature in liquids can often be found using Stokes–Einstein equation, which predicts that where
The dependence of the diffusion coefficient on temperature for gases can be expressed using Chapman–Enskog theory : where
Pressure dependence of the diffusion coefficient
For self-diffusion in gases at two different pressures, the following empirical equation has been suggested: where
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 r: , where and r depends on population densities and abiotic characteristics of the living conditions. This dependence is a formalisation of the simple rule: Animals staylonger in good conditions and leave quicker bad conditions.
The effective diffusion coefficient describes diffusion through the pore space of porous media. 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 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. 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: – solid; – liquid; – gas; – dissolved.
