# Mass Diffusivity

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

Mass diffusivity, abbreviated as $$D$$ or $$D_m$$, also called 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.  Diffusion is the spread of gases, liquids, or solids from areas of high concentration to areas of low concentration.  It is the rate one material can disperse through another material.  The higher the diffusion coefficient, the faster the diffusion will be.  The diffusion coefficient for solids tends to be much lower than the diffusion coefficient for liquids and gasses.

## Mass Diffusivity formulas

$$\large{ D = \frac{ \alpha }{ Le } }$$     (Lewis Number

$$\large{ D = \frac { \nu } { Sc } }$$     (Schmidt Number

$$\large{ D = \frac{ K \; l_c}{Sh} }$$     (Sherwood Number)

Symbol English Metric
$$\large{ D }$$ = mass diffusivity  $$\large{\frac{ft^3}{sec}}$$ $$\large{\frac{m^3}{s}}$$
$$\large{ l_c }$$ = characteristic length $$\large{in}$$ $$\large{mm}$$
$$\large{ \nu }$$  (Greek symbol nu) = kinematic viscosity $$\large{\frac{ft^2}{sec}}$$ $$\large{\frac{m^2}{s}}$$
$$\large{ Le }$$ = Lewis number $$\large{dimensionless}$$
$$\large{ K }$$ = mass transfer coefficient $$\large{dimensionless}$$
$$\large{ Sc }$$ = Schmidt number $$\large{dimensionless}$$
$$\large{ Sh }$$ = Sherwood number $$\large{dimensionless}$$
$$\large{ \alpha }$$  (Greek symbol alpha) = thermal diffusivity $$\large{\frac{ft^2}{sec}}$$ $$\large{\frac{m^2}{s}}$$