# Diffusion coefficient

In general, the diffusion coefficient (diffusion constant, diffusivity) is a measure of the rate of material transport as a result of the random thermal movement of particles (diffusion). Joos and Rillaerts have produced an equation for calculating a diffusion coefficient for the change in surface tension with respect to time due to diffusion as a result of the movement of surfactant molecules at the interface:

(σ_{t} = Surface tension at surface age t; σ_{0} = Surface tension of the pure solvent; R = Universal gas constant; T = Absolute temperature; c = Molar surfactant concentration; D_{s} = Diffusion coefficient)

The diffusion coefficient of a surfactant can be determined with the help of a bubble pressure tensiometer which measures the surface tension as a function of surface age.

As well as diffusion at the interface, the rate of change of surface tension is also determined by the adsorption at the interface, as a result of which it is also expedient to determine the adsorption coefficient. Which process requires more time depends on the concentration of the solution and to what extent the interface is already overlaid with surfactant molecules. Depending on the conditions, the diffusion or the adsorption can become the rate determining step.

## Bibliography

P. Joos, E. Rillaerts: Theory on the Determination of the Dynamic Surface Tension with the Drop Volume and Maximum Bubble Pressure Methods. J. Coll. Interf. Sci. 79/1, 1981, P. 96-100.