Constitutive equations for surface diffusion in mixtures of viscoelastic surfactants

In this paper a constitutive equation is derived for surface diffusion in multicomponent surfaces that exhibit linear viscoelastic behavior with fading memory. The equation is based on the Maxwell–Stefan theory for diffusion. The constitutive equation incorporates the effects of ordinary diffusion, forced diffusion, and diffusion arising from surface tension gradients. It also incorporates diffusion caused by inertial effects, diffusion resulting from hydrostatic normal stresses, diffusion arising from hydrodynamic viscous stresses, and contributions arising from the deformation history of the individual components. These last contributions are given in terms of memory integral expressions. The constitutive equation is derived using the jump entropy inequality.