Constitutive equations for viscoelastic surface diffusion: Effects of deformation and thermal history

In this paper we derive constitutive equations for surface diffusion in a non-isothermal fluid–fluid interface, consisting of a mixture of linear viscoelastic components with fading memory. The constitutive equation contains three main contributions to the total diffusive flux: thermal diffusion, diffusion resulting from the thermal history of the components, and mechanical diffusion. The mechanical diffusion term 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. The history terms in the constitutive equation are all expressed in terms of memory integrals. In addition to an equation for the surface mass flux vector, the analysis also provides constitutive equations for the surface thermal energy flux vector, and the surface stress tensor. All these constitutive equations are derived using the jump entropy inequality.