Surface modes on a polymer gel of finite thickness

Abstract

The fluctuations in the height of the free surface of a polymer gel of finite thickness are analyzed in the limit where the period of elastic oscillations is small compared to the viscous relaxation time. In this limit, the dominant forces in the momentum conservation equation are the elastic and surface tension forces; the viscous forces enter as a subdominant correction. Zero stress boundary conditions are applied at the free surface, while two different types of boundary conditions are considered at the other surface— for ‘‘grafted’’ gels zero displacement conditions are applied, while for ‘‘adsorbed’’ gels the displacement normal to the surface is zero but the surface is permitted to move in the lateral direction. There are multiple frequencies of oscillation, all of which are consistent with the boundary conditions, and it is found that the frequency and the decay rates of the oscillations are lower for the adsorbed gels. The static structure factor is calculated from the energy storage due to the elastic strain, surface deformation, and kinetic energy of motion. The structure factor has a peak at a nonzero value of the wave number for a grafted gel, while the maximum occurs at zero wave number for an adsorbed gel. An increase in the surface tension reduces the magnitude of the peak, and shifts it to lower values of the wave number.