Hydrodynamic surface modes on concentrated polymer solutions and gels

Abstract

We present a coupled two‐fluid model for hydrodynamic surface modes on concentrated polymer solutions and polymer gels. This model is used to investigate such surface modes in the limit of strong coupling. The surface mode dispersion relation ω(k) and the structure factor S(k,ω) of thermally induced surface fluctuations are derived in this limit for materials with a general constitutive relation η(ω). We argue for the existence of several types of surface modes, including Rayleigh elastic waves, capillary waves, and overdamped modes resulting from viscous dissipation in the solvent as well as from polymer diffusion in the case of polymer solutions. The properties of surface modes are discussed separately for the cases of polymer gels and concentrated polymer solutions. Detailed predictions for the form of the normal modes ω(k), and the surface mode structure factor S(k,ω) are given and their dependence on relevant material properties are discussed in each case. Possible experimental scenarios are anticipated and discussed. Finally, we discuss some of the limitations of the model presented and future directions to be explored.