Slip, concentration fluctuations and flow instability in sheared polymer solutions

Recent experiments suggest that shear-enhanced growth of concentration fluctuations in polymer solutions is strongly influenced by solid boundaries. We analyze the dynamics of a model of a sheared polymer solution, accounting for the effect of stress variations on mass flux and for wall-slip. If (and only if) these effects are present, the flow exhibits a boundary-localized instability consistent with experimental observations. Even in the absence of flow instability, thermally-driven concentration fluctuations are significantly enhanced near the boundary. PACS numbers: 61.25.Hq, 83.50.Lh The local composition of polymer solutions and blends can be significantly affected by flow. In particular, shear-enhanced concentration fluctuations in semidilute polystyrene (PS) solutions have been observed via light-scattering and microscopy by a number of groups (1; 2; 3; 4; 5; 6; 7; 8). A purely hydrodynamic mechanism for this phenomenon, in an unbounded flow domain, was proposed initially by Helfand and Fredrickson (HF) (9) and later extended by several authors (10; 11; 12; 13; 14). This mechanism is based on the idea that variations in polymer stress can drive a flux of polymer molecules – indeed, several authors (15; 12; 13; 16) have developed simple, two-fluid models which demonstrate quite generally that the polymer flux in a solution, j, has the general form j = −D∇n+ (D/kBT )∇ · τ , where n is the polymer number density, τ is the polymer extra stress tensor, D is the polymer gradient diffusivity, kB is the Boltzmann constant, and T is the temperature. Furthermore, a detailed kinetic theory derivation for a dilute solution (17) leads to a very similar expression for the flux. A scattering peak is predicted to arise when the diffusion and relaxation times are equal, which occurs at a wavelength of 2π/k ≈ √ Dλ which is, not coincidentally, the only inherent length scale in the problem. This length scale is observed in light scattering experiments. Hashimoto and coworkers (1; 2; 5; 8) have performed a series of experiments with PS dissolved in dioctylphthalate (DOP) Present address: 3M Corporate Process Technology Center, St. Paul, MN, 55144 Corresponding author. E-mail: [email protected]