Effective viscosity of dilute polymer solutions near confining boundaries

Stress-gradient-induced polymer migration in Taylor-Couette flow

We apply our recent continuum theory for stress-gradient-induced migration of polymers in solution (G. Zhu et al., J. Rheol., 2016, 60, 327-343) to rotational shearing flow in the gap between concentric cylinders (the so-called Taylor-Couette flow), where we have also accounted for the effect of polymer depletion from the solid boundaries on migration patterns. The steady-state distribution of dilute solutions of polymer dumbbells, obtained both using a systematic perturbation analysis in terms of the Weissenberg number (Wi) and by solving numerically the transport problem coupled to the upper-convected Maxwell equation, shows accumulation of polymers near the inner cylinder. This accumulation becomes so strong that most polymers are driven near the inner cylinder once Wi > 4. We also show that there is no first-order contribution to the polymer migration in Taylor-Couette flow due to the absence of a velocity component in the r-direction. Brownian dynamics (BD) simulations for a Hookean dumbbell give a concentration distribution in good agreement with the theoretical predictions of our theory, confirming the accuracy of the theory when the dumbbell radius of gyration is around an order of magnitude or much smaller than the gap. The demonstration of the accuracy of our continuum theory by direct molecular simulation opens the door to application of the theory to journal bearing and other lubrication flows containing polymers that may migrate due to stress gradients.

Adsorption of single polymer molecules in shear flow near a planar wall

Adsorption of homopolymers from a dilute solution to a planar wall in the presence of shear flow is studied using a bead-spring dumbbell model. The bead-bead and bead-wall interactions are described by generalized Lennard-Jones potentials. A kinetic theory incorporating bead-wall hydrodynamic interaction is developed in order to obtain an analytical expression for the steady-state dumbbell concentration profile. The concentration profile exhibits an exclusion zone in the immediate vicinity of the wall, is followed by a peak, and finally approaches the bulk concentration far away from the wall. Using the analytical expression, the amount adsorbed and the equivalent film thickness are studied as a function of flow strength and the parameters characterizing the bead-wall interaction potential. Shear flow causes migration of the dumbbells due to bead-wall hydrodynamic interaction, which leads to desorption. On increasing the flow strength, the quantity adsorbed and the film thickness decrease until complete desorption occurs. The dependence of the flow strength required for desorption on the model parameters is also studied and a scaling law is derived for the strong-interaction limit. Brownian dynamics simulations are performed to verify the predictions from the kinetic theory. Although the theory makes a number of simplifying assumptions, it captures many of the key features seen in the simulations.

Unsteady-State Flow of Flexible Polymers in Porous Media

In this paper we report an investigation of the unsteady-state flow of polymer solutions through granular porous media. The experiments were performed using high-molecular-weight nonionic and anionic polyacrylamides dissolved in water containing NaCl and model porous media obtained by packing silicon carbide (SiC) grains having a narrow grain size distribution. Before injection in porous media, the polymer solutions were carefully filtered according to a method that was proved to be efficient in removing any possibly remaining microgels. The SiC grain surface was passively oxidized by a controlled thermal treatment in order to obtain a surface partially covered by a thin silica layer having adsorption properties similar to those of quartzitic sand. By packing SiC grains of different sizes, porous media having identical adsorption properties and well-known pore throats sizes can be obtained with a good reproducibility. Parameters investigated include pore size, velocity gradient, polymer concentration, and adsorption energy. A striking unsteady-state flow behavior (pressure build-up at constant flow rate) is observed when three conditions are fulfilled: (a) the velocity gradient is larger than that known to be able to induce a coil-stretch transition, (b) the polymer adsorbs on the pore surfaces, and (c) the length of stretched macromolecules is larger than the effective pore throat diameter. When one of these conditions is not satisfied the flow remains steady. These observations are interpreted by a mechanism involving the adsorption and bridging across pore restrictions of elongated chains. We propose to refer to this peculiar mode of polymer adsorption as bridging adsorption. Copyright 2001 Academic Press.