Macromolecules in nonhomogeneous velocity gradient fields

Abstract

Some dilute solution kinetic theory results for bead-spring-type macromolecular models (linearly elastic dumbbell and Rouse) in nonuniform velocity gradient fields are obtained. It is shown that contrary to the homogeneous flow result, in general, a macromolecular solute does not move with the local center-of-mass solvent velocity in a nonhomogeneous flow. This results essentially from a unique coupling between segmental Brownian motion of the macromolecule in the flowfield and the center-of-mass translational diffusion possible only in nonhomogeneous flow. Poiseuille flow between parallel plates and circular Couette flow problems are solved for the dumbbell and some results are obtained for the Rouse model. Migration along streamlines occurs in the Poiseuille flow and migration across streamlines occurs in the Couette flow. Additional energy dissipation results for the Rouse model in Poiseuille flow relative to the simple shear flow case. Nonuniform concentration profiles are calculated in Couette flow by taking the appropriate average of the exact equation for the dumbbell configuration space distribution function.

Theory of shear-induced migration in dilute polymer solutions near solid boundaries

“…14,46,63,64 In a pressure-driven flow, this term leads to a weak driving force toward the wall, but except at the centerline of the channel where the hydrodynamic migration term vanishes by symmetry, our previous simulations show that this effect is small. 12 In nonhomogeneous flow, the term containing ١١v predicts the lag of a macromolecule behind the solvent along the streamline 33 but no cross-streamline migration, and unless the nonhomogeneity is so large that it cannot be ignored even on the length scale of the polymer molecule, this term is small. Finally, the contribution to polymer flux proportional to ١ · p predicted by several models [26][27][28][29][30][31][32][34][35][36][37] does not arise in the single-molecule limit analyzed here.…”

“…[26][27][28][29][30][31][32] In these models, a contribution to the polymer mass flux proportional to ١ · p is found, where p is the polymer contribution to the stress tensor. Turning to the molecular kinetic theory point of view for ͑infinitely͒ dilute solutions, Aubert and Tirrell 33 modeled the polymer as a flexible dumbbell in a viscous solvent and pointed out an effect in a nonhomogeneous flow field where the macromolecules lag behind the solvent motion along the streamline. In some kinetic theory developments, a contribution to the polymer flux corresponding to the divergence of the stress is found, [34][35][36][37] which is similar to the result from the two-fluid models.…”

Theoretical modeling of microstructured liquids: a simple thermodynamic approach

“…The Poisson bracket is a bilinear and antisymmetric operator, i.e., {αu, v} = α{u, v} (24) {u + v, w} = {u, w} + {v, w} (25) {u, v} = −{v, u};…”

“…Similarly, Newton's law of viscosity says that the viscous stress must be linearly proportional to the rate of strain, but the viscosity coefficient can depend non-linearly on the temperature and specific volume or pressure ( [42], pp. [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29].…”

“…Then theory is needed to project the information acquired in simple experiments to the complex reality of the process. The need for robust theories is even more pressing when tackling more complex transport phenomena, like coupled flow and heat transfer [17][18][19][20][21][22] or mass transfer [23][24][25][26][27][28][29][30]; experimental evidence on such processes is still limited [31][32][33][34][35][36].…”