Flow pattern in a polymer coil placed into a stationary longitudinal flow

Abstract

The flow pattern of solvent in a polymer coil placed into a stationary flow is examined. In contrast to the previous works, the flow of solvent at large distances from the macromolecule has a constant longitudinal gradient. The calculations are based on a simple model of macromolecule dynamics in flowing solutions proposed earlier. An analysis of the results shows that, in the first-order approximation in the longitudinal velocity at a certain threshold value of the parameter of hydrodynamic interactions P, the coil acquires a hydrodynamic boundary at which the radial component of the flow velocity is zero. The threshold value of P coincides with that for a stationary shear flow, determined earlier. At large P, i.e., large molecular mass, the hydrodynamic boundary of the coil encompasses a major part of the macromolecule, while the longitudinal intrinsic viscosity takes a form analogous to that characteristic of a suspension of solid balls with a radius equal to the radius of inertia of the polymer coil. In the second-order approximation in the flow velocity, the radial component of the flow velocity is nonzero. As a result, the mass transfer of solvent between the regions separated by the hydrodynamic boundary only slows down, without hindering the speedup of reactions by mixing the reagents and macromolecules.