Computational study of the propagation of the longitudinal velocity in a polymer melt contained within a cylinder using a scale-bridging method

Abstract

The “constitutive equation”–free scale-bridging method connecting nonequilibrium molecular dynamics and continuum fluid mechanics, that had hitherto been applied only to a parallel-plates geometry, is extended to study the flow of a polymer melt in a cylindrical pipe subject to a velocity in the direction parallel to the cylinder's axis. The system, initially at rest, is given a velocity at the cylinder's surface, and the evolution of the velocity profile within the fluid is studied, along with the time taken for the velocity to propagate toward the cylinder's axis. The said time of propagation is found to increase with the boundary velocity—a fact in contrast with the case of a Newtonian fluid for which the time of propagation is expected to be independent of the boundary velocity. For a fixed value of the boundary velocity, the propagation time is found to increase with the cylinder radius according to a power law with an exponent that is smaller than the corresponding exponent for a Newtonian fluid. For the lower values of the boundary velocity and the lower values of the radius studied, a velocity overshoot is observed at the cylinder's axis—a manifestation of elastic behavior of the fluid.