Deviations From Classical Hydrodynamic Theory in Highly Confined Planar Poiseuille Flow of a Polymer Solution

Abstract

The behaviour of polymer solutions in highly confined geometries remains a subject of interest in rheology and fluid dynamics. In this paper, we investigate how well the classical hydrodynamic description based on the Navier-Stokes equations, Fourier's Law and Fick's Law describes the flow of a highly confined polymer solution. In particular, we examine the effects of depletion of polymer concentration at the wall-fluid interface and strain rate coupling to the heat flux. We present data from molecular dynamics simulations of a model polymer solution in explicit solvent undergoing planar Poiseuille flow for channel widths ranging from around 10 solvent atomic diameters to around 80 solvent atomic diameters. We find that the classical continuum approach works very well for channels wider than 20 solvent atomic diameters. For narrower channels, we observe deviations in the velocity, temperature and concentration profiles due to density oscillations near the walls, the polymer depletion effect, and possible weak strain rate coupling. For the narrowest channel, the wall effects extend to the centre of the channel but the underlying profiles are quite well described by the classical continuum picture. By allowing very long times of order 10 4 reduced time units for relaxation to the steady state and averaging over very long runs of order 10 5 reduced time units and 16 independent ensemble members, we are able to conclude that previously reported deviations from the classical continuum predictions (I.K. Snook, P.J. Daivis, T. Kairn, J. Physics-Condensed Matter 20, 404211 (2008)) were probably the result of insufficient equilibration time. Our results are also sufficiently accurate and precise to verify the expected quartic temperature profile predicted by classical hydrodynamic theory, with only a very small deviation which we can attribute to nonlinear coupling of the heat flux vector to the strain rate.

Measuring heat flux beyond Fourier’s law

“…Han and Lee 17 also proposed a local form of the method of planes formalism [18][19][20] and captured the parallel component of the heat flux in an NEMD simulation. The strain rate coupling was also explored by Menzel et al 21 using NEMD for a polymer solution which indicates a very small value of the strain rate coupling coefficient ξ with a magnitude of approximately one in reduced units, in agreement with literature values.…”