Flows of Linear Polymer Solutions and Other Suspensions of Rod-like Particles: Anisotropic Micropolar-Fluid Theory Approach.

Vladimir Shelukhin

doi:10.3390/polym13213679

Abstract

We formulate equations governing flows of suspensions of rod-like particles. Such suspensions include linear polymer solutions, FD-virus, and worm-like micelles. To take into account the particles that form and their rotation, we treat the suspension as a Cosserat continuum and apply the theory of micropolar fluids. Anisotropy of suspensions is determined through the inclusion of the microinertia tensor in the rheological constitutive equations. We check that the model is consistent with the basic principles of thermodynamics. In addition to anisotropy, the theory also captures gradient banding instability, coexistence of isotropic and nematic phases, sustained temporal oscillations of macroscopic viscosity, shear thinning and hysteresis. For the flow between two planes, we also establish that the total flow rate depends not only on the pressure gradient, but on the history of its variation as well.

Highlights

There is a class of complex fluids which can be considered as suspensions of rod-like particles
Depending on the directional alignment of the banded structure, there are two types of shear banding for suspensions of rod-like particles: gradient banding and vorticity banding [2,3,4]
We address rheology of suspensions of rodlike particles

Summary

Introduction

There is a class of complex fluids which can be considered as suspensions of rod-like particles. Examples include linear polymer solutions, worm-like micelles, FD-virus, liquid crystals, etc Such a class enjoys interesting properties like anisotropy [1], gradient and vorticity banding [2,3,4], shear banding instabilities [5], transition between isotropic and nematic phases [6], and cluster formation [7,8]. We formulate a new mathematical model which is good for concentrated suspensions and show that it predicts anisotropy and some other properties of suspensions of rod-like particles To this end, we study Poiseuille-like shear flows. In a number of studies, the search for the rheology of suspensions of rodlike particles is reduced to establishing the relationship between stress and rate of strain in shear flows. We prove that it is precisely due to the anisotropic viscosity that these equations capture such effects as hysteresis, shear gradient banding instability and phase transition. For the flow between two planes, we establish that the total flow rate depends on the pressure gradient, but on the history of its variation as well

Anisotropic Micropolar Fluids

Poiseuille Flows

Results of Calculations

Discussion