Phenomenological theory for polymer diffusion in non-homogeneous velocity-gradient flows

Abstract

The present study concerns the phenomenon of flow-induced polymer migration. It is shown that Tirrel!'s diffusion flux can be deduced from a macroscopic modelling which involves second-order gradients and a vectorial internal variable related to the microstructure. I n contrast to Tirrell's model, however, a migration may also occur across straight streamlines. The flow down an inclined plane is examined by way of example. The roles played by the microstructure and the second gradients, respectively, are thus exhibited.

Diffusion in polyelectrolyte solutions

“…We remark also that, aside from the obvious differences due to the appearance of a tensorial variable K rather than a vectorial one, the expressions (4.3) are the direct analogues of the correspondent ones in [9]. It is worth remarking that the x2, x3, and x4 terms in (4.3) are gyroscopic in that, upon substitution in (3.7), their contribution to the entropy production vanishes.…”

“…A macroscopic (and thermodynamic) investigation of polymer diffusion in nonhomogeneous flows was developed by Drouot et al [9] by modelling the polymer solution as a fluid with a vectorial internal variable. Moreover, a macroscopic theory allows framing the scheme within a thermodynamic context, which results in the selection of physically admissible phenomena.…”

“…To get a more realistic scheme, Drouot et al [9] developed a model where the fluid with an internal variable is a polar fluid with couple stresses. Meanwhile, they allowed the constitutive properties of the solution to be described by second-order velocity gradients and showed that, accordingly, a second gradient model deprived of the internal variable is inadequate for a satisfactory account of polymer diffusion.…”

Some remarks on generalized continuum mechanics

“…The second example concerns the flow of a suspension of macromolecules down an inclined plane (cf. Drouot and Maugin [55]). The continuum modelling consists of considering a second-velocity-gradient viscous fluid in which the deformation of macromolecules is embedded by means of a symmetric tensorial internal variable of state (the so-called “conformation”).…”