Shear Thinning of a Critical Viscoelastic Fluid

TL;DR

This paper investigates the shear thinning behavior of a critical viscoelastic fluid by analyzing its frequency and shear-dependent viscosity near a critical correlation length, using a self-consistent theoretical approach.

Contribution

It introduces a theoretical framework for the shear thinning of critical viscoelastic fluids based on a one-loop self-consistent calculation of a generalized viscosity function.

Findings

Derived a form for the critical viscosity as a function of frequency and shear rate.

Calculated the scaling function G(z1,z2) within a self-consistent theory.

Provided insights into the decay rate of critical fluctuations under shear.

Abstract

The frequency and shear dependent critical viscosity at a correlation length $\xi=\kappa^{-1}$, has the form $\eta=\eta_{0}\kappa^{-x_{\eta}}G(z_{1},z_{2})$, where $z_{1}$ and $z_{2}$ are the independent dimensionless numbers in the problem defined as $z_{1}=\frac{-i\omega}{2\Gamma_{0}\kappa^{3}}$ and $z_{2}=\frac{-i\omega}{2\Gamma_{0}\kappa_{c}^{3}}$. The decay rate of critical fluctuations of correlation length $\kappa^{-1}$ is $\Gamma_{0}\kappa^{3}$ and $k_{c}$ is the effective wave number for which $\Gamma_{0}k_{c}^{3}=S$, the shear rate. The function $G(z_{1},z_{2})$ is calculated in a one loop self-consistent theory.