Shear Thinning of a Critical Viscoelastic Fluid

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.

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