Estimating the viscoelastic moduli of complex fluids using the generalized Stokes-Einstein equation

Abstract

We obtain the linear viscoelastic shear moduli of complex fluids from the time-dependent mean square displacement,, of thermally-driven colloidal spheres suspended in the fluid using a generalized Stokes-Einstein (GSE) equation. Different representations of the GSE equation can be used to obtain the viscoelastic spectrum, G(s), in the Laplace frequency domain, the complex shear modulus, G(*)(ω), in the Fourier frequency domain, and the stress relaxation modulus, G(r)(t), in the time domain. Because trapezoid integration (s domain) or the Fast Fourier Transform (ω domain) of known only over a finite temporal interval can lead to errors which result in unphysical behavior of the moduli near the frequency extremes, we estimate the transforms algebraically by the transforms algebraically by describing as a local power law. If the logarithmic slope of can be accurately determined, these estimates generally perform well at the frequency extremes.