Rheologica Acta

, Volume 39, Issue 4, pp 371–378

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

  • Thomas G. Mason

DOI: 10.1007/s003970000094

Cite this article as:
Mason, T. Rheol. Acta (2000) 39: 371. doi:10.1007/s003970000094


We obtain the linear viscoelastic shear moduli of complex fluids from the time-dependent mean square displacement, <Δr2(t)>, 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, Gr(t), in the time domain. Because trapezoid integration (s domain) or the Fast Fourier Transform (ω domain) of <Δr2(t)> 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 describing <Δr2(t)> as a local power law. If the logarithmic slope of <Δr2(t)> can be accurately determined, these estimates generally perform well at the frequency extremes.

Key words Stokes–Einstein equationBrownian motionComplex fluidsLinear viscoelastic moduliParticle diffusionEstimation methods

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Thomas G. Mason
    • 1
  1. 1.Corporate Strategic Research ExxonMobil Research and Engineering Co., Route 22 East Annandale, NJ 08801, USA e-mail: tgmason@erenj.comUS