Squires, Todd M. and Brady, John F. (2005) A simple paradigm for active and nonlinear microrheology. Physics of Fluids, 17 (7). Art. no. 073101. ISSN 1070-6631. http://resolver.caltech.edu/CaltechAUTHORS:SQUpof05
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In microrheology, elastic and viscous moduli are obtained from measurements of the fluctuating thermal motion of embedded colloidal probes. In such experiments, the probe motion is passive and reflects the near-equilibrium (linear response) properties of the surrounding medium. By actively pulling the probe through the material, further information about material properties can be obtained, analogous to large-amplitude measurements in (macro-) rheology. We consider a simple model of such systems: a colloidal probe pulled through a suspension of neutrally buoyant bath colloids. We choose a system with hard-sphere interactions but neglect hydrodynamic interactions, which is simple enough to permit analytic solutions, but nontrivial enough to raise issues important for the interpretation of experiments in active and nonlinear microrheology. We calculate the microstructural deformation for arbitrary probe size and pulling rate (expressed as a dimensionless Péclet number Pe). From this, we determine the average retarding effect on the probe due to the microstructure, as well as fluctuations about this average. The high-Pe limit is singular, giving a finite Brownian contribution even in the limit of negligible diffusion. Significantly, different results are obtained for probes driven at constant velocity and constant force. Furthermore, we demonstrate that a probe pulled with an optical tweezer (roughly a harmonic well) can behave as fixed-force, fixed-velocity, or as a mixture of those modes, depending on the strength of the trap and on the pulling speed. More generally, we discuss how these results relate to previous work on the rheology of colloidal suspensions. Not surprisingly, the present theory (which ignores hydrodynamic interactions) gives shear thinning but no shear thickening; we expect that the incorporation of hydrodynamics would result in shear thickening as well. The effective micro- and macro-viscosities, when appropriately scaled, are in semi-quantitative agreement. This seems remarkable, given the rather significant difference in the two methods of measurement. However, for more complicated or unknown materials, where such scaling relations may not be known in advance, the comparison between micro- and macro may not be so favorable, which raises important questions about the relation between micro- and macrorheology. Finally, by analogy with previous work on macrorheology, we propose methods to scale up the present (dilute) theory to account for more concentrated suspensions, and suggest new active microrheological experiments to probe different aspects of suspension behavior.
|Additional Information:||©2005 American Institute of Physics (Received 12 November 2004; accepted 23 May 2005; published online 1 July 2005) T.M.S. wishes to acknowledge the support of an NSF Applied Mathematics Postdoctoral Fellowship and a Lee A. Dubridge Prize Postdoctoral Fellowship. Conversations with Eric Weeks, Eric Furst, Ileana Carpen and Aditya Khair are gratefully acknowledged.|
|Subject Keywords:||rheology; elastic moduli; fluctuations; colloids; suspensions; deformation; Brownian motion; viscosity; non-Newtonian flow|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Archive Administrator|
|Deposited On:||13 Jan 2006|
|Last Modified:||26 Dec 2012 08:44|
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