A Caltech Library Service

Single particle motion in colloidal dispersions: a simple model for active and nonlinear microrheology

Khair, Aditya S. and Brady, John F. (2006) Single particle motion in colloidal dispersions: a simple model for active and nonlinear microrheology. Journal of Fluid Mechanics, 557 . pp. 73-117. ISSN 0022-1120. doi:10.1017/S0022112006009608.

See Usage Policy.


Use this Persistent URL to link to this item:


The motion of a single Brownian probe particle subjected to a constant external body force and immersed in a dispersion of colloidal particles is studied with a view to providing a simple model for particle tracking microrheology experiments in the active and nonlinear regime. The non-equilibrium configuration of particles induced by the motion of the probe is calculated to first order in the volume fraction of colloidal particles over the entire range of Pe, accounting for hydrodynamic and excluded volume interactions between the probe and dispersion particles. Here, Pe is the dimensionless external force on the probe, or Péclet number, and is a characteristic measure of the degree to which the equilibrium microstructure of the dispersion is distorted. For small Pe, the microstructure (in a reference frame moving with the probe) is primarily dictated by Brownian diffusion and is approximately fore–aft symmetric about the direction of the external force. In the large Pe limit, advection is dominant except in a thin boundary layer in the compressive region of the flow where it is balanced by Brownian diffusion, leading to a highly non-equilibrium microstructure. The computed microstructure is employed to calculate the average translational velocity of the probe, from which the ‘microviscosity’ of the dispersion may be inferred via application of Stokes drag law. For small departures from equilibrium (Pe), the microviscosity ‘force-thins’ proportional to $\hbox{\it Pe}^2$ from its Newtonian low-force plateau. For particles with long-range excluded volume interactions, force-thinning persists until a terminal Newtonian plateau is reached in the limit $\hbox{\it Pe}\,{\rightarrow}\,\infty$. In the case of particles with very short-range excluded volume interactions, the force-thinning ceases at $\hbox{\it Pe}\,{\sim}\, O(1)$, at which point the microviscosity attains a minimum value. Beyond $\hbox{\it Pe}\,{\sim}\, O(1)$, the microstructural boundary layer coincides with the lubrication range of hydrodynamic interactions causing the microviscosity to enter a continuous ‘force-thickening’ regime. The qualitative picture of the microviscosity variation with Pe is in good agreement with theoretical and computational investigations on the ‘macroviscosity’ of sheared colloidal dispersions, and, after appropriate scaling, we are able to make a direct quantitative comparison. This suggests that active tracking microrheology is a valuable tool with which to explore the rich nonlinear rheology of complex fluids.

Item Type:Article
Related URLs:
URLURL TypeDescription
Brady, John F.0000-0001-5817-9128
Additional Information:"Reprinted with the permission of Cambridge University Press." (Received December 12 2004). (Revised December 9 2005) Published online by Cambridge University Press 12 June 2006 The authors wish to thank Dr Johan Bergenholtz for assistance in the finite-difference solution of the Smoluchowski equation and for supplying the macroviscosity data used in figure 18. We also thank Dr Helen Wilson for fruitful discussions regarding Appendix D. The work was supported in part by grant CTS - 050070 from the National Science Foundation.
Record Number:CaltechAUTHORS:KHAjfm06b
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4125
Deposited By: Archive Administrator
Deposited On:28 Jul 2006
Last Modified:08 Nov 2021 20:15

Repository Staff Only: item control page