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Published November 10, 2011 | Published + Supplemental Material
Journal Article Open

The hydrodynamics of conned dispersions

Abstract

A method is proposed for computing the low-Reynolds-number hydrodynamic forces on particles comprising a suspension confined by two parallel, no-slip walls. This is constructed via the two-dimensional analogue of Hasimoto's solution (J. Fluid Mech., vol. 5, 1959, pp. 317–328) for a periodic array of point forces in a viscous, incompressible fluid, and, like Hasimoto, the summation of interactions is accelerated by substitution and superposition of 'Ewald-like' forcing. This method is akin to the accelerated Stokesian dynamics technique (J. Fluid Mech., vol. 448, 2001, pp. 115–146) and models the suspension dynamics with log–linear computational scaling. The effectiveness of this approach is demonstrated with a calculation of the high-frequency dynamic viscosity of a colloidal dispersion as function of volume fraction and channel width. Similarly, the short-time self-diffusivity for and the sedimentation rate of spherical particles in a confined suspension are determined. The results demonstrate the influence of confining geometry on the transport of small particles, which is becoming increasingly important for micro- and biofluidics.

Additional Information

© 2011 Cambridge University Press. Received 14 September 2010; revised 10 June 2011; accepted 17 August 2011; first published online 17 October 2011. This work was supported in part by NSF grant CBET 0506701.

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Published - Swan2011p16762J_Fluid_Mech.pdf

Supplemental Material - S002211201100351Xsup001.pdf

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