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Hydrodynamic interactions between two forced objects of arbitrary shape. II. Relative translation

Tomer Goldfriend^*

Haim Diamant^†

Thomas A. Witten^‡

Raymond & Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel

Raymond & Beverly Sackler School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel

Department of Physics and James Franck Institute, University of Chicago, Chicago, Illinois 60637, USA

^*goldfriend@tau.ac.il
^†hdiamant@tau.ac.il
^‡t-witten@uchicago.edu

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Phys. Rev. E 93, 042609 – Published 20 April, 2016

DOI: https://doi.org/10.1103/PhysRevE.93.042609

Abstract

We study the relative translation of two arbitrarily shaped objects, caused by their hydrodynamic interaction as they are forced through a viscous fluid in the limit of zero Reynolds number. It is well known that in the case of two rigid spheres in an unbounded fluid, the hydrodynamic interaction does not produce relative translation. More generally, such an effective pair-interaction vanishes in configurations with spatial inversion symmetry; for example, an enantiomorphic pair in mirror image positions has no relative translation. We show that the breaking of inversion symmetry by boundaries of the system accounts for the interactions between two spheres in confined geometries, as observed in experiments. The same general principle also provides new predictions for interactions in other object configurations near obstacles. We examine the time-dependent relative translation of two self-aligning objects, extending the numerical analysis of our preceding publication [Goldfriend, Diamant, and Witten, Phys. Fluids 27, 123303 (2015)]. The interplay between the orientational interaction and the translational one, in most cases, leads over time to repulsion between the two objects. The repulsion is qualitatively different for self-aligning objects compared to the more symmetric case of uniform prolate spheroids. The separation between the two objects increases with time $t$ as $t^{1 / 3}$ in the former case, and more strongly, as $t$ , in the latter.

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References (42)

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Hydrodynamic interactions between two forced objects of arbitrary shape. II. Relative translation

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