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Fluids 2018, 3(1), 15; https://doi.org/10.3390/fluids3010015

Elementary Flow Field Profiles of Micro-Swimmers in Weakly Anisotropic Nematic Fluids: Stokeslet, Stresslet, Rotlet and Source Flows

1
Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
2
Jožef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia
*
Author to whom correspondence should be addressed.
Received: 13 December 2017 / Revised: 22 January 2018 / Accepted: 27 January 2018 / Published: 8 February 2018
(This article belongs to the Special Issue Liquid Crystal Rheology)
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Abstract

Analytic formulations of elementary flow field profiles in weakly anisotropic nematic fluid are determined, which can be attributed to biological or artificial micro-swimmers, including Stokeslet, stresslet, rotlet and source flows. Stokes equation for a nematic stress tensor is written with the Green function and solved in the k-space for anisotropic Leslie viscosity coefficients under the limit of leading isotropic viscosity coefficient. Analytical expressions for the Green function are obtained that are used to compute the flow of monopole or dipole swimmers at various alignments of the swimmers with respect to the homogeneous director field. Flow profile is also solved for the flow sources/sinks and source dipoles showing clear emergence of anisotropy in the magnitude of flow profile as the result of fluid anisotropic viscosity. The range of validity of the presented analytical solutions is explored, as compared to exact numerical solutions of the Stokes equation. This work is a contribution towards understanding elementary flow motifs and profiles in fluid environments that are distinctly affected by anisotropic viscosity, offering analytic insight, which could be of relevance to a range of systems from microswimmers, active matter to microfluidics. View Full-Text
Keywords: elementary flow field profiles; anisotropy; micro-swimmers; nematic; non-Newtonian fluids elementary flow field profiles; anisotropy; micro-swimmers; nematic; non-Newtonian fluids
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Kos, Ž.; Ravnik, M. Elementary Flow Field Profiles of Micro-Swimmers in Weakly Anisotropic Nematic Fluids: Stokeslet, Stresslet, Rotlet and Source Flows. Fluids 2018, 3, 15.

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