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Two-dimensional motion of Brownian swimmers in linear flows

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Abstract

The motion of viruses and bacteria and even synthetic microswimmers can be affected by thermal fluctuations and by external flows. In this work, we study the effect of linear external flows and thermal fluctuations on the diffusion of those swimmers modeled as spherical active (self-propelled) particles moving in two dimensions. General formulae for their mean-square displacement under a general linear flow are presented. We also provide, at short and long times, explicit expressions for the mean-square displacement of a swimmer immersed in three canonical flows, namely, solid-body rotation, shear and extensional flows. These expressions can now be used to estimate the effect of external flows on the displacement of Brownian microswimmers. Finally, our theoretical results are validated by using Brownian dynamics simulations.

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Acknowledgments

M. Sandoval thanks Consejo Nacional de Ciencia y Tecnologia (CONACyT) and Programa de Mejoramiento de Profesorado (PROMEP) for partially funding this work. M.S. also thanks the support received from T. de la Selva, R. M. Velasco and J. I. Jimenez. A. Jimenez thanks PROMEP for partial funding.

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Authors and Affiliations

  1. Department of Physics, Universidad Autonoma Metropolitana-Iztapalapa, Mexico, Distrito Federal, 09340, Mexico

    Mario Sandoval & Alonso Jimenez

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  1. Mario Sandoval
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  2. Alonso Jimenez
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Correspondence to Mario Sandoval.

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Sandoval, M., Jimenez, A. Two-dimensional motion of Brownian swimmers in linear flows. J Biol Phys 42, 199–212 (2016). https://doi.org/10.1007/s10867-015-9401-4

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