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On the distribution and swim pressure of run-and-tumble particles in confinement

  • Barath Ezhilan (a1), Roberto Alonso-Matilla (a1) and David Saintillan (a1)

Abstract

The spatial and orientational distribution in a dilute active suspension of non-Brownian run-and-tumble spherical swimmers confined between two planar hard walls is calculated theoretically. Using a kinetic model based on coupled bulk/surface probability density functions, we demonstrate the existence of a concentration wall boundary layer with thickness scaling with the run length, the absence of polarization throughout the bulk of the channel, and the presence of sharp discontinuities in the bulk orientation distribution in the neighbourhood of orientations parallel to the wall in the near-wall region. Our model is also applied to calculate the swim pressure in the system, which approaches the previously proposed ideal-gas behaviour in wide channels but is found to decrease in narrow channels as a result of confinement. Monte Carlo simulations are also performed for validation and show excellent quantitative agreement with our theoretical predictions.

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Email address for correspondence: dstn@ucsd.edu

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These authors contributed equally to this work.

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References

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Berg, H. C. 1993 Random Walks in Biology. Princeton University Press.
Berke, A. P., Turner, L., Berg, H. C. & Lauga, E. 2008 Hydrodynamic attraction of swimming microorganisms by surfaces. Phys. Rev. Lett. 101, 038102.
Elgeti, J. & Gompper, G. 2013 Wall accumulation of self-propelled spheres. Europhys. Lett. 101, 48003.
Elgeti, J. & Gompper, G. 2015 Run-and-tumble dynamics of self-propelled particles in confinement. Europhys. Lett. 109, 58003.
Ezhilan, B. & Saintillan, D. 2015 Transport of a dilute active suspension in pressure-driven channel flow. J. Fluid Mech. 777, 482522.
Figueroa-Morales, N., Miño, G., Rivera, A., Caballero, R., Clément, E., Altshuler, E. & Lindner, A. 2015 Living on the edge: transfer and traffic of E. coli in a confined flow. Soft Matt. 11, 62846293.
Fily, Y., Baskaran, A. & Hagan, M. F. 2014 Dynamics of self-propelled particles under strong confinement. Soft Matt. 10, 56095617.
Gachelin, J., Miño, G., Berthet, H., Lindner, A., Rousselet, A. & Clément, E. 2013 Non-Newtonian viscosity of Escherichia coli suspensions. Phys. Rev. Lett. 110, 268103.
Ginot, F., Theurfauff, I., Levis, D., Ybert, C., Bocquet, L., Berthier, L. & Cottin-Bizonne, C. 2015 Nonequilibrium equation of state in suspensions of active colloids. Phys. Rev. X 5, 011004.
Hernández-Ortiz, J. P., Stoltz, C. G. & Graham, M. D. 2005 Transport and collective dynamics in suspensions of confined swimming particles. Phys. Rev. Lett. 95, 204501.
Kantsler, V., Dunkel, J., Polin, M. & Goldstein, R. E. 2013 Ciliary contact interactions dominate surface scattering of swimming eukaryotes. Proc. Natl Acad. Sci. USA 110, 11871192.
Lee, C. F. 2013 Active particles under confinement: aggregation at the wall and gradient formation inside a channel. New J. Phys. 15, 055007.
Li, G. & Ardekani, A. M. 2014 Hydrodynamic interaction of microswimmers near a wall. Phys. Rev. E 90, 013010.
Li, G., Bensson, J., Nisimova, L., Munger, D., Mahautmr, P., Tang, J. X., Maxey, M. R. & Brun, Y. V. 2011 Accumulation of swimming bacteria near a solid surface. Phys. Rev. E 84, 041932.
Mallory, S. A., Sarić, A., Valeriani, C. & Cacciuto, A 2014 Anomalous thermomechanical properties of a self-propelled colloidal fluid. Phys. Rev. E 89, 052303.
Molaie, M., Barry, M., Stocker, R. & Sheng, J. 2014 Failed escape: solid surfaces prevent tumbling of Escherichia coli . Phys. Rev. Lett. 113, 068103.
Ray, D., Reichhardt, C. & Olson Reichhardt, C. J. 2014 Casimir effect in active matter systems. Phys. Rev. E 90, 013019.
Saintillan, D. & Shelley, M. J. 2013 Active suspensions and their nonlinear models. C. R. Phys. 14, 497517.
Solon, A. P., Fily, Y., Baskaran, A., Cates, M. E., Kafri, Y., Kardar, M. & Tailleur, J. 2015a Pressure is not a state function for generic active fluids. Nat. Phys. 11, 673678.
Solon, A. P., Stenhammar, J., Wittkowski, R., Kardar, M., Kafri, Y., Cates, M. E. & Tailleur, J. 2015b Pressure and phase equilibria in interacting active Brownian spheres. Phys. Rev. Lett. 114, 198301.
Takatori, S. C. & Brady, J. F. 2015 Towards a thermodynamics of active matter. Phys. Rev. E 91, 032117.
Takatori, S. C., Yan, W. & Brady, J. F. 2014 Swim pressure: stress generation in active matter. Phys. Rev. Lett. 113, 028103.
Volpe, G., Buttinoni, I., Vogt, D., Kümmerer, H.-J. & Bechinger, C. 2011 Microswimmers in patterned environments. Soft Matt. 7, 88108815.
Winkler, R. G., Wysocki, A. & Gompper, G. 2015 Virial pressure in systems of active Brownian particles. Soft Matt. 11, 66806691.
Wysocki, A., Elgeti, J. & Gompper, G. 2015 Giant adsorption of microswimmers: duality of shape asymmetry and wall curvature. Phys. Rev. E 91, 050302.
Yang, X., Manning, M. L. & Marchetti, M. C. 2014 Aggregation and segregation of confined active particles. Soft Matt. 10, 64776484.
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On the distribution and swim pressure of run-and-tumble particles in confinement

  • Barath Ezhilan (a1), Roberto Alonso-Matilla (a1) and David Saintillan (a1)

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