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

Published online by Cambridge University Press:  17 September 2015

Barath Ezhilan ,
Roberto Alonso-Matilla  and
David Saintillan
Barath Ezhilan
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA
Roberto Alonso-Matilla
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA
David Saintillan*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Biological Fluid Dynamics: Micro-organism dynamics Complex Fluids: Suspensions
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 781 , 25 October 2015 , R4
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Copyright
© 2015 Cambridge University Press 

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Footnotes

‡

These authors contributed equally to this work.

References

Berg, H. C. 1993 Random Walks in Biology. Princeton University Press.Google Scholar
Berke, A. P., Turner, L., Berg, H. C. & Lauga, E. 2008 Hydrodynamic attraction of swimming microorganisms by surfaces. Phys. Rev. Lett. 101, 038102.CrossRefGoogle ScholarPubMed
Elgeti, J. & Gompper, G. 2013 Wall accumulation of self-propelled spheres. Europhys. Lett. 101, 48003.CrossRefGoogle Scholar
Elgeti, J. & Gompper, G. 2015 Run-and-tumble dynamics of self-propelled particles in confinement. Europhys. Lett. 109, 58003.CrossRefGoogle Scholar
Ezhilan, B. & Saintillan, D. 2015 Transport of a dilute active suspension in pressure-driven channel flow. J. Fluid Mech. 777, 482–522.CrossRefGoogle Scholar
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, 6284–6293.CrossRefGoogle Scholar
Fily, Y., Baskaran, A. & Hagan, M. F. 2014 Dynamics of self-propelled particles under strong confinement. Soft Matt. 10, 5609–5617.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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.Google Scholar
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.CrossRefGoogle ScholarPubMed
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, 1187–1192.CrossRefGoogle ScholarPubMed
Lee, C. F. 2013 Active particles under confinement: aggregation at the wall and gradient formation inside a channel. New J. Phys. 15, 055007.CrossRefGoogle Scholar
Li, G. & Ardekani, A. M. 2014 Hydrodynamic interaction of microswimmers near a wall. Phys. Rev. E 90, 013010.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
Mallory, S. A., Sarić, A., Valeriani, C. & Cacciuto, A 2014 Anomalous thermomechanical properties of a self-propelled colloidal fluid. Phys. Rev. E 89, 052303.CrossRefGoogle ScholarPubMed
Molaie, M., Barry, M., Stocker, R. & Sheng, J. 2014 Failed escape: solid surfaces prevent tumbling of Escherichia coli . Phys. Rev. Lett. 113, 068103.Google Scholar
Ray, D., Reichhardt, C. & Olson Reichhardt, C. J. 2014 Casimir effect in active matter systems. Phys. Rev. E 90, 013019.CrossRefGoogle ScholarPubMed
Saintillan, D. & Shelley, M. J. 2013 Active suspensions and their nonlinear models. C. R. Phys. 14, 497–517.CrossRefGoogle Scholar
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, 673–678.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
Takatori, S. C. & Brady, J. F. 2015 Towards a thermodynamics of active matter. Phys. Rev. E 91, 032117.CrossRefGoogle ScholarPubMed
Takatori, S. C., Yan, W. & Brady, J. F. 2014 Swim pressure: stress generation in active matter. Phys. Rev. Lett. 113, 028103.CrossRefGoogle ScholarPubMed
Volpe, G., Buttinoni, I., Vogt, D., Kümmerer, H.-J. & Bechinger, C. 2011 Microswimmers in patterned environments. Soft Matt. 7, 8810–8815.CrossRefGoogle Scholar
Winkler, R. G., Wysocki, A. & Gompper, G. 2015 Virial pressure in systems of active Brownian particles. Soft Matt. 11, 6680–6691.CrossRefGoogle ScholarPubMed
Wysocki, A., Elgeti, J. & Gompper, G. 2015 Giant adsorption of microswimmers: duality of shape asymmetry and wall curvature. Phys. Rev. E 91, 050302.CrossRefGoogle ScholarPubMed
Yang, X., Manning, M. L. & Marchetti, M. C. 2014 Aggregation and segregation of confined active particles. Soft Matt. 10, 6477–6484.CrossRefGoogle ScholarPubMed