Hostname: page-component-745bb68f8f-f46jp Total loading time: 0 Render date: 2025-01-11T23:56:41.333Z Has data issue: false hasContentIssue false
  • English
  • Français

The force on a boundary in active matter

Published online by Cambridge University Press:  13 November 2015

Wen Yan Open the ORCID record for Wen Yan [Opens in a new window]  and
John F. Brady
Wen Yan
Affiliation:
Department of Mechanical and Civil Engineering, California Institute of Technology, Pasadena, CA 91125, USA
John F. Brady*
Affiliation:
Division of Chemistry and Chemical Engineering and Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
*
†Email address for correspondence: jfbrady@caltech.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We present a general theory for determining the force (and torque) exerted on a boundary (or body) in active matter. The theory extends the description of passive Brownian colloids to self-propelled active particles and applies for all ratios of the thermal energy $k_{B}T$ to the swimmer’s activity $k_{s}T_{s}={\it\zeta}U_{0}^{2}{\it\tau}_{R}/6$, where ${\it\zeta}$ is the Stokes drag coefficient, $U_{0}$ is the swim speed and ${\it\tau}_{R}$ is the reorientation time of the active particles. The theory, which is valid on all length and time scales, has a natural microscopic length scale over which concentration and orientation distributions are confined near boundaries, but the microscopic length does not appear in the force. The swim pressure emerges naturally and dominates the behaviour when the boundary size is large compared to the swimmer’s run length $\ell =U_{0}{\it\tau}_{R}$. The theory is used to predict the motion of bodies of all sizes immersed in active matter.

JFM classification

Complex Fluids: Colloids Biological Fluid Dynamics: Micro-organism dynamics Low-Reynolds-number flows: Stokesian dynamics
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 785 , 25 December 2015 , R1
Check for updates
Copyright
© 2015 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anderson, J. L. 1989 Colloid transport by interfacial forces. Annu. Rev. Fluid Mech. 21 (1), 61–99.CrossRefGoogle Scholar
Asakura, S. & Ooswa, F. 1954 On the interaction of two bodies immersed in a solution of macromolecules. J. Chem. Phys. 22, 1255–1256.CrossRefGoogle Scholar
Bialké, J., Löwen, H. & Speck, T. 2013 Microscopic theory for the phase separation of self-propelled repulsive disks. Europhys. Lett. 103 (3), 30008.CrossRefGoogle Scholar
Brady, J. F. 1993 Brownian-motion, hydrodynamics, and the osmotic-pressure. J. Chem. Phys. 98 (4), 3335–3341.CrossRefGoogle Scholar
Brady, J. F. 2011 Particle motion driven by solute gradients with application to autonomous motion: continuum and colloidal perspectives. J. Fluid Mech. 667, 216–259.CrossRefGoogle Scholar
Brady, J. F. & Morris, J. F. 1997 Microstructure of strongly sheared suspensions and its impact on rheology and diffusion. J. Fluid Mech. 348, 103–139.CrossRefGoogle Scholar
Buttinoni, I., Bialké, J., Kümmel, F., Löwen, H., Bechinger, C. & Speck, T. 2013 Dynamical clustering and phase separation in suspensions of self-propelled colloidal particles. Phys. Rev. Lett. 110, 238301.CrossRefGoogle ScholarPubMed
Cates, M. E., Marenduzzo, D., Pagonabarraga, I. & Tailleur, J. 2010 Arrested phase separation in reproducing bacteria creates a generic route to pattern formation. Proc. Natl Acad. Sci. USA 107 (26), 11715–11720.CrossRefGoogle ScholarPubMed
Ezhilan, B., Alonso-Matilla, R. & Saintillan, D. 2015 On the distribution and swim pressure of run-and-tumble particles in confinement. J. Fluid Mech. 781, R4.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
Fily, Y. & Marchetti, M. C. 2012 Athermal phase separation of self-propelled particles with no alignment. Phys. Rev. Lett. 108 (23), 235702.CrossRefGoogle ScholarPubMed
Foss, D. R. & Brady, J. F. 2000 Brownian dynamics simulation of hard-sphere colloidal dispersions. J. Rheol. 44, 629–651.CrossRefGoogle Scholar
Lauga, E. & Powers, T. R. 2009 The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 72, 096601.CrossRefGoogle Scholar
Palacci, J., Sacanna, S., Steinberg, A. P., Pine, D. J. & Chaikin, P. M. 2013 Living crystals of light-activated colloidal surfers. Science 339 (6122), 936–940.CrossRefGoogle ScholarPubMed
Ray, D., Reichhardt, C. & Reichhardt, C. J. O. 2014 Casimir effect in active matter systems. Phys. Rev. E 90 (1), 013019.CrossRefGoogle ScholarPubMed
Saintillan, D. & Shelley, M. J. 2015 Theory of active suspensions. In Complex Fluids in Biological Systems (ed. Spagnolie, S. E.), chap. 9, pp. 319–355. Springer.CrossRefGoogle Scholar
Shklyaev, S., Brady, J. F. & Córdova-Figueroa, U. M. 2014 Non-spherical osmotic motor: chemical sailing. J. Fluid Mech. 748, 488–520.CrossRefGoogle Scholar
Smallenburg, F. & Löwen, H. 2015 Swim pressure on walls with curves and corners. Phys. Rev. E 92 (3), 032304.Google ScholarPubMed
Solon, A. P., Fily, Y., Baskaran, A., Cates, M. E., Kafri, Y., Kardar, M. & Tailleur, J. 2015 Pressure is not a state function for generic active fluids. Nature Phys. 11, 673–678.CrossRefGoogle Scholar
Squires, T. M. & Brady, J. F. 2005 A simple paradigm for active and nonlinear microrheology. Phys. Fluids 17 (7), 73101.CrossRefGoogle Scholar
Stenhammar, J., Marenduzzo, D., Allen, R. J. & Cates, M. E. 2014 Phase behaviour of active Brownian particles: the role of dimensionality. Soft Matt. 10, 1489–1499.CrossRefGoogle ScholarPubMed
Stenhammar, J., Tiribocchi, A., Allen, R. J., Marenduzzo, D. & Cates, M. E. 2013 Continuum theory of phase separation kinetics for active Brownian particles. Phys. Rev. Lett. 111 (14), 145702.CrossRefGoogle ScholarPubMed
Takatori, S. C. & Brady, J. F. 2014 Swim stress, motion, and deformation of active matter: effect of an external field. Soft Matt. 10 (47), 9433–9445.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 (2), 028103.CrossRefGoogle ScholarPubMed
Toner, J., Tu, Y. & Ramaswamy, S. 2005 Hydrodynamics and phases of flocks. Ann. Phys. 318 (1), 170–244.CrossRefGoogle Scholar
Wysocki, A., Winkler, R. G. & Gompper, G. 2014 Cooperative motion of active Brownian spheres in three-dimensional dense suspensions. Europhys. Lett. 105 (4), 48004.CrossRefGoogle Scholar
Yan, W. & Brady, J. F. 2015 The swim force as a body force. Soft Matt. 11 (31), 6235–6244.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