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Kinetic Models for Biologically Active Suspensions

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Natural Locomotion in Fluids and on Surfaces

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 155))

Abstract

Biologically active suspensions, such as suspensions of swimming microorganisms, exhibit fascinating dynamics including large-scale collective motions and pattern formation, complex chaotic flows with good mixing properties, enhanced passsive tracer diffusion, among others. There has been much recent interest in modeling and understanding these effects, which often result from long-ranged fluid-mediated interactions between swimming particles. This paper provides a general introduction to a number of recent investigations on these systems based on a continuum mean-field description of hydrodynamic interactions. A basic kinetic model is presented in detail, and an overview of its applications to the analysis of coherent motions and pattern formation, chemotactic interactions, and the effective rheology in active suspensions, is given.

AMS(MOS) subject classifications. 35Q35, 35Q92, 76D07, 76T20, 76Z99

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Notes

  1. 1.

    Note that a very similar model was also proposed independently and around the same time by Subramanian and Koch [47].

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Authors and Affiliations

  1. Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    David Saintillan

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  1. David Saintillan
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Correspondence to David Saintillan .

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Editors and Affiliations

  1. Courant Institute of Math Sciences, New York University, Mercer Street 251, New York City, 10012, New York, USA

    Stephen Childress

  2. Massachusetts Institute of Technology, Massachusetts Avenue 77, Cambridge, 02139, Massachusetts, USA

    Anette Hosoi

  3. , Department of Mechanical Engineering, The University of Michigan, Auto Lab 2027, Ann Arbor, 48109, Michigan, USA

    William W. Schultz

  4. , Mechanical and Aerospace Engineering, Cornell University, Ithaca, 14850, New York, USA

    Jane Wang

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Saintillan, D. (2012). Kinetic Models for Biologically Active Suspensions. In: Childress, S., Hosoi, A., Schultz, W., Wang, J. (eds) Natural Locomotion in Fluids and on Surfaces. The IMA Volumes in Mathematics and its Applications, vol 155. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3997-4_4

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