Effective rheological properties in semi-dilute bacterial suspensions

Mykhailo Potomkin, Shawn D. Ryan, Leonid Berlyand

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Interactions between swimming bacteria have led to remarkable experimentally observable macroscopic properties such as the reduction in the effective viscosity, enhanced mixing, and diffusion. In this work, we study an individual-based model for a suspension of interacting point dipoles representing bacteria in order to gain greater insight into the physical mechanisms responsible for the drastic reduction in the effective viscosity. In particular, asymptotic analysis is carried out on the corresponding kinetic equation governing the distribution of bacteria orientations. This allows one to derive an explicit asymptotic formula for the effective viscosity of the bacterial suspension in the limit of bacterium non-sphericity. The results show good qualitative agreement with numerical simulations and previous experimental observations. Finally,we justify our approach by proving existence, uniqueness, and regularity properties for this kinetic PDE model.

Original languageEnglish (US)
Pages (from-to)580-615
Number of pages36
JournalBulletin of Mathematical Biology
Volume78
Issue number3
DOIs
StatePublished - Mar 29 2016

All Science Journal Classification (ASJC) codes

  • Neuroscience(all)
  • Immunology
  • Mathematics(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Environmental Science(all)
  • Pharmacology
  • Agricultural and Biological Sciences(all)
  • Computational Theory and Mathematics

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