title: Effective Rheological Properties in Semi-dilute Bacterial Suspensions.
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.
authors.affiliation: Department of Mathematics, The Pennsylvania State University, University Park, PA, 16802, USA. mup20@psu.edu.
authors.forename: Mykhailo
authors.initials: M
authors.lastname: Potomkin
authors.affiliation: Department of Mathematical Sciences, Liquid Crystal Institute, Kent State University, Kent, OH, 44240, USA.
authors.forename: Shawn D
authors.initials: SD
authors.lastname: Ryan
authors.affiliation: Department of Mathematics, The Pennsylvania State University, University Park, PA, 16802, USA.
authors.forename: Leonid
authors.initials: L
authors.lastname: Berlyand
mesh_terms: D018407:Bacterial Physiological Phenomena; D003198:Computer Simulation; D005583:Fourier Analysis; D007700:Kinetics; D055641:Mathematical Concepts; D008954:Models, Biological; D012212:Rheology; D013535:Suspensions; D014783:Viscosity
chemical_list: D013535:Suspensions
keywords: Asymptotic analysis; Bacterial suspension; Effective viscosity; Kinetic models