Kinetic models of swimming bacteria in semi-dilute limit

Leonid Berlyand
Department of Mathematics, Pennsylvania State University

(November 21, 2011 2:30 PM - 3:30 PM)

Kinetic models of swimming bacteria in semi-dilute limit

Abstract

Bacteria are the most abundant organisms on Earth and they significantly influence carbon cycling and sequestration, decomposition of biomass, and transformation of contaminants in the environment. This motivates our study of the basic principles of bacterial behavior and its control. We have conducted analytical, numerical and experimental studies of suspensions of swimming bacteria. In particular, our studies reveal that active swimming of bacteria drastically alters the material properties of the suspension: the experiments with bacterial suspensions confined in thin films indicate a 7-fold reduction of the effective viscosity and a 10-fold increase of the effective diffusivity of the oxygen and other constituents of the suspending fluid. The principal mechanism behind these unique macroscopic properties is self-organization of the bacteria at the microscopic level - a multiscale phenomenon. Understanding the mechanism of self-organization in general is a fundamental issue in the study of biological and inanimate system. Our work in this area includes * Numerical modeling. Bacteria are modeled as self-propelled point force dipoles subject to two types of forces: hydrodynamic interactions with the surrounding fluid and excluded volume interactions with other bacteria modeled by a Lennard-Jones-type potential. This model, allowing for numerical simulations of a large number of particles, is implemented on the Graphical Processing Units (GPU), and is in agreement with experiments. * Analytical study of dilute suspensions. We introduced a model for swimming bacteria and obtained explicit asymptotic formula for the effective viscosity in terms of known physical parameters. This formula is compared with that derived in our PDE model for a dilute suspension of prolate spheroids driven by a stochastic torque, which models random reorientation of bacteria ("tumbling"). It is shown that the steady-state probability distributions of single particle configurations are identical for the dilute and semi-dilute models in the limiting case of particles becoming spheres. Thus, a deterministic system incorporating pairwise hydrodynamic interactions and excluded volume constraints behaves as a system with a random stochastic torque. This phenomenon of stochasticity arising from a deterministic system is referred to as self-induced noise. * Kinetic collisional model-work in progress. Most of the previous work on bacterial suspensions ignores collisions. These inelastic interactions lead to an alignment of the nearby-swimming bacteria, which has been indeed observed experimentally. To understand the onset of collective motion in the above model, we investigate the correlation of bacterial velocities and orientations as a function of the interparticle distance. We seek to capture a phase transition in the bacterial suspension - an appearance of correlations and local preferential alignment with an increase of concentration. A probabilistic model for the distribution function for bacterial positions and orientations will be derived in the presence of self-induced noise. Collaborators: PSU students S. Ryan and B. Haines, and DOE scientists I. Aronson and D. Karpeev (both Argonne Nat. Lab)