Current Research
I am currently using Homogenization and PDE techniques to numerically and analytically study the interaction of self-propelling bacteria in fluid. Consider a basic bacterium such as E. Coli (image from Food Poison Journal)
Consider a bacterium as a prolate spheroid
We then model the bacterium as a point force dipole, (verified exp. by K. Drescher, R. Goldstein et al.)
Key Feature: Fluid velocity due to a dipole diverges (1/r^2) as interparticle distance goes to zero. Thus we introduce size via the Lennard-Jones Potential. The size of bacterium is controlled by the parameter defining the radius of repulsion in the L-J Potential. This also models soft collisions -- as particle become close the L-J Potential slows them and pushes them apart. We fix the shape parameter B (Bretheron constant) as the force dipole is shrunk to a point.
"A force dipole model for semi-dilute suspensions of swimming bacteria." Poster presented at MBI, Ohio State University Nov. 2011
"A force dipole model for semi-dilute suspensions: Effective Viscosity and Correlations." Poster presented at Workshop on the Physics of Bacterial Communities, Argonne National Laboratory / Notre Dame University, Chicago, Illinois June 2012
Consider a bacterium as a prolate spheroid
We then model the bacterium as a point force dipole, (verified exp. by K. Drescher, R. Goldstein et al.)
Key Feature: Fluid velocity due to a dipole diverges (1/r^2) as interparticle distance goes to zero. Thus we introduce size via the Lennard-Jones Potential. The size of bacterium is controlled by the parameter defining the radius of repulsion in the L-J Potential. This also models soft collisions -- as particle become close the L-J Potential slows them and pushes them apart. We fix the shape parameter B (Bretheron constant) as the force dipole is shrunk to a point.
"A force dipole model for semi-dilute suspensions of swimming bacteria." Poster presented at MBI, Ohio State University Nov. 2011
"A force dipole model for semi-dilute suspensions: Effective Viscosity and Correlations." Poster presented at Workshop on the Physics of Bacterial Communities, Argonne National Laboratory / Notre Dame University, Chicago, Illinois June 2012
What's new?
Current Research
Suspensions of Bacteria in Fluid