## Beyond Stokes Flow, Complex Biofluids – Motility in Highly Heterogeneous, Viscoelastic Media

- March 2, 2015
- 1 p.m.
- LeConte 312

## Abstract

Stokes flow or zero Reynolds number flow is a fluid regime where inertial forces are negligible compared to viscous forces. Typically these are systems where the fluid velocities are very slow, the viscosities are very large, or the length-scales are very small. Stokes flow has application in studying motility of microorganisms, microfluidic flows and many other systems.

The method of regularized Stokeslets is a Lagrangian method for computing Stokes flow driven by distributed forces. The method is based on the superposition of exact solutions of the Stokes equations when concentrated forces are given by smooth localized approximations of a delta distribution. We have developed and implemented a regularized image system for Stokes flow outside a solid sphere. In order to satisfy zero-flow boundary conditions at the surface of a sphere, we extend the method of images derived for a standard (singular) Stokeslet to produce an exact cancellation of the regularized flow at the boundary. The method of regularized Stokeslets has the advantage resulting in bounded velocity fields even for isolated forces or for distributions of forces along curves. This advantage facilitates the simulation of ciliary beating, flagellar motion, and particle suspensions.

Filamentous networks and elastic polymers immersed in a viscous fluid are central to many processes in biology. For some microorganisms, such as sperm during fertilization, those complex structures create barriers that need to be penetrated. We present simple model of a discrete viscoelastic network coupled to a Stokesian fluid. The network is comprised of a set of cross-linked nodes with links modeled by simple viscoelastic elements. Computational rheometry tests are used to characterize the viscoelastic structures. We study the effect of highly heterogeneous viscoelastic media on swimming patterns using simple model of a flagellar swimmer. We study how perturbed scaffolds affect the swimmer. We find that regions of high force density concentrations can significantly change a swimming pattern of a microorganism.