Computational Models of Microscopic Fluid Flows with Biological Applications

Ricardo Cortez

Department of Mathematics, Tulane University

The term Biofluid dynamics refers to the motion of fluids generated in biological and biomedical phenomena. These include blood flow in capillaries, the flows surrounding moving cells, bacteria, spermatozoa, and more. Many of these phenomena involve a flexible, elastic body exerting forces to the fluid in order to propel itself or generate flows that are advantageous in some way. These phenomena are of interest to scientists who study how the fluid environment and the forces generated on the elastic bodies combine to produce organism behaviors observed in the laboratory. I will present the main ideas behind a computational model called ``the method of regularized Stokeslets" that is widely used to study microscopic flows generated by flagella (like those attached to bacteria and sperm cells). The presentation will be based on vector calculus and introductory partial differential equations. I will show simulations of flagellar motions that aim to understand the effect of asymmetry in the flagellar beat patterns as well as interactions with a nearby surface, which is important in fertilization.