Active Matter Invasion of a Viscous Fluid and a No-Flow Theorem
Saverio Spagnolie, Associate Professor
University Of Wisconsin-Madison
Abstract: Suspensions of active particles in fluids exhibit incredibly rich behavior, from organization on length scales much longer than the individual particle size to mixing flows and negative viscosities. We will discuss the dynamics of hydrodynamically interacting motile and non-motile stress-generating swimmers or particles as they invade a surrounding viscous fluid, modeled by coupled equations for particle motions and viscous fluid flow. Depending on the nature of their self-propulsion, colonies of swimmers can either exhibit a dramatic splay, or instead a cascade of transverse concentration instabilities as the group moves into the bulk. A stability analysis of concentrated distributions of particles matches the results of our full numerical simulations, and provides some exciting connections to classical hydrodynamic instabilities in seemingly unrelated inertial flows. Along the way we will prove a very surprising “no-flow theorem”: particle distributions initially isotropic in orientation lose isotropy immediately but in such a way that results in no fluid flow *anywhere* and *at any time*.
Bio: Saverio Spagnolie is an associate professor in mathematics at the University of Wisconsin-Madison, with a courtesy appointment in chemical and biological engineering. Using classical methods of applied mathematics and the development of novel numerical methods, he studies problems in biological propulsion, soft matter, sedimentation, and complex fluids. Before arriving in Madison, Saverio received a Ph.D. in mathematics at the Courant Institute of Mathematical Sciences, then held postdoctoral positions in the Mechanical/Aerospace Engineering department at UCSD and in the School of Engineering at Brown University.