Vibration-Induced Propulsion of a Rigid Body in a Viscous Liquid

Abstract: The study of propulsion in viscous liquids for rigid bodies driven by a time-periodic mechanism M (vibration-induced motion), appears in many engineering contexts, from underwater robotics to the delivery of drugs inside the human body. As such, an important question regarding the mechanics of such devices is the following: under what conditions does M cause the body to propel (as opposed to, say, perpetually oscillate back-and-forth)? Mathematically, this system can be modeled as a coupled fluid-structure interaction problem as follows: consider a rigid body B, contained in a Navier-Stokes liquid occupying the whole space outside of B, which moves (without constraint) under the action of a time-periodic force f. In this talk, we provide quantitative sufficient conditions that ensure f propels Β; namely, the center of mass of Β can cover any given distance in a finite time. This is part of a joint work with Giovanni P. Galdi along with Joris Edelmann and Thomas Richter (University of Magdeburg, Germany).