Capillary waves in a drop of active matter

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Suspensions of self-propelled particles, such as swimming microorganisms, are able to convert chemical energy into the mechanical energy of motion, giving rise to dynamical collective states that cannot be described by traditional statistical mechanics. Understanding such far-from-equilibrium active systems is an important challenge not only for physical and mathematical sciences, but also for biology and ecology. This project will explore the interplay of capillary and active phenomena. It will focus on the wave motion of interfaces between an active suspension and the surrounding fluid medium. Despite its importance, this problem has received little attention. This problem will be approached in a semi-numerical and semi-analytical way. Numerical simulations will be performed using several common models of active matter. Their results will be compared with analytical models obtained under a set of simplifying assumptions. Eventually, comparisons will be made with the existing experimental data.Keywords: Fluid dynamics, mathematical biology, numerical simulations