UNC-CH Physics and Astronomy Thesis Defense

Thomas Dombrowski

“From Single to Collective: Model Swimmers at Intermediate Reynolds Numbers”

Biological and artificial swimmers exist across a broad range of length scales, spanning from micron-sized bacteria and self-propelled nanoparticles to large aquatic organisms and marine robots on the order of meters. Swimming can be categorized by the Reynolds number (Re) which characterizes the relative importance of inertial over viscous forces. Microscopic swimmers at low Re, where viscosity dominates, swim differently than high-Re swimmers, where inertia dominates. Between the two extremes resides the intermediate Reynolds (Re_int) regime (Re ~ 0.1 – 1000), where both viscosity and inertia play a role. Mesoscopic organisms i.e. those that operate at intermediate Re are diverse both in size, ~ 0.5mm – 50cm, and in swimming mechanisms. Most prior studies on Re_int motility have focused on the details of specific organisms. As a result, few general models exist and there is a lack of understanding regarding the unifying physical mechanisms that swimmers at Re_int exhibit. In this defense, I use computational fluid dynamics to model and characterize mesoscale swimmers, examine their pairwise interactions, and ultimately build a framework to understand their collective behavior.

I will first show a simple model swimmer used to understand the transition from Stokes (Re = 0) to intermediate Reynolds numbers. My swimmer is a dumbbell which consists of two unequal spheres that oscillate in antiphase generating nonlinear steady streaming (SS) flows. Steady streaming is the nonzero time averaged flow around an oscillating rigid body at intermediate Re. I show computationally that the SS flows enable the swimmer to propel itself and switch direction as Re increases. I quantify the transition in the swimming direction by collapsing my data on a critical Re and show that the transition in swimming direction corresponds to the reversal of the SS flows. I find that the switch in swim direction also corresponds to a switch in power and recovery strokes. I next show that from more than 5,600 simulations of initial configurations, the swimmers either formed a total of four distinct stable pairs or diverged in swimming paths. I also investigated how the stable pairs’ fluid flow fields evolved across Re and connected them to transitions in pair swimming behavior. Finally, I found that the stable pairs can act as the framework for collective behavior. I also discovered higher order interactions which point to a complexity that pairwise interactions cannot capture. These developments show that steady streaming can be an important physical mechanism in motility at Re_int both in biological organisms and in the design of artificial swimmers. Even for a simple model, inertia can induce hydrodynamic interactions which generate novel phase behavior, steady states, and transitions.