Jan Moláček

Exotic states of bouncing and walking droplets

We present the results of an integrated experimental and theoretical investigation of droplets bouncing on a vibrating fluid bath. A comprehensive series of experiments provides the most detailed characterisation to date of the systems dependence on fluid properties, droplet size, and vibrational forcing. A number of new bouncing and walking states are reported, including complex periodic and aperiodic motions. Particular attention is given to the first characterisation of the different gaits arising within the walking regime. In addition to complex periodic walkers and limping droplets, we highlight a previously unreported mixed state, in which the droplet switches periodically between two distinct walking modes. Our experiments are complemented by a theoretical study based on our previous developments [J. Molacek and J. W. M. Bush, J. Fluid Mech.727, 582–611 (Year: 2013);10.1017/jfm.2013.279J. Molacek and J. W. M. Bush, J. Fluid Mech.727, 612–647 (Year: 2013)]10.1017/jfm.2013.280, which provide a basis for rationalising all observed bouncing and walking states.

A quasi-static model of drop impact

We develop a conceptually simple theoretical model of non-wetting drop impact on a rigid surface at small Weber numbers. Flat and curved impactor surfaces are considered, and the influence of surface curvature is elucidated. Particular attention is given to characterizing the contact time of the impact and the coefficient of restitution, the goal being to provide a reasonable estimate for these two parameters with the simplest model possible. Approximating the shape of the drop during impact as quasi-static allows us to derive the governing differential equation for the droplet motion from a Lagrangian. Predictions of the resulting model are shown to compare favorably with previously reported experimental results.

The fine art of surfacing: Its efficacy in broadcast spawning

Many organisms reproduce by releasing gametes into the surrounding fluid. For some such broadcast spawners, gametes are positively or negatively buoyant, and, as a result, fertilization occurs on a two-dimensional surface rather than in the bulk of the air or water. We here rationalize this behaviour by considering the encounter rates of gametes on the surface and in the fluid bulk. The advantage of surfacing is quantified by considering an infinitely wide body of water of constant depth. Differential loss rates at the surface and in the bulk are considered and their influence on the robustness of surface search assessed. For small and moderate differential loss rates, the advantage of surfacing is very robust and significant; only for large loss rate differences can the advantage of surfacing be nullified.