Promenading pairs of walking droplets: Dynamics and stability

Abstract

We present the results of an integrated experimental and theoretical investigation of the promenade mode, a bound state formed by a pair of droplets walking side by side on the surface of a vibrating fluid bath. Particular attention is given to characterizing the dependence of the promenading behavior on the vibrational forcing for drops of a given size. We also enumerate the different instabilities that may arise, including transitions to smaller promenade modes or orbiting pairs. Our theoretical developments highlight the importance of the vertical bouncing dynamics on the stability characteristics. Specifically, quantitative comparison between experiment and theory prompts further refinement of the stroboscopic model [A. U. Oza et al., J. Fluid Mech. 737, 552 (2013)] through inclusion of phase adaptation and reveals the critical role that impact phase variations play in the stability of the promenading pairs.