Mass-Spring Model of a Self-Pulsating Drop

Self-pulsating sessile drops are a striking example of the richness of far-from-equilibrium liquid/liquid systems. The complex dynamics of such systems is still not fully understood, and simple models are required to grasp the mechanisms at stake. In this article, we present a simple mass-spring mechanical model of the highly regular drop pulsations observed in Pimienta, V.; Brost, M.; Kovalchuk, N.; Bresch, S.; Steinbock, O. Complex shapes and dynamics of dissolving drops of dichloromethane. Angew. Chem, Int. Ed. 2011, 50, 10728-10731. We introduce an effective time-dependent spreading coefficient that sums up all of the forces (due to evaporation, solubilization, surfactant transfer, coffee ring effect, solutal and thermal Marangoni flows, drop elasticity, etc.) that pull or push the edge of a dichloromethane liquid lens, and we show how to account for the periodic rim breakup. The model is examined and compared against experimental observations. The spreading parts of the pulsations are very rapid and cannot be explained by a constant positive spreading coefficient or superspreading.