Universality of Scaling Laws Governing Contact and Spreading Time Spans of Bouncing Liquid Marbles and its Physical Origin.

Abstract

The impact of liquid marbles coated with a diversity of hydrophobic powders with various solid substrates, including hydrophobic, hydrophilic, and superhydrophobic ones, was investigated. The contact time of the bouncing marbles was studied. Universal scaling behavior of the contact time tc as a function of the Weber number (We) was established; the scaling law tc = tc(We) was independent of the kind of powder and the type of solid substrate. The total contact time consists of spreading time and retraction time. It is weakly dependent on We and this is true for all kinds of studied powders and substrates. This observation hints to the surface tension/inertia spring model governing the impact. By contrast, the spreading time ts scales as [Formula: see text], n = 0.28 - 0.30 ± 0.002. We relate the origin of this scaling law to the viscous dissipation occurring within the spreading marbles. The retraction time tr grows weakly with the Weber number. The scaling law was changed at threshold values of We ≅ 15-20. It is reasonable to explain this change with the breaking of the Leidenfrost regime of spreading under high values of We.