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

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 <i>t</i>_c as a function of the Weber number (<i>We</i>) was established; the scaling law <i>t</i>_c = <i>t</i>_c(<i>We</i>) 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 <i>We</i> 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 <i>t</i>_s scales as , <i>n</i> = 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 <i>t</i>_r grows weakly with the Weber number. The scaling law was changed at threshold values of <i>We</i> ≅ 15–20. It is reasonable to explain this change with the breaking of the Leidenfrost regime of spreading under high values of <i>We</i>.