Enhanced slipperiness through rapid drop motion on liquid-infused surfaces

Introducing a lubricant layer between a fluid and a solid substrate endows slippery liquid-infused surfaces (SLISs) with excellent interfacial properties, such as a low sliding angle, repellency toward various liquids, icephobicity, and self-healing capability. Previous studies found that the friction force of a sliding drop on SLISs obeys the Landau-Levich-Derjaguin (LLD) theory, i.e., <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:msub> <a:mi>F</a:mi> <a:mi>η</a:mi> </a:msub> <a:mo>∼</a:mo> <a:msup> <a:mtext>Ca</a:mtext> <a:mrow> <a:mn>2</a:mn> <a:mo>/</a:mo> <a:mn>3</a:mn> </a:mrow> </a:msup> </a:mrow> </a:math> , with being the capillary number. In this paper, however, our experiments show that this scaling law holds only at low capillary numbers. We find a distinct decrease in the scaling exponent as the drop accelerates: In the rapid sliding regime, SLISs demonstrate even greater slipperiness than that predicted by the LLD theory. Numerical simulations reveal that this unexpected behavior originates from the incompletely developed state of the back meniscus, while the influence of the front meniscus is insignificant. Compared with the prediction of the Bretherton model, the back meniscus possesses a shorter shear length and a thicker shear layer, therefore reducing friction and enhancing surface slipperiness. An analytical solution is derived to describe the incompletely developed meniscus. This work offers insights into the abnormal frictional behavior when the capillary number of a moving drop exceeds <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mn>4</b:mn> <b:mo>×</b:mo> <b:msup> <b:mn>10</b:mn> <b:mrow> <b:mo>−</b:mo> <b:mn>3</b:mn> </b:mrow> </b:msup> </b:mrow> </b:math> .