Hyperslip velocity of melting ice sliding down inclined parallel ridges

A geometric and physical model for melting ice sliding over inclined superhydrophobic (SH) surfaces with parallel ridges is presented. By analyzing the micro-shear flows of molten liquid films between the ice layer and SH surfaces, the hyperslip velocities of melting ice sliding are investigated. The stick-slip boundary condition of the SH surface is used to establish the dual-series equations analytically, and the numerical solutions are implemented by truncating Fourier series and transforming the dual-series equations into linear algebraic equations to determine the hyperslip velocities of melting ice sliding. The numerical results indicate that the non-dimensional hyperslip velocities increase nonlinearly from near 0 to approximately 1.1 for longitudinal sliding and from near 0 to approximately 0.55 for transverse sliding with an increasing air groove ratio (a). The hyperslip velocities increase with increasing delta at the beginning initially (delta < 1), after which they tend toward asymptotic solutions as delta = 1. The hyperslip velocity ratio (W-h/U-h) shows that longitudinal ridges are at least twice as effective as transverse ridges in enhancing the ice hyperslip velocity, with the velocities accounting for more than 60% of the ice sliding velocities for arbitrary theta at a = 0.95 and delta = 0.1. The relative deviations between the numerical and asymptotic solutions are less than 5% at delta = 1, with the maximum relative deviation occurring at a = 0.65 for arbitrary theta.