Quantitative relations between droplet jumping and anti-frosting effect on superhydrophobic surfaces

Abstract

Superhydrophobic surfaces have been confirmed to have the capacity for delaying the condensation frosting, and the self-propelled droplet jumping phenomenon further enhances this effect, for its contribution in the fast removal of condensates from the surface. However, only few but unclear and incomplete quantitative conclusions have been made on how the droplet jumping aid the anti-frosting. Here, standing on the shoulders of previous works, we finally elucidate this query by establishing a quantitative relation between the capacity of droplet jumping and the anti-frosting effect. Two representative parameters, including the average distance (L) and the degree of closeness (D/L) between adjacent droplets, are proposed to evaluate the capacity of droplet jumping, and the anti-frosting effect is evaluated by the frost propagation velocity (vfrost). Models based on the ice-bridge growth theory are built to deduce the mathematical relation, vfrost ∝ (1 + D/L)/L, between the droplet jumping capacity and the frost propagation, and this relation is well validated against our experiments on surfaces made by two substrate materials with different micro/nano structures. Furthermore, the thermal conductivity and specific heat capacity of the substrate also relate to the frost propagation. These results pioneer in quantitatively clarifying the anti-frosting effect by the droplet jumping, which shall further promote the anti-frosting application of the superhydrophobic surface.