The coalescence-induced self-propelled droplet jumping on superhydrophobic surfaces has a large number of potential applications such as enhancement of condensation heat transfer, self-cleaning, and anti-icing, which becomes a current hotspot. At present, most of the research studies focus on the self-propelled jumping of two identical droplets; however, the jumping induced by unequal-sized droplets is much closer to actuality. In this paper, the coalescence-induced self-propelled jumping of binary unequal-sized droplets is simulated and all energy terms are studied. The normalized liquid bridge width induced by unequal-sized droplets is a function of the square root of the normalized time, and the maximum jumping velocity is a function of the radius ratio as well. The maximum jumping velocity descends with the decrease in the radius ratio and contact angle, and the critical radius ratio shows an upward trend with the decrease in the contact angle. Furthermore, all energy terms decline with the decrease in the radius ratio. The effective energy conversion rate of binary equal-sized jumping is very low, less than 3% in our results. This rate of binary unequal-sized jumping further reduces due to the existence of asymmetric flow. This work helps for a better understanding of the characteristics of coalescence-induced self-propelled droplet jumping.

An unstructured finite-volume time-domain method (UFVTDM) is developed to solve two-dimensional transient heat conduction in multilayer functionally graded materials (FGMs). A four-node quadrilateral grid and a three-node triangular grid are employed to deal with mixed-grid problems. The accuracy of the method is improved by treating the quadrilateral grid as a bilinear element with consideration of both the linear term and the constant term. The improvement is validated to be vital to avoid violent numerical oscillation when applying the method to heat point-source problems. The accuracy and capability of the UFVTDM are validated by numerical tests.

The coalescence-induced self-propelled droplet jumping behaviors on superhydrophobic surfaces have attracted extensive interest, due to a huge application potential. The coalescence and jumping of two droplets with different radius ratios are numerically simulated, and the jumping velocity is theoretically analyzed. The jumping type changes from the vertical motion to the upward rotation motion, with the decrease of radius ratio. The droplet is not able to jump when the radius ratio is smaller than 0.4. The jumping velocity reaches several peak values when the radius ratio is smaller than 0.7. The maximum jumping velocities are theoretically predicted, which is based on the law of conservation of energy. The viscous dissipation energy which should not be ignored is the main and direct source of the errors.