Asymmetric coalescence-induced droplet jumping on hydrophobic fibers

Abstract

Coalescence of two unequal-sized droplets on hydrophobic fibers is more common in nature. To elucidate the mechanism of merged droplets jumping on hydrophobic fibers, a new theoretical model for two unequal-sized droplets coalescence was first developed, which considered the effects of contact angle hysteresis and droplet-fiber contact area. Then, the influences of Ohnesorge number (Oh), droplet radius ratio (n), droplet-fiber radius ratio (k) and contact angle (CA) on the dimensionless jumping velocity (U/vci) were studied theoretically. The value of U/vci increased with the increase of n, k and CA but decreased as Oh increased. The dimensionless jumping velocity for two unequal-sized droplets coalescence on hydrophobic fibers still followed the capillary-inertial scaling law with U/vci ≈ 0.45 when n = 0.5. In addition, the effects of k and CA on the critical jumping radius ratio were the critical jumping radius ratio being reduced as k and CA increased, and the minimal critical jumping radius ratio was approximately 0.1. These findings will help to characterize coalescence-induced droplet jumping on hydrophobic fibers.