Lattice Boltzmann modeling for the coalescence between a free droplet in gases and a sessile droplet on wettable substrate with contact angle hysteresis

Abstract

The coalescence between a free droplet and a sessile droplet on wettable substrate is numerically studied. The axisymmetric lattice Boltzmann method for two-phase flows is used in modeling. Here the contact angle hysteresis (prescribed by advancing angle [Formula: see text] and receding angle [Formula: see text]) is taken into account. The effects of Ohnesorge number ( Oh), contact angle and its hysteresis, and the radius of the free droplet on the coalescence dynamics are investigated in detail. The Oh numbers ranging from 0.02 to 0.15 here makes the radius of the liquid bridge r and the time t follow power law. Also, Oh has remarkable impact on the development of capillary wave and on the amount of kinetic energy released from coalescence. It is found that the curve of the wetting radius varying with time includes several plateau stages, which is a typical characteristic for the effect of contact angle hysteresis. The larger window of contact angle hysteresis would result in smaller steady wetting radius after coalescence. Compared with the existence of contact angle hysteresis, the absence of contact angle hysteresis makes the droplets system release more kinetic energy during the coalescence but the released kinetic energy decays more rapidly and soon reduces to zero. Oppositely, if the contact angle hysteresis exists, the released kinetic energy would oscillate for a period of time before approaching zero.