Numerical simulations of a droplet slipping along a filament with Lattice Boltzmann Method

Abstract

In this paper, a droplet slipping along a filament under gravity is numerically simulated with a two-phase lattice Boltzmann method. In the simulations, a droplet encompasses the bottom end of the filament as an initial state. Here the contact angle hysteresis for non-ideal surface, prescribed by advancing angle θ A and receding angle θ R , is taken into account. Besides, the dimensionless parameters: Ohnesorge number ( O h ), Bond number ( B o ), and the initial wetting length ( l w 0 ∗ ) are considered. The contact angle hysteresis tends to prevent the motion of contact lines, but gravity would drive the droplet to slip accompanied by its surface’s deformation. Accordingly, four dynamic modes for droplet moving on wetting filament and two for non-wetting filament have been identified for the first time. In addition, three maps of modes distribution depending on [ θ R , θ A ] , B o , O h , and l w 0 ∗ are shown clearly. It is indicated that both the contact angle hysteresis and the sharp point at the bottom end of filament, are able to result in the contact line pinning, which has decisive effect on the motion modes of droplet. It is also found that the breakup of droplet during the slipping process can only occur for wetting filament, but for non-wetting filament, the droplet either keeps suspended at the end of filament, or detaches from the filament completely. It is more likely for droplet to fall down from the filament at smaller O h . Adopting larger l w 0 ∗ , the droplet tends to be hung at the end of wetting filament, but oppositely, for the non-wetting filament, the whole droplet is inclined to depart from filament totally. These results could be beneficial to the understanding of droplet’s dynamical behavior on filament.