ABSTRACT
Controlling and predicting the motion of droplets on a heterogeneous substrate have received widespread attention. In this paper, we numerically simulate the droplet sliding through a "chemical step", that is, different wetting properties at two sides of the step, on a tilted substrate by the multiphase lattice Boltzmann method (LBM). Three kinds of equilibrium statuses are reproduced by observing the deformation of the droplet and the velocities of the front contact line. This study shows the droplet obtains a driving force to break through the step by deformation in the initial stage that the droplet is blocked. The droplet spreads to two sides along the step when the front end is blocked and is stretched after the front end is passed over the step. The lengths of the lateral spreading and the longitudinal stretching and the time required to pass over the step depend on the strength of the step. In the sliding process, the kinetic energy is converted into surface energy as the droplet is blocked, and the gravitational potential energy is converted into surface and kinetic energy following the droplet passes over the step. If the droplet can slide through the step, the more strength in the step, the more the gravitational potential energy is converted, and the more the surface energy increases. When the strength of the step is small, unbalanced Young's force hinders the contact line moving forward after the central part of the front end of the droplet breaks through the step. While the velocity of droplet sliding slows down with the increasing strength of the step, the unbalanced Young's force pushes the contact line forward against the resistance. These observations throw insight into the dynamics of the droplets sliding on a heterogeneous surface, which may facilitate potential applications like microfluidics and liquid transportation.
ABSTRACT
Contact angle is an essential physical quantity that characterizes the wettability of a substrate. Although it is widely used in the studies of surface wetting, capillary phenomena, and moving contact lines, the contact angle measurements in simulations and experiments are still complicated and time-consuming. In this paper, we present an efficient scheme for the measurement of contact angle on curved wetting surfaces in lattice Boltzmann simulations. The measuring results are in excellent agreement with the theoretical predictions without considering the gravity effect. A series of simulations with various drop sizes and surface curvatures confirm that the present scheme is grid-independent. Then, the scheme is verified in gravitational environments by simulating the deformations of sessile and pendent droplets on the curved wetting surface. The numerical results are highly consistent with experimental observations and support the theoretical analysis that the microscopic contact angle is independent of gravity. Furthermore, the method utilizes only the microscopic geometry of the contact angle and does not depend on the droplet profile; therefore, it can be applied to nonaxisymmetric shapes or moving contact lines. The scheme is applied to capture the dynamic contact angle hysteresis on homogeneous or chemically heterogeneous curved surfaces. Importantly, the accurate contact angle measurement enables the dynamic mechanical analysis of moving contact lines. The present measurement is simple and efficient and can be extended to implementations in various multiphase lattice Boltzmann models.
ABSTRACT
The boundary treatment is fundamental for modeling fluid flows especially in the lattice Boltzmann method; the curved boundary conditions effectively improve the accuracy of single-phase simulations with complex-geometry boundaries. However, the conventional curved boundary conditions usually cause dramatic mass leakage or increase when they are directly used for multiphase flow simulations. We find that the principal reason for this is the absence of a nonideal effect in the curved boundary conditions, followed by a calculation error. In this paper, incorporating the nonideal effect into the linear interpolation scheme and compensating for the interpolating error, we propose a multiphase curved boundary condition to treat the wetting boundaries with complex geometries. A series of static and dynamic multiphase simulations with large density ratio verify that the present scheme is accurate and ensures mass conservation.
