Lattice Boltzmann modeling of contact angle and its hysteresis in two-phase flow with large viscosity difference

Abstract

Contact angle hysteresis is an important physical phenomenon omnipresent in nature and various industrial processes, but its effects are not considered in many existing multiphase flow simulations due to modeling complexity. In this work, a multiphase lattice Boltzmann method (LBM) is developed to simulate the contact-line dynamics with consideration of the contact angle hysteresis for a broad range of kinematic viscosity ratios. In this method, the immiscible two-phase flow is described by a color-fluid model, in which the multiple-relaxation-time collision operator is adopted to increase numerical stability and suppress unphysical spurious currents at the contact line. The contact angle hysteresis is introduced using the strategy proposed by Ding and Spelt [Ding and Spelt, J. Fluid Mech. 599, 341 (2008)JFLSA70022-112010.1017/S0022112008000190], and the geometrical wetting boundary condition is enforced to obtain the desired contact angle. This method is first validated by simulations of static contact angle and dynamic capillary intrusion process on ideal (smooth) surfaces. It is then used to simulate the dynamic behavior of a droplet on a nonideal (inhomogeneous) surface subject to a simple shear flow. When the droplet remains pinned on the surface due to hysteresis, the steady interface shapes of the droplet quantitatively agree well with the previous numerical results. Four typical motion modes of contact points, as observed in a recent study, are qualitatively reproduced with varying advancing and receding contact angles. The viscosity ratio is found to have a notable impact on the droplet deformation, breakup, and hysteresis behavior. Finally, this method is extended to simulate the droplet breakup in a microfluidic T junction, with one half of the wall surface ideal and the other half nonideal. Due to the contact angle hysteresis, the droplet asymmetrically breaks up into two daughter droplets with the smaller one in the nonideal branch channel, and the behavior of daughter droplets is significantly different in both branch channels. Also, it is found that the contact angle hysteresis is strengthened with decreasing the viscosity ratio, leading to an earlier droplet breakup and a decrease in the maximum length that the droplet can reach before the breakup. These simulation results manifest that the present multiphase LBM can be a useful substitute to Ba et al. [Phys. Rev. E 88, 043306 (2013)PLEEE81539-375510.1103/PhysRevE.88.043306] for modeling the contact angle hysteresis, and it can be easily implemented with higher computational efficiency.

Wetting boundary condition for the color-gradient lattice Boltzmann method: Validation with analytical and experimental data

“…Their approach is based on the geometrical formulation proposed by Ding and Spelt (2007) . This method accurately simulates wetting phenomena on a flat surface ( Huang et al, 2014;Li et al, 2016;Liu et al, 2015 ) and can be extended to 3D ( Yu et al, 2017 ), but the implementation for arbitrary surfaces is not obvious. Leclaire et al (2017) proposed a way to find the proper direction of the color gradient ∇ N based on the recurrence relation for the secant method.…”

“…Liu et al (2015) showed an implementation of this wetting boundary condition in the 2D CG-LBM. Their approach is based on the geometrical formulation proposed by Ding and Spelt (2007) .…”

A lattice Boltzmann method for axisymmetric multicomponent flows with high viscosity ratio

“…By introducing the source terms in the same fashion as Premanath and Abraham [31], Mukherjee and Abraham [32] extended the high-density-ratio model of Lee and Lin [33] As reviewed above, all types of the (Cartesian) multiphase, multicomponent LBMs have been extended to the axisymmetric versions except the colorgradient model. Compared to other multiphase multicomponent LBMs, the color-gradient model has its own advantages such as low spurious velocities, high numerical accuracy, strict mass conservation for each fluid, and good numerical stability for a broad range of fluid properties [38]. In addition, the color-gradient model has been widely employed to simulate immiscible multicomponent flow problems, in particular those in porous media and microfluidic devices [39,40,41,42].…”

“…In addition, the color-gradient model has been widely employed to simulate immiscible multicomponent flow problems, in particular those in porous media and microfluidic devices [39,40,41,42]. Recently, it was also extended to model the thermocapillary flows [43,44] and the contact-line dynamics with the contact angle hysteresis [45,38]. In view of the advantages and great success of the color-gradient model, it is necessary to develop an axisymmetric version of the color-gradient LBM that allows for the solution of multicomponent flows at the computational 4 cost of a 2D simulation.…”

“…In addition, the axisymmetric multicomponent LBM is implemented in a MRT framework in order to minimize spurious velocities and increase the numerical stability of solving large viscosity ratio problems [48,49,50,38]. The capability and accuracy of this method are tested by several typical flow cases, including simulations of a static droplet, oscillation of a viscous droplet, and breakup of a liquid thread.…”