Scheme for contact angle and its hysteresis in a multiphase lattice Boltzmann method

Abstract

In this paper, a scheme for specifying contact angle and its hysteresis is incorporated into a multiphase lattice Boltzmann method. The scheme is validated through investigations of the dynamic behaviors of a droplet sliding along two kinds of walls: a smooth (ideal) wall and a rough or chemically inhomogeneous (nonideal) wall. For an ideal wall, the wettability of solid substrates is able to be prescribed. For a nonideal wall, arbitrary contact angle hysteresis can be obtained through adjusting advancing and receding angles. Significantly different phenomena can be recovered for the two kinds of walls. For instance, a droplet on an inclined ideal wall under gravity is impossible to stay stationary. However, the droplet on a nonideal wall may be pinned due to contact angle hysteresis. The steady interface shapes of the droplet on an inclined nonideal wall under gravity or in a shear flow quantitatively agree well with the previous numerical studies. Besides, the complex motion of a droplet creeping like an inchworm could be simulated. The scheme is found suitable for the study of contact line problems with and without contact angle hysteresis.

Lattice Boltzmann simulation of multiple droplets impingement and coalescence in an inkjet-printed line patterning process

“…The numerical results (shown in Figure 2) detect a linear relationship between the pressure difference of the droplet and the inverse of its radius, which satisfies the Laplace law. We get σ = 0.011κ through linear fit for both 2D and 3D cases and the results agree well with the Wang's simulations (Wang, Huang, and Lu 2013). In addition, the ratio of σ to κ is kept constant as the grid resolution changes.…”

“…Ding and Spelt (2007) proposed a geometric formulation that was mathematically equivalent to the surface-energy formulation of diffuse interface simulations. This geometrical formulation has been employed in the phase-field models to investigate the dynamics of droplets impinging on non-ideal surfaces with contact angle hysteresis (Wang, Huang, and Lu 2013). We incorporate this geometrical formulation in our LBM model for the wetting boundary condition.…”

A hybrid phase field multiple relaxation time lattice Boltzmann method for the incompressible multiphase flow with large density contrast

“…Recently, the free energy based phase field lattice Boltzmann method (LBM, which is a kineticbased mesoscopic approach for fluid dynamic simulation [1]) [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] has attracted much attention for simulation of multiphase flow problems. It has been continuously refined and applied to simulate problems involving bubble dynamics [19], contact line dynamics [11,[20][21][22], the multiphase flow in microfluidic devices [23], and others [24][25][26]. The popularity mainly attributes to the advantages of LBM for the flow field simulation and phase field method [27,28] for the interface capturing.…”

Wetting boundary conditions in numerical simulation of binary fluids by using phase‐field method: some comparative studies and new development

“…Because CubSE avoids the appearance of the wall layer (a layer enriched with one of the fluids while depleted in the other) [18,19], it has been employed by many others [20][21][22][23][24][25]. It has been employed for contact angle hysteresis (CAH) modeling by Ding and Spelt (in PF simulation) [30], and by Wang et al (in LBM simulation) [31]. Qian et al used a somewhat different form of SE, which employed a sine function [28] (denoted as SinSE).…”

“…The special feature of this formulation is that the local microscopic contact angle is always enforced. It has been employed for contact angle hysteresis (CAH) modeling by Ding and Spelt (in PF simulation) [30], and by Wang et al (in LBM simulation) [31]. Yet another recent development of WBC was proposed by Lee and Kim [32] on the basis of a characteristic interpolation (denoted as CI), which was claimed to possess certain numerical advantages.…”