Entropic lattice Boltzmann method for multiphase flows: Fluid-solid interfaces

The recently introduced entropic lattice Boltzmann model (ELBM) for multiphase flows [A. Mazloomi M., S. S. Chikatamarla, and I. V. Karlin, Phys. Rev. Lett. 114, 174502 (2015)] is extended to the simulation of dynamic fluid-solid interface problems. The thermodynamically consistent, nonlinearly stable ELBM together with a polynomial representation of the equation of state enables us to investigate the dynamics of the contact line in a wide range of applications, from capillary filling to liquid drop impact onto a flat surfaces with different wettability. The static interface behavior is tested by means of the liquid column in a channel to verify the Young-Laplace law. The numerical results of a capillary filling problem in a channel with wettability gradient show an excellent match with the existing analytical solution. Simulations of drop impact onto both wettable and nonwettable surfaces show that the ELBM reproduces the experimentally observed drop behavior in a quantitative manner. Results reported herein demonstrate that the present model is a promising alternative for studying the vapor-liquid-solid interface dynamics.

Figure 1

Equilibrium contact angle for a liquid drop confined inside the channel as a function of the adhesion parameter ${\kappa }_w$ (27): a comparison between the contact angles derived from Eq. (37) (circle) and the simulation results (cross). The dashed line shows a fit of the numerical results. The surface tension is $\sigma =0.353$, the liquid density is ${\rho }_l=7.82$, and the vapor density is ${\rho }_v=0.071$. The channel dimension is $300\times 70$ lattice nodes.

Figure 2

Schematic representation of the confined liquid column (red) in a rectangular channel. The liquid column of length $L_l$ moves along the channel under a wettability step imposed on the bottom ($z=0$) and on the top ($z=H$) walls. The dynamic contact angles are ${\theta }^{+}$ and ${\theta }^{-}$.

Figure 3

History of the centroid velocity $U$ of the liquid column: The line shows the analytical solution (39) and the circles show the simulation. The inset shows the center-of-mass position $X$: The line is the analytical solution (38) and the circles are the simulation. The height of the channel $H=60$ and the dynamic contact angles are ${\theta }^{+}=69.2^{\circ }$ and ${\theta }^{-}=63.{15}^{\circ }$. Time and space are given in lattice units.

Figure 4

Reduced maximum diameter of the spreading drop as a function of the Weber number. Circles show the ELBM simulation and squares the experimental data [43]. The solid line corresponds to the scaling law (42).

Figure 5

Snapshots of a drop impacting on a wettable surface: left, experiment [44]; right, simulation, with $\mathrm{Re}=764$ and $\mathrm{We}=31.5$.

Figure 6

Evolution of droplet diameter on a hydrophilic surface. The solid line is the ELBM simulation and the circles show the experiment [44].

Figure 7

Snapshots of the lamella stabilization simulation on a superhydrophobic surface at $\mathrm{We}=85$ and $\mathrm{Re}=60$.

Figure 8

Drop impact on a hydrophilic surface. The nondimensional thickness of the lamella at the symmetry center $h_c^{*}=h_c/D_0$ versus the nondimensional time $t^{*}=t{U}_0/D_0$ is shown. Open symbols denote the ELBM simulation at various impact conditions, closed circles denote the experiment [46], and the solid line shows the analytical estimate of Ref. [47], Eq. (43).

Figure 9

Drop impact on a superhydrophobic surface. The nondimensional thickness of the lamella at the symmetry center $h_c^{*}=h_c/D_0$ versus the nondimensional time $t^{*}=t{U}_0/D_0$ is shown. Open symbols denote the ELBM simulation at various impact conditions and the line shows the analytical estimate of Ref. [47], Eq. (43).

Figure 10

Drop impact onto a superhydrophobic surface. The thickness of the lamella is shown as a function of the impact Weber number. Closed circles show the ELBM simulation result for the thickness of the lamella at the symmetry axis, at the time instant $t^{*}=1, h_{c1}^{*}=h_c^{*}\left(1\right)$, and dashed lines are fitting curves of the numerical results to guide the eye. Also shown are asymptotic values for $h_{c1}^{*}$ for $\mathrm{We}>40$: $h_{c1}^{*}=0.2571$ (the ELBM) and $h_{c1}^{*}=0.2496$ (from Ref. [47])). Open circles show the ELBM simulation result for the minimal thickness of the lamella $h_m^{*}$.