Chemical-potential-based lattice Boltzmann method for nonideal fluids

Chemical potential, as an important thermodynamic quantity, has been popularly used in thermodynamic modeling for complex systems, especially for those involving the phase transitions and chemical reactions. Here we present a chemical-potential-based multiphase lattice Boltzmann model, in which the nonideal force is directly evaluated by a chemical potential. The numerical computation is more efficient than the pressure-tensor-based model [Wen et al. Europhys. Lett. 112, 44002 (2015)] because the calculations of the pressure tensor and its divergence are avoided. We have derived several chemical potentials of the popular equations of state from the free-energy density function. The theoretical analyses and numerical results support that the present model satisfies thermodynamics and Galilean invariance. An effective chemical-potential boundary condition is also implemented to investigate the wettability of a solid surface, and the contact angle can be linearly tuned by the surface chemical potential.

Figure 1

Two-phase coexistence density curves of (a) PR for water, (b) PR for methane, (c) CS and (d) RKS EOSs compared with the theoretical predictions solved by the Maxwell equal-area construction.

Figure 2

Drop coalescence with the different reference frames at (a) $t=1500$, (b) $t=3500$, (c) $t=6000$, and (d) $t=10000$ time steps. The blue contours have a static reference frame, while the reference frame velocities are 0.02 for the black lines, the red circles and the green circles with the angles $0^{\circ },{23}^{\circ },{45}^{\circ }$, respectively.

Figure 3

Contact angles obtained on solid surfaces with different chemical potentials by using RKS EOS: (a) $\theta ={30}^{\circ }$ at $\mu =-0.23$, (b) $\theta ={60}^{\circ }$ at $\mu =-0.13$, (c) $\theta ={105}^{\circ }$ at $\mu =0$, (d) $\theta ={135}^{\circ }$ at $\mu =0.09$, (e) $\theta ={160}^{\circ }$ at $\mu =0.15$, (f) $\theta ={180}^{\circ }$ at $\mu =0.18$.

Figure 4

Contact angle increasing with the chemical potential of the solid surface at the reduced temperature 0.8, (a) PR for water, (b) PR for methane, (c) CS, and (d) RKS EOSs.

Figure 5

The spurious currents of a rest drop surrounded by gas. The red solid symbols $\begin{array}{c}★,•\end{array}$, and $\begin{array}{c}♦\end{array}$ represent the spurious currents on the present model with the temperatures 0.80, 0.85, and 0.90, respectively. The blue hollow symbols $\begin{array}{c}\diamond ,○\end{array}$, and $\begin{array}{c}\star \end{array}$ represent the spurious currents on the pressure-tensor-based model with the temperatures 0.80, 0.85, and 0.90, respectively.

Figure 6

The spurious currents of a sessile drop on the horizontal surfaces with different wettability at the temperatures 0.80, 0.85, and 0.90.