Improved lattice Boltzmann model for moving contact-line with soluble surfactant

Abstract

Modeling moving contact-line with surfactant has become a widely sought methodology due to its scientific relevance and extensive applications. Within the phase field framework, we present an improved lattice Boltzmann (LB) model for simulating moving contact-line dynamics with soluble surfactant. In this model, a LB equation is used to solve the Navier–Stokes equations, and another two LB equations are utilized to solve the two Cahn–Hilliard-like equations. The modified chemical potentials are incorporated in the LB model by using an equivalent variant of the free energy functional and the corresponding equilibrium distribution functions are also amended. These modifications could circumvent the degraded accuracy of previous LB models in capturing the interfacial behavior and surfactant distribution, and also improve the well-posedness of the LB model. In addition, a dynamic contact angle formulation is introduced to account for the surfactant effect on surface wettability and the resulting contact angle is further implemented in the LB model via a popular geometrical wetting approach. We comprehensively evaluate the numerical performance of the LB model by simulating some benchmark problems. It is found that the LB model achieves a higher accuracy than previous LB models in solving the phase field and surfactant profiles, and also numerical prediction of moving contact-line dynamics with surfactant shows good agreement with the analytical solution. Finally, the LB model is applied to investigate droplet shearing dynamics on solid substrate. The influences of capillary number and solid wetting property on droplet deformation and breakup are analyzed in detail.