Modeling surfactant-laden droplet dynamics by lattice Boltzmann method

Abstract

Based on the phase-field theory, we present an improved lattice Boltzmann (LB) method for simulating droplet dynamics with soluble surfactants. This method takes advantage of three sets of particle distribution functions for solving the coupled system of two Cahn–Hilliard-like equations and incompressible Navier–Stokes equations. The phase-field model is formulated from the perspective of the Ginzburg–Landau free energy functional, where some modifications introduced circumvent unphysical behavior of the interfacial layer and improve the well-posedness of the model. We also give a comprehensive review on the existing surface tension force formulations and demonstrated that the popular potential form is artificial; instead, an alternative potential surface tension force is deduced. The equation of state accounting for the influence of the surfactant concentration on interfacial tension can be directly incorporated into the present approach, further improving the flexibility of the method. Besides, a linear equilibrium distribution function and a proper source term are introduced into the LB method for surfactants such that it can recover the correct physical formulations for a surfactant-laden multiphase system. An abundance of numerical experiments is carried out to validate the LB method, and the numerical performances of the tensor and potential surface tension forces are also evaluated. It is reported that the potential scheme achieves a better accuracy in solving interfacial dynamics at low surfactant concentrations and also is in favor of lower spurious velocities. In addition, the numerical predictions of surfactant-laden droplet dynamics show good agreement with the literature data.