A multiphase lattice Boltzmann method for simulating immiscible liquid-liquid interface dynamics

• A multiphase lattice Boltzmann method is validated with a simple source-term.
• Four test cases are considered and found to be coherent with theory.
• The proposed method is consistent with various finite-element methods.
• An application with a trapped hexane bubble inside a structured pore is presented.

The simulation of immiscible liquid–liquid interface dynamics using the lattice Boltzmann method is studied in this work. The capabilities of the proposed model are investigated and validated with the inclusion of an external forcing term, e.g. the force of gravity. Fundamental tests are performed to further validate the performance of the method for computing multiphase flows. Four theoretical test cases are studied: (1) two-phase Poiseuille flow with variable density and viscosity ratios; (2) two-phase flow subject to hydrostatic pressure; (3) two-dimensional bubble dynamics; and (4) capillary-gravity wave. The four test cases provide clear quantitative results. In particular, the results of the proposed formulation for the test case with two-dimensional bubble dynamics are compared with the results of three different finite element methods. We found that the proposed lattice Boltzmann method is consistent with these standard approaches, and that the relative standard deviation between all codes is less than 1% for several flow quantities. Most of the test cases in this study use real liquid properties for the dimensionless density and viscosity ratios. In this context, the real immiscible liquids are mercury, water, and hexane. In addition, a final application test case is studied, where a hexane bubble under gravity is initially trapped inside a structured pore that is completely water-wet. A methodology using the bisection method to find the critical Bond number for which the transition from a trapped to a non-trapped bubble occurs is proposed.