Simulations of gravity-driven flow of binary liquids in microchannels

In this work a free-energy binary liquid lattice-Boltzmann scheme is used to simulate Taylor/Bretherton flow in a micro-channel where elongated gas bubbles move through a liquid with thin liquid films between the bubbles and the channel walls. The numerical scheme has a diffuse interface, and a main focus of our work is to assess resolution requirements for correctly resolving the liquid film and bubble motion. The simulations are two-dimensional and span a capillary number range of 0.05–1.0 where the capillary number is based on the liquid dynamic viscosity, the velocity of the bubble, and the interfacial tension. The flow is driven by a body force, and periodic boundary conditions apply in the streamwise direction. We obtain grid independent results as long as the liquid film thickness is at least twice the width of the diffuse interface, with film thicknesses in accordance to literature results. We also show that the results in terms of film thicknesses are largely insensitive to the liquid–gas viscosity ratio and wettability parameters.

► We model Bretherton flow by the diffuse interface model. ► The lattice Boltzmann method (LBM) free-energy binary liquid model was chosen as a framework for the diffuse interface model. ► Grid requirements for the film thickness resolution were thoroughly studied. ► Results show that uniform density LBM free-energy binary liquid model is suitable to simulate Bretherton phenomena in the range of small Reynolds number.