Lattice Boltzmann simulation of drop splitting in a fractal tree-like microchannel

Fractal tree-like microchannel is advantageous to faster emulsification and droplet production in microchannels. Although computer simulation is becoming a powerful tool for design and optimization, precise treatment of a large number of walls in fractal tree-like microchannel is troublesome. The numerical roughness caused by traditional bounce-back boundary condition may accumulate and generate large errors in flow pattern recognization. In this paper, an approach integrating Immersed Boundary Method (IBM), Phase-Field Model (PFM) and Lattice Boltzmann Method (LBM) is developed, aiming to accurately simulate droplet splitting in fractal tree-like microchannel system involving surfactants and wetting boundary walls. Then the operating conditions including capillary number, flow rate ratio and wetting boundary conditions were optimized. We found that the capillary number in 0.02 ∼ 0.05 and flow rate ratio in 1/3.6 ∼ 1/9 can accelerate emulsification. Hydrophobic-lipophilic walls generate a slug-like water drop of bullet shape and thin oil film between the drop and walls, facilitating drop movement in microchannel. The effects of surfactant, Marangoni stress and interfacial tension force on droplet splitting were investigated. The contact walls at the corner and forks resist the surfactant migration, and therefore enrich surfactant at the upstream end of drop interface, leading to uneven distribution of interfacial tension. The breaking interfaces and the interfaces contacting with wall or fork are subjected to opposite reaction of Marangoni stress and tend to be thinner and finally deform or break.