Numerical Investigation on Head-On Collisions of Binary Micro-Droplets by an Improved Multiphase Lattice Boltzmann Flux Solver

Head-on collisions of binary micro-droplets are of great interest in both academic research and engineering applications. Numerical simulation of this problem is challenging due to complex interfacial changes and large density ratio between different fluids. In this work, the recently proposed lattice Boltzmann flux solver (LBFS) is applied to study this problem. The LBFS is a finite volume method for the direct update of macroscopic flow variables at cell centers. The fluxes of the LBFS are reconstructed at each cell interface through lattice moments of density distribution functions (DDFs). As compared with conventional multiphase lattice Boltzmann method, the LBFS can be easily applied to study complex multiphase flows with large density ratio. In addition, external forces can be implemented more conveniently and the tie-up between the time step and mesh spacing is also removed. Moreover, it can deal with complex boundary conditions directly as those do in the conventional Navier-Stokes solvers. At first, the reliability of the LBFS is validated by simulating a micro-droplet impacting on a dry surface at density ratio 832 (air to water). The obtained result agrees well with experimental measurement. After that, numerical simulations of head-on collisions of two micro droplets are carried out to examine different collisional behaviors in a wide range of Reynolds numbers and Weber numbers of 100 ≤ Re ≤ 2000 and 10 ≤ We ≤ 500. A phase diagram parameterized by these two control parameters is obtained to classify the outcomes of these collisions. It is shown that, at low Reynolds number (Re=100), two droplets will be coalescent into a bigger one for all considered Weber numbers. With the increase of the Reynolds number, separation of the collision into multiple droplets appears and the critical Weber number for separation is decreased. When the Reynolds number is sufficiently high, the critical Weber number for separation is between 20 and 25.