Mixing and Interpenetration in a Three-Dimensional Buoyancy-Driven Flow of Two Immiscible Liquids: A GPU Based LBM Approach

The Buoyancy-driven flow of two immiscible liquids having varying density and viscosity is studied in a three-dimensional inclined confined channel. Initially, the heavier/lighter liquids occupy the upper/lower parts of the channel, respectively, which is an unstable configuration. The numerical simulations are performed using a multiphase lattice Boltzmann method (LBM) that is further implemented on the graphics processing unit (GPU). The three-dimensional flow dynamics and the associated physics are studied based on various parameters such as viscosity ratios (m), Atwood numbers (At) and Reynolds numbers (Re). The results were presented in the form of iso-surface/contour plots, average density profiles, and lengths of interpenetration. It is observed that larger interpenetration occurs with iso-viscous liquids having higher density gradients (higher At). The Reynolds number had a non-monotonic effect on the axial lengths of interpenetration (Lp∗); Lp∗ increases till Re = ۵۰۰ and then decreases for Re = ۱۰۰۰. At larger Re, due to the development of Kelvin-Helmholtz instabilities higher transverse interpenetration is observed.

Keywords:

Buoyancy , driven flow , Length of interpenetration , Immiscible fluids , Kelvin , Helmholtz instabilities , Lattice Boltzmann method