Lattice Boltzmann Model Simulation of Bubble Deformation and Breakup Induced by Micro-Scale Couette Flow

Understanding the morphology of transformation of a single bubble immersed in a liquid undergoing a shear flow is essential in the prediction of bubble deformation and breakup phenomena which is commonly found in many applications involving complex liquid-gas multiphase flow. In flows with a continuous liquid phase, bubbles may breakup as a response to the excessive shear above a critical threshold and this phenomenon is of special interest in many industrial applications. Moreover, modelling the bubble size distribution after breakup occurs is of paramount importance in applications such as manufacturing and processing of emulsions and polymer blends, aerosols and drug transportation system. In this study, the deformation and breakup of a single bubble released in a fully developed laminar Couette flow are evaluated under different spanwise positions as well as under different initial bubble diameter. The simulation is carried out using multiphase Shan-Chen (SC) Lattice Boltzmann Model (LBM). Lattice Boltzmann Model (LBM) is widely used for multiphase flow modelling due to its simplicity and versatility. The LBM is based on modelling a fictional fluid via a single particle probability distribution function. This approach is derived from Kinetic Theory, in contrast with standard Computational Fluid Dynamics (CFD) solvers which are based on discretizing Navier-Stokes equations. These particles stream and collide according to a prescribed set of speeds, referred as a lattice, on the nodes of a Cartesian grid. The system approaches its equilibrium state after collision of the particles happens. Distribution function is then allowed to propagate via lattice links to the neighbouring node. The resulting equation is linear in the convective term, explicit and second-order accurate in the limit of low Mach numbers. The LBM is especially suitable to simulate multiphase flows; several models have been developed such as the free-energy model, the colour-gradient model, the kinetic-theory-based model and the pseudopotential model. This last model, also referred to as the Shan-Chen LBM, was used in this study to deal with the multiphase flow in a single component fluid due to its conceptual simplicity and computational efficiency. Our study shows the transition between deformation and breakup experienced by a bubble immersed in a plane Couette liquid flow, described under different Capillary numbers (Ca_с), liquid-gas viscosity ratios and relative initial spanwise position of the bubble with respect to the channel centreline. A critical Capillary number Ca_c = 0.31 was found at the onset of the breakup with bubble centroid location varying as a function of the rest of parameters. The results obtained with SC-LBM are in excellent agreement with those obtained by Taylor.