(258g) Lattice Boltzmann Simulation of Mixing Process Inside Micro-Droplets in a Gas - Liquid Taylor Flow

Mixing of two fluids in microfluidic system is of essential interest in nowadays chemical engineering. Since the flows in simple microchannels under typical operating conditions are predominantly laminar and uniaxial, molecular diffusion becomes the major driving force for the mixing of fluid streams. Considering the low diffusion capability, mixing process is still not fast enough even at the micro-scale of ~100 mm. As an alternative, droplet-based microfluidic system has become one of the promising solutions, which takes advantage of the internal recirculation inside droplets to increase the convective mass transfer between streams. Micro-droplets in a continuous gas-liquid Taylor flow behave like micro-liter even nano-liter batch reactors to precisely control the underlying hydrodynamics and mixing processes inside droplets so that the product processes possess well-defined residence time distribution and intensified micro-scale mixing.

LBM has experienced rapid development and attracted increasing interests during the past two decades in simulating multiphase/multicomponent flows owing to its excellent numerical stability and constitutive versatility, especially on solving the challenge of moving and deformable interfaces. Three LB models for multiphase flows have emerged, i.e. free-energy approach, Shan & Chen scheme and color-gradient method, where the color-field LBM is quite appropriate to simulate the gas-liquid dispersed microfluidic system for its capability to independently tune the viscosity, interfacial tension and interface thickness under the modeling scheme. On the basis of the simple color-field two-phase method (Latva-Kokko and Rothman, 2005), we further introduced a third component, which perfectly acted as a standard tracer to track the behavior of one of fluid steams without any impact on bulk flow field. This newly established method was then used to study the hydrodynamics and liquid mixing performance inside micro-slugs/droplets in a microchannel with the gas-liquid Taylor flow. The micro-LIF measurements of ethanol mixing process in the ethanol-air system were carried out to provide experimental foundations to validate the simulation analysis. Also, the comparison of the liquid mixing behaviors in a simple laminar flow and a droplet-based flow in microchannels has been made to verify the intensification effect of the internal recirculation inside independent micro-droplets.

M. Latva-Kokko, Daniel H. Rothman, Diffusion properties of gradient-based lattice Boltzmann models of immiscible fluids. Physical Review E 71,056702 (2005)