Lattice Boltzmann study of mass transfer for two-dimensional Bretherton/Taylor bubble train flow

Abstract

This work presents a procedure for the determination of the volumetric mass transfer coefficient in the context of lattice Boltzmann simulations for the Bretherton/Taylor bubble train flow for capillary numbers 0.1<Ca<1.0. We address the case where the hydrodynamic pattern changes from having a vortex in the slug (Ca<0.7) to not having it (Ca>0.7) [1]. In the latter case the bubble shape is asymmetric and cannot be approximated through flat surfaces and circular circumferences as is often done in the literature [2,3]. When the vortex is present in the slug, the scalar concentration is well mixed and it is common to use periodic boundary conditions and the inlet/outlet-averaged concentration as the characteristic concentration. The latter is not valid for flows where the tracer is not well mixed, i.e. Ca>0.7. We therefore examine various boundary conditions (periodic, open, open with more than 1 unit cell) and definitions of the characteristic concentration to estimate mass transfer coefficients for the range of capillary numbers 0.1<Ca<1.0. We show that the time-dependent volume averaged concentration taken as the characteristic concentration produces the most robust results and that all strategies presented in the literature are extreme limits of one unified equation. Finally, we show good agreement of simulation results for different Peclet numbers with analytical predictions of van Baten and Krishna [2].