Vof-simulation of Rising Air Bubbles with Mass Transfer to the Ambient Liquid

This paper presents numerical simulations of two-phase flow with highdensity ratio, taking into account mass transport of a soluble component and its interfacial mass transfer. The mathematical model and the numerical method allow for different solubility of the species in the respective fluid phases, while volume changes due to mass transfer are neglected. The discontinuous changes in species concentrations at the interface are modeled by means of Henry’s law. Simulations are carried out with an extended version of the highly parallelized code FS3D, which employs an advanced Volume-Of-Fluid (VOF) method. Transfer and transport of oxygen is examined in case of single bubbles as well as bubble chains rising in aqueous solutions. Numerical simulations show good qualitative agreement with experimental data and render the observed mass transfer phenomena correctly. INTRODUCTION Many industrial applications based on two-fluid systems involve mass transfer operations such as extraction, gas scrubbing and waste water treatment in bioreactors. Examples in Chemical Engineering include bubble columns, loop reactors or agitated stirred reactors. For the design of efficient two-phase mass transfer reactors detailed knowledge of, say, particle sizes and shapes, slip velocities, internal circulation, swarm behavior, particle induced turbulence, particle size distributions (including coalescence and break-up) as well as the influence of surfactive species are of fundamental importance. Optimization of mass transfer units additionally requires profound understanding of the underlying mass transport and mass transfer processes. Here, numerical simulations provide a helpful tool to reduce the usually large experimental expenses for reactor design. Due to the increase in computational power, numerical simulations of two-phase flows based on continuum mechanical models with free interfaces become feasible and prove extremely useful for a better understanding of fundamental processes and phenomena. TPST-2005 10 Workshop on Transport Phenomena in Two-phase Flow Bothe and Warnecke, VOF-Simulation of rising air bubbles 62 Recently, much work has been devoted to this subject. Mass transfer of a dilute component between spherical drops and the ambient liquid has been studied in [1-3], while small surface deformations of axis-symmetric drops are allowed in [4]. The numerical simulations presented there assume that species concentrations are continuous at the phase boundary, i.e. the distribution coefficient (Henry coefficient in this context) of the dissolved species equals 1. Mass transfer due to the dissolution of a rising droplet of liquid CO2 in the surrounding water has been investigated in [5, 6], taking into account the volume changes of the droplet. In case of dissolution of bubbles, the effect of surfactants has been studied numerically in [7, 8]. While the above mentioned contributions consider spherical or ellipsoidal drops or bubbles, theoretical studies of mass transfer across dynamically deforming interfaces require numerical methods that resolve the free phase boundary. Based on the VOF-method, mass transfer across such strongly deforming interfaces has been computed numerically in [9, 10]. The simulations presented in [9] are in 2D, either planar or axis-symmetric, with Henry coefficient equal to 1.0. The present paper is closely related to [10], where transfer of oxygen is simulated for air bubbles rising in water or aqueous solutions, taking into account the realistic jump discontinuity of the oxygen profiles at the phase boundary. Main emphasis is on single bubbles in liquids of higher viscosity to gather information about the relevant length scales involved. Furthermore, bubble chains are considered as a first step towards a better understanding of mass transfer in bubble swarms. GOVERNING EQUATIONS The motion of fluid particles is modeled as a two-phase flow with free phase boundary, based on continuum mechanics. We consider isothermal flows of two Newtonian fluids of constant density which are immiscible on the molecular scale. Inside the phases, balance of mass and momentum then leads to the Navier-Stokes equations, i.e.