(149i) Boundary Integral Simulations of Dissolving Drops Flowing through Circular Tubes

Recent years have seen an upsurge in the literature reporting the microfluidic measurement of the kinetics of ‘fast’ gas-liquid reactions (e.g.CO₂ and switchable solvents), by recording the shrinkage of bubbles in segmented flows of these gas-liquid combinations in microfluidic channels.  A critical aspect of the deconvolution of bubble shrinkage data to deduce dissolution and kinetic constants is the knowledge of how dissolution influences the velocity field in the liquid slug, and hence, the mass transport characteristics.  While there have been extensive studies of the flow characteristics in liquid slugs segmented by undissolving bubbles, there is no literature on the corresponding problem with dissolving ones.

This research examines the dissolution of drops confined in a tube using a boundary integral method (a bubble, which is a drop with low viscosity, would be a special case of this study).  Drop dissolution is modeled using an interfacial mass balance as a discontinuity of the normal components of the inner and outer fluid velocities at the drop interface.  The effects of the dissolution rate on the film thickness and the inter-drop separation distance are examined as a function of the capillary number and the viscosity ratio.  The results demonstrate that depending on the dissolution rate, the degree of mixing can change appreciably from one slug to the next.  A curious result is that the film thickness and the droplet separation distance can change significantly beyond a critical capillary number, producing flow patterns within a liquid slug that are completely different from those known for the undissolving bubble case.   These flow patterns have the potential to reduce the length scale for diffusion within a slug and improve mixing.  However, they also induce cross-talk between adjacent liquid slugs and complicate data interpretation. These results will ultimately guide the selection of operating regimes that enable convenient interpretation of data from reacting gas-liquid segmented flows to obtain kinetic constants.