Calculating the volume of elongated bubbles and droplets in microchannels from a top view image

Abstract

We present a theoretical model to calculate the volume of non-wetting bubbles and droplets in segmented microflows from given dimensions of the microchannel and measured lengths of bubbles and droplets. Despite the importance of these volumes in interpreting experiments on reaction kinetics and transport phenomena, an accurate model like the one we present here did not yet exist. The model has its theoretical basis in the principle of interfacial energy minimization and is set up such that volume calculations are possible for a wide variety of channel geometries. We successfully validated our model with the 3D numerical energy minimization code SURFACE EVOLVER for the three most commonly used channel geometries in the field of microfluidics and provide accurate user-friendly equations for these geometries.