On the estimation of the size of a droplet emerging from a pore opening into a crossflow field.

The problem of terminating a droplet at the surface of a membrane in a crossflow field is an important topic in the context of controlled emulsification of fluids for use in pharmaceutical and other industries. Some of these industries struggle to produce emulsions of uniform sizes for their products requiring higher levels of precision. In this work, we comprehensively investigated one such technique in which droplets were produced membrane openings and were terminated a crossflow field. Conditions of permeation and termination were identified. A model was developed to estimate the size of the emerging droplets from information about the interfacial properties, geometry, and operating conditions (, pressure and crossflow velocity). Three forces, including capillary pressure, interfacial tension, and drag forces, were identified that account for a developed torque balance, which was then used to determine the onset of breakup of an emerging droplet. A comprehensive computational fluid dynamics (CFD) analysis has been conducted to highlight the physics involved in the process and also to provide scenarios for comparison exercises. The effects of crossflow velocity, applied pressure, and viscosity contrasts have been studied. It has been determined that the emerging droplet experiences deformation along the crossflow field because of the hydrodynamic drag. The receding portion of the contact line at the surface of the membrane wraps around the pore opening, generating an interfacial tension force that produces an opposing torque due to the crossflow drag and capillary pressure. Using this phenomenon, a framework for estimating the size of the droplet upon breakup is established. Comparisons with the results obtained from the CFD analysis under different conditions show very good agreement, which builds confidence in the modeling approach.