Dynamics of step-emulsification: From a single to a collection of emulsion droplet generators

Abstract

Microfluidics has proven to be an efficient tool for making fine and calibrated emulsion droplets. The parallelization of drop makers is required for producing large amounts. Here, we investigate the generation of emulsion drops along a series of shallow microchannels emerging in a deep one, in other words the step-emulsification process. The dynamics of a single drop maker is first characterized as a function of interfacial tension and viscosities of both phases. The characteristic time scale of drop formation, namely, the necking time that finally sets drop size, is shown to be principally governed by the outer phase viscosity to interfacial tension ratio with a minor correction linked to the viscosity ratio. The step emulsification process experiences a transition of fragmentation regime where both the necking time and drop size suddenly raise. This transition, that corresponds to a critical period of drop formation and thus defines a maximum production rate of small droplets, is observed to be ruled by the viscosity ratio of the two phases. When drops are produced along an array of microchannels with a cross flow of the continuous phase, a configuration comparable to a one-dimensional membrane having rectangular pores, a drop boundary layer develops along the drop generators. In the small drop regime, the local dynamics of drop formation is shown to be independent on the emulsion cross flow. Moreover, we note that the development of the drop boundary layer is even beneficial to homogenize drop size along the production line. On the other hand, in the large drop regime, drop collision can trigger fragmentation and thus lead to size polydispersity.