Pinch-off dynamics of droplet formation in microchannel flow

Abstract

This work explores droplet breakup dynamic and pinch-off for the two-phase flow through a microfluidic T-channel. A mathematical model includes three differential equations that have been solved using the finite element method in the squeezing and dripping regime for a wide range of interfacial tension (0.005<σcd<0.1), viscosity ratio (1<μr<20), flow rate ratios (2<qr<25), density factor (0.5<ρr,d<2), and contact angle (105°<θc<160°). Based on the evolution of the interface, the droplet formation stages are classified as filling, necking, and pinch-off. This study underlines that the interfacial tension and density of the dispersed phase are dominating parameters in determining the pinch-off stage. Interface evolution, pressure difference (Pd-Pc), the velocity of the dispersed phase in the neck section (ud) of the droplet thread, and droplet pinch-off time (td) are analyzed and discussed. The interface evolution in the neck region exhibits rapid transformations during the pinch-off stage, while negligible changes are observed in another segment of the droplet. In the region of the neck, pressure difference (Pd-Pc) abruptly increases. Moreover, the pressure difference (Pd-Pc)max reduction is inversely correlated with the Ca number. The evolution time of pinching is increased with decreasing the interfacial tension (σcd). The maximum positive velocity of the dispersed phase appears in the thread's neck section during the pinching process. It is located at the forward end of the neck. The maximum negative velocity of the dispersed phase is observed at the back end of the neck. Fluid dynamics during the pinch-off stage have been explored by total energy balancing and developed an analytical model to establish a relation between interfacial tension, density of dispersed phase, size of neck cross-section, and the pinch-off time (td∝ρd1/2,td∝1/σcd1/2, td∝lnr1/2). The results obtained through analytical and numerical methods for pinch-off time demonstrate satisfactory agreement.