Computational analysis of interface evolution and droplet pinch-off mechanism in two-phase liquid flow through T-junction microfluidic system

Abstract: This work has explored interface evolution and pinch-off mechanism of the droplet formation in two-phase flow through cross-flow microfluidic device. The two-dimensional mathematical model equations have been solved using the finite element method under the squeezing regime ($Ca_c < 10^{-2}$) for wide range of flow rates ($Qr = 0.1 - 10$) and fixed contact angle ($\theta=135^o$). The droplet formation process has been classified into various instantaneous stages as initial, filling, squeezing, pinch-off and stable droplet through microscopic visualization of interface evolution in phase profiles. The dynamics of interface, and point pressure in both phases is further gained and discussed. Maximum pressure in the continuous phase varied linearly with Qr. The droplet pinch-off mechanism has been thoroughly elucidated by determining the local radius of the curvature ($R_{c,min}$) and neck width (2r) during the squeezing and pinch-off stages. At the pinch-off point, both $R_{c,min}$ and 2r are non-linearly related to Qr. Further, the topological dynamics of interface has been explored by analyzing the Laplace pressure ($p_{\text{L}}$), acting on the interface curvature, evaluated using (a) pressure sensors in both phases, (b) local radius of curvature, and (c) minimum radius of curvature. The insights obtained from the present work can reliably be used in designing the model and prototypes of microfluidic devices for generating monodispersed droplets in emulsions, and the droplet breakup mechanism would help accurate prediction of the pinch-off moment. The proposed knowledge provides detailed insights of the interface evolution and droplet pinch-off to a precision of 10 $\mu$s and resolution of 10 $\mu$m, equivalent to experimental flow visualization with a high-speed ($10^{5}$ fps) and high-resolution (10 $\mu$m pixel size) camera.