Fundamental understanding of two-phase flow and the concomitant implications of wall wettability and viscosity are critical in areas like microfluidics and lab on chip applications. In this work, numerical investigation of the displacement of two immiscible fluids in a T-junction is presented. The study reveals the interplay of critical physicochemical determinants like capillarity, viscosity, and wettability on the dynamics of two-phase flow. Temporal evolution of the displacement of dispersed phase resulting into different regimes like squeezing, dripping, necking, droplet formation, and jetting for a combination of capillary numbers, viscosity ratios, and wettability scenarios is furnished in detail in order to elucidate the mechanism of droplet formation through the displacement behavior of two-phase flow. The findings establish the surface wettability to be the dominating factor in determining the time evolution of the dispersed liquid interface at a lower capillary number. With the increase in the hydrophobicity of the surface, the liquid interface transits from squeezing to dripping and then to droplet formation at a low capillary number. However, irrespective of wettability, the regime changes from jetting to parallel flows due to an increase in capillary number beyond a critical limit. Furthermore, the phenomenon of squeezing, necking, and breakage occurs relatively earlier with the increase in viscosity ratio and hydrophobicity of the surface. These results may bear significant implications toward designing of droplet dispensing systems with the substrate wettability as a critical controlling parameter.

We investigate the dynamics of two immiscible fluids in a cross-junction via three-dimensional numerical simulations using the volume of fluid approach to track the dispersed phase's evolution. Different regimes, namely the dripping, squeezing, and jetting dynamics, have been observed for different dimensionless parameters, and we unveil a transition in regimes due to the concomitant interplay of capillarity, viscosity, and wettability. Our results reveal that hydrophobic channel surfaces favor a transition from squeezing to dripping behavior at a lower value of the capillary number. Moreover, higher viscosity ratios advance the process of squeezing, necking, and breakage on hydrophobic surfaces. A wettability–capillarity regime map is also presented that will have significant implications regarding the choice of substrate wettability, fluid properties, and flow rate in droplet dispensing devices.

Inertia has always proven to be a key parameter in controlling regime transitions when simple drops impact a liquid surface. However, the scenario of compound drops impacting a liquid surface has received the least attention, and poses the question of whether any factor besides inertia can act as a switching criterion for regime transition. Through axisymmetric two-dimensional volume-of-fluid based computations of a compound drop falling with a certain velocity in a liquid pool, we demonstrate a non-trivial switching from jetting to large bubble entrapment phenomenon by decreasing the radius ratio of the compound drop, under identical inertial condition. Six different regimes that can be categorized into fundamental regimes of pre-jetting, jetting, transition, and bubble entrapment are mapped on the radius ratio–Weber number plane. Hence, with a suitable combination of radius ratio and impact velocity, the interplay of inertia and buoyancy forces can be exploited to achieve the final outcome of a secondary drop or an entrapped bubble. Our results reveal that the strength of buoyancy force decreases with decrease in the radius ratio of compound drops and, as a result, the intervening physics changes from crater expansion to wave swell retraction and finally to roll jet formation with decrease in radius ratio. These results are further explained in light of capillary wave propagation and vortex formation and may turn out to be of immense consequence in providing insight into the underlying complex physical mechanisms dictating intricate control on compound drop impact events.