Different stages of liquid film growth in a microchannel: Two-phase lattice boltzmann study

Abstract

A free energy model is used to describe the droplet formation and break-up process in a T-junction bio-microchannel. Droplets are created as a result of interaction of two immiscible liquids. Different stages for the droplet formation process are analyzed which are: a) growing in the x and y directions, b) growing in the x direction and c) detachment process. The effects of capillary number and flow rate ratio on the droplet formation stages are also studied. The influences of Capillary number, flow rate ratio, viscosity ratio and geometrical parameters on droplet break up, droplet size and detachment time are systematically studied. By increasing the flow rate ratio; the duration of droplet formation and the length of the x-growth stage are decreased for small capillary numbers. For larger capillary numbers; the droplet penetrates toward the downstream; therefore, the length of the x-growth stage is increased. The start of detachment process in the microchannel is also reported, which is related to narrowing of the neck of the liquid film. The results show that the detachment time is increased by decreasing the Capillary number. For Ca>0.02, the detachment time is independent of the flow rate ratios. Moreover; the effects of viscosity ratios on detachment time are not significant in comparison to the effects of capillary number. For Ca<0.04, the size of the droplet is independent of the viscosity ratio, but after the critical Capillary number (i.e., Ca=0.04), the size of the droplet is varied by the viscosity ratio. The time between two consecutive drops is also decreased by increasing the Capillary number. Moreover, this time is decreased by increasing the flow rate ratio until Ca=0.04. After this Capillary number, the flow rate ratios have no significant effect on the time between two consecutive droplets. An exhaustive validation study is performed including (a) the Laplace equation in the stationary droplet; (b) a contact angle test; (c) Taylor deformation test in shear flow and (d) comparison of the droplet length as a function of flow rate ratio between the present work and other studies.