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.

Effects of capillary number and flow rates on the hydrodynamics of droplet generation in T-junction microfluidic systems

“…The droplet detachment time ( dd ) shows a complex dependence on the flow rate ratio ( r ) and c . Such behaviour of dd is qualitatively consistent with the previous studies (Husny and Cooper-White, 2006;Nazari et al, 2018) for varied geometrical arrangements of the microfluidic devices. In particular, a smaller value of dd is favorable to produced mono-dispersed droplets of uniform size.…”

Three-Dimensional Mathematical Model of the Liquid Film Downflow on a Vertical Surface

“…Additionally, equations for determining the averaged film thickness, the averaged velocity vectors over the film thickness, the longitudinal and vertical velocity components, and the initial angle of streamline deviation from the vertical axis were analytically obtained.Energies 2020, 13, 1938 2 of 15 the fluid film movement, heat and mass transfer in column equipment, the separation of gas-liquid mixtures, and fluid flow in heat exchangers. Scientists for the above purpose have investigated the heat and mass transfer processes occurring in microchannels [3][4][5][6] and free and induced liquid film flow over different surfaces [7][8][9][10][11][12][13][14][15][16][17][18] and inside of different channels [19][20][21][22][23][24][25]. This flow occurs due to the influence of various forces, which determine the film formation or destruction, and the inclination angle of the surface.…”

“…This flow occurs due to the influence of various forces, which determine the film formation or destruction, and the inclination angle of the surface. At the same time, the developed mathematical models and correlation coefficients proposed for them should consider each of the above process features, and the possibility of changing the physical state of the flow components forms a liquid film (condensation, evaporation).The liquid film motion inside of microchannels was considered in [3][4][5][6] by the application of numerical and experimental methods as well as developing mathematical models. The research [3] describes the development of the criterion model for the prediction of the critical heat flux premature caused by periodic liquid film movement in microchannels.…”

“…The obtained results consider the mass exchange between two phases by numerical simulation for the case of laminar flow and multiphase VOF (volume of fluid) model with the indirect comparison between the numerical simulation and experimental results. The Lattice Boltzmann method (LBM) is commonly used for liquid flow motion in microchannels [5,6], especially in cases of studying hydrodynamic phenomena during the heat-mass transfer processes [6], which involve formation and breakup process of the liquid film in this channel type.Studies on falling film flow on vertical and angled surfaces have been carried out in [7-13] by experimental and numerical methods. These studies use the VOF model.…”

“…The liquid film motion inside of microchannels was considered in [3][4][5][6] by the application of numerical and experimental methods as well as developing mathematical models. The research [3] describes the development of the criterion model for the prediction of the critical heat flux premature caused by periodic liquid film movement in microchannels.…”