Numerical study of freezing efficiency for a moving droplet in the microchannel

Abstract: In microfluidic devices, droplets serving as carriers for chemical reactors or biomass can form stably encapsulated particles during the freezing process, holding significant importance in pharmaceuticals and microchemical reaction control. This study couples the Volume of Fluid (VOF) method with an enthalpy-porous media phase change model to distinguish the water (ice)-oil two-phase system and the water-ice two-phase system, respectively.The simulation reveals two distinct solidification patterns: Pattern I exhibits a uniform and symmetric pattern, occurring at lower Reynolds numbers (Re) or droplet-to-channel diameter ratios (D/W), resulting in a relatively even solid shell along the interface with synchronized solidification fronts in both flow and spanwise directions, dominated by heat conduction. Pattern II shows a shear-constraint cooperative non-uniform pattern at higher Reynolds numbers and D/W ratios, where flow dynamics and spatial confinement couple, leading to faster solidification at the tail region and an asymmetric solidification front. Through comprehensive analysis of the numerical results, we derived the characteristic behavior of the Stefan number (Ste), Reynolds number (Re), and D/W ratios on the freezing time. We established a unified scaling relation for the freezing time: t_\text{final}\sim18.02 S t e^{-0.91}{ Re }^{-0.12} (D / W)^{1.42}. The results demonstrates that increasing Stefan number and Reynolds number shortens the freezing time, whereas increasing droplet D/W ratio extends it. Furthermore, the fitted coefficients reveals that temperature and droplet size exert a more pronounced influence on droplet freezing. Our results demonstrate good consistency with those in the literature, while indeed incorporating the effects of motion, which represents a novel aspect.