Geometric influence of width ratio and contraction ratio on droplet dynamics in microchannel using a 3D numerical simulation

Microchannel geometry is an important factor in determining droplet dynamics in droplet-based microfluidic systems, much like fluid properties and flow conditions. In this context, two important geometric parameters—the contraction ratio ($C_{\mathrm{II}}$) and the width ratio ($C_I$)—that are limited to particular value ranges are taken into consideration for evaluation. These parameters interact with the capillary number ($\mathrm{Ca}$) and viscosity ratio ($\lambda$) to affect different aspects of droplet migration and manipulation, such as trap and squeeze regimes. A theoretical model is proposed, and a three-dimensional numerical simulation method is used in this work. This model predicts the change from trap to squeeze, which is caused by the interaction of the previously mentioned variables. Interestingly, an inverse correlation exists between the width ratio and the critical capillary number for this transition, which is determined as $\mathrm{Ca}\ge f(\lambda ,C_{\mathrm{II}})/C_I$. Furthermore, the investigation explores the droplet elongation and velocity ratio during their passage through the microchannel. By matching input parameters with microchannel geometry, this information may be useful for the design of microfluidic systems, which would facilitate the careful control and manipulation of droplets.