Comprehensive Analysis and CFD Modeling of Slug and Detachment Length in the T-Junction Micro-Channel Using RSM

This study employs mathematical modeling and Computational Fluid Dynamics (CFD) to investigate the impact of contact angle, flow rate, and surface tension on slug and detachment length in a T-junction microchannel. The simulation focuses on creating a microdroplet at the center of the microchannel, surrounded by the continuous phase, exploring various flow patterns. Response Surface Methodology (RSM) is utilized to model two responses: the detachment length of slugs and the slug length. Three independent factors—Weber number in the dispersed phase (Wed), capillary number in the continuous phase (Cac), and contact angle (θ)—are considered at different levels based on CFD calculations. The Central Composite Design (CCD) is employed for experimental design, and 186 simulations are conducted to predict slug and detachment length. Furthermore, two quadratic correlations, Equations (12) and (13), with R2 values of 0.9780 and 0.9273, were developed, representing slug length and detachment length, respectively. These correlations are crucial for optimizing microfluidic device design and operation and by accurately predicting outcomes under different conditions, these equations help fine-tune systems for better efficiency and reliability. In conclusion, our study bridges gaps in understanding slug behavior within microchannels and offers insights into optimizing microfluidic systems through mathematical modeling and CFD simulations.