Optimizing droplet coalescence dynamics in microchannels: A comprehensive study using response surface methodology...

Droplet coalescence in microchannels is a complex phenomenon influenced by various parameters such as droplet size, velocity, liquid surface tension, and droplet-droplet spacing. In this study, we thoroughly investigate the impact of these control parameters on droplet coalescence dynamics within a sudden expansion microchannel using two distinct numerical methods. Initially, we employ the boundary element method to solve the Brinkman integral equation, providing detailed insights into the underlying physics of droplet coalescence. Furthermore, we integrate Response Surface Methodology (RSM) to effectively optimize droplet coalescence dynamics, harnessing the power of machine learning algorithms. Our results showcase the efficacy of these computational techniques in enhancing experimental efficiency. Through rigorous evaluation utilizing Regression Coefficient and Mean Absolute Error metrics, we ascertain the accuracy of our estimations. Our findings highlight the significant influence of key parameters, specifically the non-dimensional initial distance of the droplets (D), viscosity ratio ( $$ ), Capillary number (Ca), and width (w), as identified by the non-dimensional final droplet-droplet spacing (DD), velocity of the first droplet (V_FD), and velocity of the second droplet (V_BD), respectively. This comprehensive approach provides valuable insights into droplet coalescence phenomena and offers a robust framework for optimizing microfluidic systems. The most influential parameters on DD are the values of A_d and D, while viscosity has the lowest influence on DD. The most influential parameters on droplet velocity are viscosity and channel width, whereas the initial distance and Ca have the least influence on droplet velocity. The comparison of different machine learning algorithms indicates that the best ones for predicting DD, V_FD, and V_BD are function, SMOreg, Lazy-IBK, and Meta-Bagging, respectively.