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 ( μ ), Capillary number (Ca), and width (w), as identified by the non-dimensional final droplet-droplet spacing (DD), velocity of the first droplet (VFD), and velocity of the second droplet (VBD), 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 Ad 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, VFD, and VBD are function, SMOreg, Lazy-IBK, and Meta-Bagging, respectively.

Department of Mechanical Engineering University of Gonabad Gonabad Iran

Department of Physics Shiraz University of Technology Shiraz 71555 313 Iran

Faculty of Mechanical Engineering Tarbiat Modares University Tehran 141171 3116 Iran

Faculty of Mechatronics Informatics and Interdisciplinary Studies Technical University of Liberec Liberec Czech Republic

Institute for Nanomaterials Advanced Technologies and Innovation Technical University of Liberec 46117 Liberec Czech Republic

Institute of Ship Technology Ocean Engineering and Transport Systems University of Duisburg Essen 47057 Duisburg Germany

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