Generalized correlation for predicting the droplet size in a microfluidic flow-focusing device under the effect of surfactant

This paper describes an investigation on the dynamic behavior of droplet formation in a microfluidic flow-focusing device (MFFD) under the effect of surfactant using a phase-field method and the Koterweg stress applied in Navier–Stokes equations. The effects of variously important parameters, such as capillary number (Ca0), water fraction (wf), the viscosity ratio (α), and particularly surfactant concentration (cb), were examined. Consequently, the numerical results match the experimental ones. Additionally, the droplet formation is significantly affected by the surfactant, and the droplet size decreases with increasing cb for the whole range of both wf and Ca0. Based on the extensive study, the phase diagrams with two main modes, namely, dropping and threading, are provided. A mountain shape of the dropping mode was found, and this mode can be extended for higher wf with the presence of surfactant. In particular, new generalized correlations as a function of wf, Ca0, and cb are first proposed for predicting quickly and effectively the droplet size. Furthermore, the droplet formation depends significantly on α. With the presence of surfactant, smaller size of the droplet forms and the threading mode occurs at very high α. The results obtained in this study are very useful for understanding the dynamic behavior of droplet formation in MFFDs, which can be used in potential applications such as biomedical and drug delivery systems.