Hydrodynamics of a droplet passing through a microfluidic T-junction

We develop a phase-field multiphase lattice Boltzmann model to systematically investigate the dynamic behaviour of a droplet passing through a microfluidic T-junction, especially focusing on the non-breakup of the droplet. Detailed information on the breakup and non-breakup is presented, together with the quantitative evolutions of driving and resistance forces as well as the droplet deformation characteristics involved. Through comparisons between cases of non-breakup and breakup, we find that the appearance of tunnels (the lubricating film between droplet and channel walls) provides a precondition for the final non-breakup of droplets, which slows down the droplet deformation rate and even induces non-breakup. The vortex flow formed inside droplets plays an important role in determining whether they break up or not. In particular, when the strength of vortex flow exceeds a critical value, a droplet can no longer break up. Additionally, more effort has been devoted to investigating the effects of viscosity ratio between disperse and continuous phases and width ratio between branch and main channels on droplet dynamic behaviours. It is found that a large droplet viscosity results in a small velocity gradient in a droplet, which restricts vortex generation and thus produces lower deformation resistance. Consequently, it is easier to break up a droplet with larger viscosity. Our work also reveals that a droplet in small branch channels tends to obstruct the channels and have small vortex flows, which induces easier breakup too. Eventually, several phase diagrams for droplet flow patterns are provided, and the corresponding power-law correlations ($l_{0}/w=\unicode[STIX]{x1D6FD}Ca^{b}$, where $l_{0}/w$ is dimensionless initial droplet length and $Ca$ is capillary number) are fitted to describe the boundaries between different flow patterns.