Lattice Boltzmann simulation of the trapping of a microdroplet in a well of surface energy

In this paper, a three-dimensional phase-field lattice Boltzmann method is used to simulate the dynamical behavior of a droplet, subject to an outer viscous flow, in a microchannel that contains a cylindrical hole etched into its top surface. The influence of the capillary number and the hole diameter (expressed as the ratio of hole diameter to channel height, b) is investigated. We demonstrate numerically that the surface energy gradient induced by the hole can create an anchoring force to resist the hydrodynamic drag from the outer flow, resulting in the droplet anchored to the hole when the capillary number is below a critical value. As b increases, the droplet can be anchored more easily. For b < 2, the droplet partially enters into the hole and forms a spherical cap; whereas for b > 2, the spherical cap of droplet reaches the top wall of the hole, making the hole depth into an additional important parameter. These observations are consistent with the previously reported experiments. However, the droplet does not fully fill the hole for b > 2, departing from the expectation of Dangla et al. [R. Dangla, S. Lee, C. N. Baroud, Trapping microfluidic drops in wells of surface energy, Phys. Rev. Lett. 107 (2011) 124501]. Also, it is observed in the anchored state that the rear of the droplet rests at a small distance away from the junction. Finally, the droplet undergoes a slow-down process only when its rear passes through the hole, regardless of b.