Modeling and simulation of the penetration of a compound droplet into a throat in a pore-throat structure

We present a theoretical and numerical study of a compound droplet flowing through a single pore-throat structure. By quantifying the capillary pressures in the pore and throat under various geometrical conditions, we derive a theoretical model to predict whether the compound droplet is able to penetrate into the throat in a pore-throat structure. Meanwhile, the lattice Boltzmann simulations are conducted to assess the capability and accuracy of the theoretical model. Through a combination of theoretical analysis and lattice Boltzmann simulations, we then investigate the effect of inner droplet size, compound droplet size, and surface wettability on the invasion behavior of a compound droplet. The results show that with increasing the inner droplet size or the compound droplet size, the compound droplet undergoes the transition from the state where the entire compound droplet can pass through the throat to the state where only a part of outer droplet penetrates into and blocks the throat. Although the theoretical predictions show good agreement with the simulation results for most of the cases investigated, it is found that the proposed theoretical model is not applicable to the cases in which the droplets are intermediate-wetting or wetting to the solid surface. This is because the shape of newly formed interface in the pore significantly deviates from the initial circle, which violates the assumption made in the derivation of the theoretical model.