Release of a trapped droplet in a single micro pore throat

Abstract The critical condition (i.e., critical capillary number Cac) for the release of trapped droplets is of practical importance in enhanced oil recovery and droplet microfluidics. In a recent study, Cac was obtained for a long droplet with a size much larger than the channel size. However, in real applications, trapped droplets are often finite with a size comparable to the channel, in which capillary and hydrostatic pressures alternate significantly. We hypothesize that Cac of finite droplets has a discrepancy from that of long droplets. Microfluidic experiments were performed to obtain the critical condition for the release of a finite droplet trapped in a single pore throat. A theoretical prediction via analyzing capillary and hydrostatic pressures was derived for Cac of both finite and long droplets. We find that Cac strongly depends on the droplet-to-channel size ratio (i.e., the droplet-to-convergent channel length ratio L/Lc). In particular, Cac increases with L/Lc for finite droplets (i.e., L/Lc   1), as demonstrated in previous studies. Via theoretical analysis, we established a predictive criterion for Cac versus L/Lc, and this criterion quantitatively agrees well with experimental data for both finite and long droplets.