Release of a trapped droplet in a single micro pore throat

The critical condition (i.e., critical capillary number Ca_c) for the release of trapped droplets is of practical importance in enhanced oil recovery and droplet microfluidics. In a recent study, Ca_c 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 Ca_c 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 Ca_c of both finite and long droplets. We find that Ca_c strongly depends on the droplet-to-channel size ratio (i.e., the droplet-to-convergent channel length ratio L/L_c). In particular, Ca_c increases with L/L_c for finite droplets (i.e., L/L_c < 1) but shows an opposite tendency for long droplets (i.e., L/L_c > 1), as demonstrated in previous studies. Via theoretical analysis, we established a predictive criterion for Ca_c versus L/L_c, and this criterion quantitatively agrees well with experimental data for both finite and long droplets.