Pattern transitions and nonmonotonic changes in finger width due to the flow rate in partially miscible viscous fingering

The displacement of a viscous fluid by another less viscous fluid in Hele-Shaw cells produces a finger-like pattern known as viscous fingering (VF). In addition to the immiscible and fully miscible systems, a third category of VF has drawn the attention: VF in partially miscible systems. Our previous experimental study showed that the VF pattern in a partially miscible system transforms into a multiple droplet pattern due to phase separation and that the droplets spontaneously move. Here, we experimentally investigate the effect of the flow rate on VF in a partially miscible system. We show that droplets are suppressed and a VF-dominated pattern in which the fingers are wider than those of the immiscible VF is formed under an intermediate flow rate. For a large flow rate, the typical finger width is similar to that of the immiscible VF. As a result, we identify a non-monotonic relation between the finger width and the flow rate. We elucidate the mechanism based on an area measurement of the less viscous solution and a velocity measurement of the droplets. In addition, a numerical simulation for VFs in the partially miscible system can reproduce the suppression of the droplet formation and the finger widening and show that the finger width becomes constant or decreases with Pe, which implies that the increase in finger width can be suppressed with an increase in Pe. Therefore, the numerical results support the experimental ones.