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 porous media or Hele-Shaw cells produces a fingerlike interfacial pattern known as viscous fingering (VF). Classically, the dynamics of VF have been divided into two categories depending on whether the two fluids are fully miscible or immiscible. However, very recently, attention has been drawn to a third category of VF: 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 multiple droplets are suppressed and a viscous finger-dominated pattern in which the fingers are wider than those of the corresponding immiscible VF is formed under an intermediate flow rate. For a large flow rate, the typical finger width is similar to that of the corresponding immiscible VF. As a result, we identify a nonmonotonic relation between the finger width and the flow rate (or capillary number), which is not observed in fully miscible and immiscible systems and is a specific characteristic of partially miscible systems. We elucidate the mechanism behind these observations based on an area measurement of the less-viscous solution and a velocity measurement of the spontaneous movement 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, which are observed in the experiment with low and intermediate flow rate, and also show that the finger width becomes constant with Pe at high flow rates or seems to decrease with Pe, which implies that the increase in finger width can be suppressed with an increase in Pe. Moreover, the numerical simulation can support the validity of the mechanism discussed in the experimental part.