## 3 Results and Discussion
### Reverse Injection Displacement Pattern (Skim Milk Injected into Citric Acid)  
We also conducted experiments in which the displacing and displaced fluids were exchanged. The aqueous citric acid solution was first saturated in the Hele-Shaw cell as a displaced fluid, and skim milk was then injected as a displacing fluid. Figure 6 shows displacement patterns when the skim milk is injected into citric acid under different injection rates and citric acid concentrations. Stable displacement appears at a higher injection rate, whereas a higher citric acid concentration leads to displacement instability. The observed trend is similar to that when the fluid pair is not reversed. However, the displacement patterns are different. The growing front of the displacement pattern has a flower-like appearance of wide fingers. Such patterns might occur because of the asymmetry in the diffusion coefficients of the two mixing species. The precipitated casein likely has higher mobility in water (skim milk), reducing overall gel formation at the interface [18]. Resistance to finger widening was also reduced because there was a low amount of gel formation at the interface of the skim milk and aqueous citric acid solution.  
Figure 5: (**a**) Top view of displacement patterns when the gap widths are 0.4 and 0.8 mm and injection rates were varied from 15 to 50 mL/h. The volume of the injected aqueous citric acid solution is 2 mL. (**b**) Side view illustration of how the finger width changes with gap width \(b\). The sphere-like shape represents the aqueous citric acid solution.  
Gel formation occupies the whole skim milk, at a citric acid concentration of 15 wt%. The area displaced by skim milk appears smaller (colored area), even though the injection volume is the same. This result suggests that the water from the milk leaks into citric acid and appears transparent, whereas gel formation accumulates close to the injection source.  
To further confirm the mixing of water from milk with citric acid, additional experiments were performed by adding methyl red to the skim milk side. The displacement pattern when the skim milk was doped with the methyl red pH indicator is shown in Figure 7. The pink part is the mixing region where the water was contained in skim milk combined with the aqueous citric acid solution. This pink region is not observable in Figure 6; however, with the help of the methyl red pH indicator, this mixing region can be observed in Figure 7. The dark red indicates gel formation resulting from casein micelle precipitation. The dark red part spreads over the entire region of skim milk, which confirms that the precipitation of casein micelles is asymmetric and accumulated throughout the  
Figure 6: Displacement patterns when skim milk (pink) is injected into citric acid (white) upon injection rates of 15, 50, 150, and 500 mL/h and citric acid concentrations of 0.0 (pure water), 0.50, 1.5, 5.0, and 15 wt%. Images were taken when the injection volume was 2 mL, and the gap width \(b\) was 0.4 mm.  
skim milk. Even at a high citric acid concentration, with a large amount of gel formation, mixing between skim milk and citric acid occurs because the gel does not solidify at the interface. Therefore, it can be inferred that the asymmetry of gel formation greatly affected the different displacement patterns between the reversed injection and direct injection experiments.