Numerical study of the indentation formation of a compound droplet in a constriction

A compound droplet deforming in a constricted tube widely appears in drug delivery and microfluidic devices. In such a constriction, an indentation can present at the trailing surface of the droplet. However, this aspect has not been fully investigated and understood so far. This study focuses on the effects of some dimensionless parameters on the negative curvature, i.e., indentation, at the trailing surface of a compound droplet moving through a constricted tube. The presence of the constriction at the middle of the tube length enhances the droplet indentation. Numerical results were obtained for the capillary number Ca (varied in range of 0.1–1.0), the inner-to-outer droplet radius ratio R21 (varied in range of 0.2–0.9), the droplet-to-tube radius ratio R10 (varied in range of 0.2–0.9), the inner-to-outer interfacial tension coefficient ratio σ21 (varied in range of 0.1–6.4), and the normalized depth of the constriction d/R (varied in range of 0.0–0.8). The results reveal that the most influencing factor is Ca, increasing its value leads to the increment of the maximum indentation at the trailing surface of the inner and outer droplets. The indentation is also increased with increasing the value of R10 and d/R. In contrast, increasing R21 results in a decrease in the indentation at the trailing surface of the outer droplet. When increasing σ21, the indentation at the trailing surface of the inner one is quickly suppressed, while the outer droplet is minorly affected. We also point out the patterns of the trailing surface of the inner and outer droplets and their transitions from one to the other patterns in the diagrams based on these parameters.