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Capillary droplets form due to surface tension when two immiscible fluids are mixed. We describe the motion of gravity-driven capillary droplets flowing through narrow constrictions and obstacle arrays in both simulations and experiments. Our new capillary deformable particle model recapitulates the shape and velocity of single oil droplets in water as they pass through narrow constrictions in microfluidic chambers. Using this experimentally validated model, we simulate the flow and clogging of single capillary droplets in narrow channels and obstacle arrays and find several important results. First, the capillary droplet speed profile is nonmonotonic as the droplet exits the narrow orifice, and we can tune the droplet properties so that the speed overshoots the terminal speed far from the constriction. Second, in obstacle arrays, we find that extremely deformable droplets can wrap around obstacles, which leads to decreased average droplet speed in the continuous flow regime and increased probability for clogging in the regime where permanent clogs form. Third, the wrapping mechanism causes the clogging probability in obstacle arrays to become nonmonotonic with surface tension Γ. At large Γ, the droplets are nearly rigid and the clogging probability is large since the droplets can not squeeze through the gaps between obstacles. With decreasing Γ, the clogging probability decreases as the droplets become more deformable. However, in the small-Γ limit, the clogging probability increases since the droplets are extremely deformable and wrap around the obstacles. The results from these studies are important for developing a predictive understanding of capillary droplet flows through complex and confined geometries.
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The obstacle problem in no-tension structures and cable nets
We consider the problem of finding a net that supports prescribed point forces, yet avoids certain obstacles, with all the elements of the net being under compression (or all being under tension), and being confined within a suitable bounding box. In the case of masonry structures, when described through the simple, no-tension constitutive model, this consists, for instance, in finding a strut net that supports the forces, is contained within the physical structure, and avoids regions that may be not accessible. We solve such a problem in the two-dimensional case, where the prescribed forces are applied at the vertices of a convex polygon, and we treat the cases of both single and multiple obstacles. By approximating the obstacles by polygonal regions, the task reduces to identifying the feasible domain in a linear programming problem. For a single obstacle we show how the region Γ available to the obstacle can be enlarged as much as possible in the sense that there is no other strut net, having a region Γ ′ available to the obstacle with Γ ⊂ Γ ′ . The case where some of the forces are reactive is also treated.
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- PAR ID:
- 10405894
- Date Published:
- Journal Name:
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Volume:
- 479
- Issue:
- 2269
- ISSN:
- 1364-5021
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1098/rspa.2022.0229
