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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. 

Distributions of strictly positive numbers are common and can be characterized by standard statistical measures such as mean, standard deviation, and skewness. We demonstrate that for these distributions the skewnessD₃is bounded from below by a function of the coefficient of variation (CoV) δ as D₃ > δ − 1/δ. The results are extended to any distribution that is bounded with minimum value x_min and/or bounded with maximum value x_max. We build on the results to provide bounds for kurtosis D₄, and conjecture analogous bounds exists for higher statistical moments. 

Abstract Wind-blown dust plays a critical role in numerous geophysical and biological systems, yet current models fail to explain the transport of coarse-mode particles (>5 μm) to great distances from their sources. For particles larger than a few microns, electrostatic effects have been invoked to account for longer-than-predicted atmospheric residence times. Although much effort has focused on elucidating the charging processes, comparatively little effort has been expended understanding the stability of charge on particles once electrified. Overall, electrostatic-driven transport requires that charge remain present on particles for days to weeks. Here, we present a set of experiments designed to explore the longevity of electrostatic charge on levitated airborne particles after a single charging event. Using an acoustic levitator, we measured the charge on particles of different material compositions suspended in atmospheric conditions for long periods of time. In dry environments, the total charge on particles decayed in over 1 week. The decay timescale decreased to days in humid environments. These results were independent of particle material and charge polarity. However, exposure to UV radiation could both increase and decrease the decay time depending on polarity. Our work suggests that the rate of charge decay on airborne particles is solely determined by ion capture from the air. Furthermore, using a one-dimensional sedimentation model, we predict that atmospheric dust of order 10 μm will experience the largest change in residence time due to electrostatic forces.