We demonstrate conditions that give rise to cave-like features commonly found in dissolving cliffsides with a minimal two-phase physical model. Alcoves that are wider at the top and tapered at the bottom, with sharp-edged ceilings and sloping floors, are shown to develop on vertical solid surfaces dissolving in aqueous solvents. As evident from descending plumes, sufficiently large indentations evolve into alcoves as a result of the faster dissolution of the ceiling due to a solutal Rayleigh-Bénard density inversion instability. By contrast, defects of size below the boundary layer thickness set by the critical Rayleigh number smooth out, leading to stable planar interfaces. The ceiling recession rate and the alcove opening area evolution are shown to be given to first-order by the critical Rayleigh number. By tracking passive tracers in the fluid phase, we show that the alcoves are shaped by the detachment of the boundary layer flow and the appearance of a pinned vortex at the leading edge of the indentations. The attached boundary layer past the developing alcove is then found to lead to rounding of the other sides and the gradual sloping of the floor.

We investigate mucosalivary dispersal and deposition on horizontal surfaces corresponding to human exhalations with physical experiments under still-air conditions. Synthetic fluorescence tagged sprays with size and speed distributions comparable to human sneezes are observed with high-speed imaging. We show that while some larger droplets follow parabolic trajectories, smaller droplets stay aloft for several seconds and settle slowly with speeds consistent with a buoyant cloud dynamics model. The net deposition distribution is observed to become correspondingly broader as the source height $H$ is increased, ranging from sitting at a table to standing upright. We find that the deposited mucosaliva decays exponentially in front of the source, after peaking at distance $x = 0.71$\,m when $H = 0.5$\,m, and $x = 0.56$\,m when $H=1.5$\,m, with standard deviations $\approx 0.5$\,m. Greater than 99\% of the mucosaliva is deposited within $x = 2$\,m, with faster landing times {\em further} from the source. We then demonstrate that a standard nose and mouth mask reduces the mucosaliva dispersed by a factor of at least a hundred compared to the peaks recorded when unmasked.

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We investigate the development of mobility inversion and fingering when a granular suspension is injected radially between horizontal parallel plates of a cell filled with a miscible fluid. While the suspension spreads uniformly when the suspension and the displaced fluid densities are exactly matched, even a small density difference is found to result in a dense granular front which develops fingers with angular spacing that increase with granular volume fraction and decrease with injection rate. We show that the time scale over which the instability develops is given by the volume fraction dependent settling time scale of the grains in the cell. We then show that the mobility inversion and the non-equilibrium Korteweg surface tension due to granular volume fraction gradients determine the number of fingers at the onset of the instability in these miscible suspensions.

We demonstrate conditions that give rise to cave-like features commonly found in dissolving cliffsides with a minimal two-phase physical model. Alcoves that are wider at the top and tapered at the bottom, with sharp-edged ceilings and sloping floors, are shown to develop on vertical solid surfaces dissolving in aqueous solutions. As evident from descending plumes, sufficiently large indentations evolve into alcoves as a result of the faster dissolution of the ceiling due to a solutal Rayleigh-Bénard density inversion instability. By contrast, defects of size below the boundary layer thickness set by the critical Rayleigh number smooth out, leading to stable planar interfaces. The ceiling recession rate and the alcove opening area evolution are shown to be given to first order by the critical Rayleigh number. By tracking passive tracers in the fluid phase, we show that the alcoves are shaped by the detachment of the boundary layer flow and the appearance of a pinned vortex at the leading edge of the indentations. The attached boundary layer past the developing alcove is then found to lead to rounding of the other sides and the gradual sloping of the floor.