TY - JOUR
T1 - Draining and spreading along geometries that cause converging flows
T2 - Viscous gravity currents on a downward-pointing cone and a bowl-shaped hemisphere
AU - Xue, Nan
AU - Stone, Howard A.
N1 - Publisher Copyright:
© 2021 American Physical Society.
PY - 2021/4
Y1 - 2021/4
N2 - When a viscous liquid is released on an inclined solvophilic substrate, it spreads downwards by gravity and tends to coat the substrate. Here we report the gravitational axisymmetric spreading of a viscous liquid with a fixed volume on inclined geometries that cause converging flows, for example, on the inside of a downward-pointing hollow cone (funnel) and the lower part of a sphere (bowl). For the limit that the effect of surface tension is negligible, we analytically determine the thickness profile as well as the time-dependent position of the front of the spreading liquid. In the typical scenario that a liquid spreads on a geometry such as an inclined plate, the thickness of the front of the spreading liquid monotonically decreases in time throughout the spreading and a fingering instability occurs while the liquid film thins. However, we show that on an inclined geometry, where convergence of the flow occurs, the thickness of the spreading front first decreases in time and then increases. We also predict a critical volume Vc such that a fingering instability occurs if the volume of the spreading liquid is less than Vc. Experiments of axisymmetric spreading on a downward-pointing cone (funnel) are then performed and the measured position of the front and the critical liquid volume of the fingering instability agree with our theoretical predictions. This study highlights the effect of a geometry that focuses and thickens a thin film.
AB - When a viscous liquid is released on an inclined solvophilic substrate, it spreads downwards by gravity and tends to coat the substrate. Here we report the gravitational axisymmetric spreading of a viscous liquid with a fixed volume on inclined geometries that cause converging flows, for example, on the inside of a downward-pointing hollow cone (funnel) and the lower part of a sphere (bowl). For the limit that the effect of surface tension is negligible, we analytically determine the thickness profile as well as the time-dependent position of the front of the spreading liquid. In the typical scenario that a liquid spreads on a geometry such as an inclined plate, the thickness of the front of the spreading liquid monotonically decreases in time throughout the spreading and a fingering instability occurs while the liquid film thins. However, we show that on an inclined geometry, where convergence of the flow occurs, the thickness of the spreading front first decreases in time and then increases. We also predict a critical volume Vc such that a fingering instability occurs if the volume of the spreading liquid is less than Vc. Experiments of axisymmetric spreading on a downward-pointing cone (funnel) are then performed and the measured position of the front and the critical liquid volume of the fingering instability agree with our theoretical predictions. This study highlights the effect of a geometry that focuses and thickens a thin film.
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U2 - 10.1103/PhysRevFluids.6.043801
DO - 10.1103/PhysRevFluids.6.043801
M3 - Article
AN - SCOPUS:85105476761
SN - 2469-990X
VL - 6
JO - Physical Review Fluids
JF - Physical Review Fluids
IS - 4
M1 - 043801
ER -