TY - JOUR
T1 - Gravitational drainage on a vertical substrate of a narrow width
AU - Xue, Nan
AU - Stone, Howard A.
N1 - Funding Information:
The authors thank Jens Eggers for reading the original manuscript and constructive discussions. The authors thank the anonymous referees for their valuable suggestions for improvement of the original manuscript. N.X. acknowledges Princeton University through a Charlotte Elizabeth Procter Fellowship.
Publisher Copyright:
©2022 American Physical Society
PY - 2022/1
Y1 - 2022/1
N2 - The effect of a single, vertical edge on a draining liquid film was studied recently [Phys. Rev. Lett. 125, 064502 (2020)PRLTAO0031-900710.1103/PhysRevLett.125.064502]. In this experimental study, we characterize the structure of a liquid film, draining due to gravity, on a vertical, narrow substrate. We show that surface tension affects the draining film at the two vertical edges. The edge effects propagate into the film to eventually influence the shape over the entire width. Interferometry is performed to measure the film thickness profile. A motorized stage is used to vertically translate the thin film and the substrate, which extends the range of the measurements. Our experiments show that the thickness of the liquid film scales with the well-known Jeffreys' solution, which is the thickness of a draining film on a vertical substrate of infinite width. However, due to the existence of the two vertical edges, near the top contact line, the film thickness changes sharply near the edges and is flat near the middle of the substrate. In contrast, away from the top contact line, the edge effects propagate towards the middle, and the overall horizontal film shape eventually becomes approximately quartic. Further, we identify characteristic length scales in the vertical direction, which combine the effects of the surface tension, viscosity, and gravitational drainage. These length scales, respectively, highlight the effects from the vertical edges and the top contact line, and the experimental results are in agreement with the scaling arguments.
AB - The effect of a single, vertical edge on a draining liquid film was studied recently [Phys. Rev. Lett. 125, 064502 (2020)PRLTAO0031-900710.1103/PhysRevLett.125.064502]. In this experimental study, we characterize the structure of a liquid film, draining due to gravity, on a vertical, narrow substrate. We show that surface tension affects the draining film at the two vertical edges. The edge effects propagate into the film to eventually influence the shape over the entire width. Interferometry is performed to measure the film thickness profile. A motorized stage is used to vertically translate the thin film and the substrate, which extends the range of the measurements. Our experiments show that the thickness of the liquid film scales with the well-known Jeffreys' solution, which is the thickness of a draining film on a vertical substrate of infinite width. However, due to the existence of the two vertical edges, near the top contact line, the film thickness changes sharply near the edges and is flat near the middle of the substrate. In contrast, away from the top contact line, the edge effects propagate towards the middle, and the overall horizontal film shape eventually becomes approximately quartic. Further, we identify characteristic length scales in the vertical direction, which combine the effects of the surface tension, viscosity, and gravitational drainage. These length scales, respectively, highlight the effects from the vertical edges and the top contact line, and the experimental results are in agreement with the scaling arguments.
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U2 - 10.1103/PhysRevFluids.7.014001
DO - 10.1103/PhysRevFluids.7.014001
M3 - Article
AN - SCOPUS:85123212166
SN - 2469-990X
VL - 7
JO - Physical Review Fluids
JF - Physical Review Fluids
IS - 1
M1 - 014001
ER -