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Speed of rolling droplets

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Title: Speed of rolling droplets
Authors: Yariv, E
Schnitzer, O
Item Type: Journal Article
Abstract: We analyze the near-rolling motion of two-dimensional nonwetting drops down a gently inclined plane. Inspired by the scaling analysis of Mahadevan & Pomeau [Phys. Fluids 11, 2449 (1999)], we focus upon the limit of small Bond numbers, B≪1, where the drop shape is nearly circular and the internal flow is approximately a rigid-body rotation except close to the flat spot at the base of the drop. Our analysis reveals that the leading-order dissipation is contributed by both the flow in the flat-spot region and the correction to rigid-body rotation in the remaining liquid domain. The resulting leading-order approximation for the drop velocity U is given by We analyze the near-rolling motion of two-dimensional nonwetting drops down a gently inclined plane. Inspired by the scaling analysis of Mahadevan & Pomeau [Phys. Fluids 11, 2449 (1999)], we focus upon the limit of small Bond numbers, B≪1, where the drop shape is nearly circular and the internal flow is approximately a rigid-body rotation except close to the flat spot at the base of the drop. Our analysis reveals that the leading-order dissipation is contributed by both the flow in the flat-spot region and the correction to rigid-body rotation in the remaining liquid domain. The resulting leading-order approximation for the drop velocity U is given by We analyze the near-rolling motion of two-dimensional nonwetting drops down a gently inclined plane. Inspired by the scaling analysis of Mahadevan & Pomeau [Phys. Fluids 11, 2449 (1999)], we focus upon the limit of small Bond numbers, B≪1, where the drop shape is nearly circular and the internal flow is approximately a rigid-body rotation except close to the flat spot at the base of the drop. Our analysis reveals that the leading-order dissipation is contributed by both the flow in the flat-spot region and the correction to rigid-body rotation in the remaining liquid domain. The resulting leading-order approximation for the drop velocity U is given by μUγ∼α2Bln1B, wherein μ is the liquid viscosity, γ the interfacial tension and α the inclination angle.
Issue Date: 3-Sep-2019
Date of Acceptance: 12-Aug-2019
URI: http://hdl.handle.net/10044/1/72842
DOI: https://dx.doi.org/10.1103/PhysRevFluids.4.093602
ISSN: 2469-990X
Publisher: American Physical Society
Journal / Book Title: Physical Review Fluids
Volume: 4
Copyright Statement: ©2019 American Physical Society
Keywords: Science & Technology
Physical Sciences
Physics, Fluids & Plasmas
Physics
Publication Status: Published
Article Number: ARTN 093602
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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