Dynamics of droplets on cones: Self-propulsion due to curvature gradients
We study the dynamics of droplets driven by a gradient of curvature, as may be achieved by placing a drop on the surface of a cone. The curvature gradient induces a pressure gradient within the drop, which in turn leads to spontaneous propulsion of the droplet. To investigate the resulting driving f...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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Royal Society of Chemistry
2019
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| _version_ | 1826256683292164096 |
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| author | McCarthy, J Vella, D Castrejón-Pita, A |
| author_facet | McCarthy, J Vella, D Castrejón-Pita, A |
| author_sort | McCarthy, J |
| collection | OXFORD |
| description | We study the dynamics of droplets driven by a gradient of curvature, as may be achieved by placing a drop on the surface of a cone. The curvature gradient induces a pressure gradient within the drop, which in turn leads to spontaneous propulsion of the droplet. To investigate the resulting driving force we perform a series of experiments in which we track a droplet's displacement, s, from the apex of a cone whose surface is treated to exhibit near-zero pinning effects. We find an s ∼ t1/4 scaling at sufficiently late times t. To shed light upon these dynamics, we perform an asymptotic calculation of the equilibrium shape of a droplet on a weakly curved cylinder, deriving the curvature-induced force responsible for its propulsion. By balancing this driving force with viscous dissipation, we recover a differential equation for the droplet displacement, whose predictions are found to be in good agreement with our experimental results. |
| first_indexed | 2024-03-06T18:06:07Z |
| format | Journal article |
| id | oxford-uuid:017b6508-8d2c-4536-ad2b-8c03a9118aef |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T18:06:07Z |
| publishDate | 2019 |
| publisher | Royal Society of Chemistry |
| record_format | dspace |
| spelling | oxford-uuid:017b6508-8d2c-4536-ad2b-8c03a9118aef2022-03-26T08:35:13ZDynamics of droplets on cones: Self-propulsion due to curvature gradientsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:017b6508-8d2c-4536-ad2b-8c03a9118aefEnglishSymplectic Elements at OxfordRoyal Society of Chemistry2019McCarthy, JVella, DCastrejón-Pita, AWe study the dynamics of droplets driven by a gradient of curvature, as may be achieved by placing a drop on the surface of a cone. The curvature gradient induces a pressure gradient within the drop, which in turn leads to spontaneous propulsion of the droplet. To investigate the resulting driving force we perform a series of experiments in which we track a droplet's displacement, s, from the apex of a cone whose surface is treated to exhibit near-zero pinning effects. We find an s ∼ t1/4 scaling at sufficiently late times t. To shed light upon these dynamics, we perform an asymptotic calculation of the equilibrium shape of a droplet on a weakly curved cylinder, deriving the curvature-induced force responsible for its propulsion. By balancing this driving force with viscous dissipation, we recover a differential equation for the droplet displacement, whose predictions are found to be in good agreement with our experimental results. |
| spellingShingle | McCarthy, J Vella, D Castrejón-Pita, A Dynamics of droplets on cones: Self-propulsion due to curvature gradients |
| title | Dynamics of droplets on cones: Self-propulsion due to curvature gradients |
| title_full | Dynamics of droplets on cones: Self-propulsion due to curvature gradients |
| title_fullStr | Dynamics of droplets on cones: Self-propulsion due to curvature gradients |
| title_full_unstemmed | Dynamics of droplets on cones: Self-propulsion due to curvature gradients |
| title_short | Dynamics of droplets on cones: Self-propulsion due to curvature gradients |
| title_sort | dynamics of droplets on cones self propulsion due to curvature gradients |
| work_keys_str_mv | AT mccarthyj dynamicsofdropletsonconesselfpropulsionduetocurvaturegradients AT vellad dynamicsofdropletsonconesselfpropulsionduetocurvaturegradients AT castrejonpitaa dynamicsofdropletsonconesselfpropulsionduetocurvaturegradients |