Longitudinal thermocapillary slip about a dilute periodic mattress of protruding bubbles
A common realization of superhydrophobic surfaces comprises of a periodic array of cylindrical bubbles which are trapped in a periodically grooved solid substrate. We consider the thermocapillary animation of liquid motion by a macroscopic temperature gradient which is longitudinally applied over su...
| Κύριοι συγγραφείς: | , |
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| Μορφή: | Journal article |
| Γλώσσα: | English |
| Έκδοση: |
Oxford University Press
2021
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| _version_ | 1826307549237870592 |
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| author | Yariv, E Kirk, TL |
| author_facet | Yariv, E Kirk, TL |
| author_sort | Yariv, E |
| collection | OXFORD |
| description | A common realization of superhydrophobic surfaces comprises of a periodic array of cylindrical bubbles which are trapped in a periodically grooved solid substrate. We consider the thermocapillary animation of liquid motion by a macroscopic temperature gradient which is longitudinally applied over such a bubble mattress. Assuming a linear variation of the interfacial tension with the temperature, at slope $\sigma _T$, we seek the effective velocity slip attained by the liquid at large distances away from the mattress. We focus upon the dilute limit, where the groove width $2c$ is small compared with the array period $2l$. The requisite velocity slip in the applied-gradient direction, determined by a local analysis about a single bubble, is provided by the approximation $$\begin{align*}& \pi \frac{G\sigma_T c^2}{\mu l} I(\alpha), \end{align*}$$wherein $G$ is the applied-gradient magnitude, $\mu $ is the liquid viscosity and $I(\alpha )$, a non-monotonic function of the protrusion angle $\alpha $, is provided by the quadrature, $$\begin{align*}& I(\alpha) = \frac{2}{\sin\alpha} \int_0^\infty\frac{\sinh s\alpha}{ \cosh s(\pi-\alpha) \sinh s \pi} \, \textrm{d} s. |
| first_indexed | 2024-03-07T07:04:47Z |
| format | Journal article |
| id | oxford-uuid:724698e1-50e9-4912-adf0-785c11f79915 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:04:47Z |
| publishDate | 2021 |
| publisher | Oxford University Press |
| record_format | dspace |
| spelling | oxford-uuid:724698e1-50e9-4912-adf0-785c11f799152022-04-22T07:51:14ZLongitudinal thermocapillary slip about a dilute periodic mattress of protruding bubblesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:724698e1-50e9-4912-adf0-785c11f79915EnglishSymplectic ElementsOxford University Press2021Yariv, EKirk, TLA common realization of superhydrophobic surfaces comprises of a periodic array of cylindrical bubbles which are trapped in a periodically grooved solid substrate. We consider the thermocapillary animation of liquid motion by a macroscopic temperature gradient which is longitudinally applied over such a bubble mattress. Assuming a linear variation of the interfacial tension with the temperature, at slope $\sigma _T$, we seek the effective velocity slip attained by the liquid at large distances away from the mattress. We focus upon the dilute limit, where the groove width $2c$ is small compared with the array period $2l$. The requisite velocity slip in the applied-gradient direction, determined by a local analysis about a single bubble, is provided by the approximation $$\begin{align*}& \pi \frac{G\sigma_T c^2}{\mu l} I(\alpha), \end{align*}$$wherein $G$ is the applied-gradient magnitude, $\mu $ is the liquid viscosity and $I(\alpha )$, a non-monotonic function of the protrusion angle $\alpha $, is provided by the quadrature, $$\begin{align*}& I(\alpha) = \frac{2}{\sin\alpha} \int_0^\infty\frac{\sinh s\alpha}{ \cosh s(\pi-\alpha) \sinh s \pi} \, \textrm{d} s. |
| spellingShingle | Yariv, E Kirk, TL Longitudinal thermocapillary slip about a dilute periodic mattress of protruding bubbles |
| title | Longitudinal thermocapillary slip about a dilute periodic mattress of protruding bubbles |
| title_full | Longitudinal thermocapillary slip about a dilute periodic mattress of protruding bubbles |
| title_fullStr | Longitudinal thermocapillary slip about a dilute periodic mattress of protruding bubbles |
| title_full_unstemmed | Longitudinal thermocapillary slip about a dilute periodic mattress of protruding bubbles |
| title_short | Longitudinal thermocapillary slip about a dilute periodic mattress of protruding bubbles |
| title_sort | longitudinal thermocapillary slip about a dilute periodic mattress of protruding bubbles |
| work_keys_str_mv | AT yarive longitudinalthermocapillaryslipaboutadiluteperiodicmattressofprotrudingbubbles AT kirktl longitudinalthermocapillaryslipaboutadiluteperiodicmattressofprotrudingbubbles |