Pasias, Georgios;
(2022)
Developed liquid film passing a trailing edge under the action of gravity and capillarity.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
We consider a fully developed liquid film flow passing the trailing edge of a plate or a corner, under the vertical action of gravity and the influence of surface tension. We use asymptotic analysis and triple deck theory in order to analyse the details of the flow in the vicinity of the trailing edge and beyond. Our analytical solutions are compared with numerical ones obtained using MATLAB. This analysis is conducted considering different Froude numbers which result in different interaction details and flow characteristics. Firstly we consider the flow when g = O(1) over a length-scale x = O(ϵ^(−1)), where g and ϵ are the inverse Froude and Reynolds numbers respectively. There we try to control the emergence of a hydraulic jump depending on the upstream eigensolutions. We then focus on the case where g = O(ϵ^(4/7)). This part concentrates on a relatively small region near the plate edge, where a viscous-inviscid interaction exists. At this stage the vertical displacement of the lower and upper fluid surface causes a vertical pressure gradient due to streamline curvature. This interacts with the surface tension and weakly with the hydrostatic pressure. The different flow behaviors there are analysed both analytically and numerically. Completing the interactive stage analysis we move to even smaller length scales to accommodate some singular behaviors near the trailing edge due to the sudden loss of the no slip condition. This leads up to a square Rayleigh stage where we find capillary ripples upstream and algebraic growth downstream. Moving further away from the trailing edge we come across an Euler region. There we examIne the flow after the interactive description fails, predicting an expansive singularity. In the Euler region we also simulate the flow around a corner. Finally we examine the case where g = O(ϵ^(2/7) ). There the details on how the streamline curvature serves to regularise the edge singularity are described and demonstrated numerically.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Developed liquid film passing a trailing edge under the action of gravity and capillarity |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2022. Original content in this thesis is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) Licence (https://creativecommons.org/licenses/by-nc/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request. |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10152957 |
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