Interfacial stability and self-similar rupture of evaporating liquid layers under vapor recoil
We investigate interfacial stability of an evaporating viscous liquid layer above/below a horizontal heated substrate in the framework of a long-wave model that accounts for surface tension, positive/negative gravity, and evaporation effects of mass loss and vapor recoil. With the time-dependent lin...
| Main Authors: | , |
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| Format: | Journal Article |
| Language: | English |
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2018
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| Online Access: | https://hdl.handle.net/10356/89722 http://hdl.handle.net/10220/47129 |
| _version_ | 1811695511645716480 |
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| author | Wei, Tao Duan, Fei |
| author2 | School of Mechanical and Aerospace Engineering |
| author_facet | School of Mechanical and Aerospace Engineering Wei, Tao Duan, Fei |
| author_sort | Wei, Tao |
| collection | NTU |
| description | We investigate interfacial stability of an evaporating viscous liquid layer above/below a horizontal heated substrate in the framework of a long-wave model that accounts for surface tension, positive/negative gravity, and evaporation effects of mass loss and vapor recoil. With the time-dependent linear stability analysis, it is found that the interface instability is enhanced by vapor recoil with time using an effective growth rate. The destabilizing mechanism of vapor thrust competes with the stabilizing surface tension, and the effects of the latter are not asymptotically negligible near rupture, reflected by a rescaled effective interfacial pressure. A two-dimensional nonlinear evolution is investigated for the quasi-equilibrium evaporating layers with different evaporative conditions for Rayleigh–Taylor unstable and sessile layers. For weak mass loss and strong vapor recoil, the well-defined capillary ridges emerge around a deepening narrow valley with increasing wavelength under a positive gravity, while, on the basis of initial condition, main and secondary droplets are either coalesced partially or separated by a sharp dry-out point under a negative gravity. The rupture location depends strongly on the characteristics of a given initial condition, except for the random perturbation. For both the cases, an increase in the modified evaporation number tends to reduce the rupture time tr and droplet thickness remarkably. Similarity analysis along with numerical strategy is presented for the final stage of touch-down dynamics, determined by a physical balance between the vapor recoil and capillary force. The evaporation-driven rupture with a significant vapor recoil and negligible mass loss is shown to contain a countably infinite number of similarity solutions whose horizontal and vertical length scales behave as (tr − t)1/2 and (tr − t)1/3. The first similarity solution represents a stable single-point rupture. |
| first_indexed | 2024-10-01T07:24:38Z |
| format | Journal Article |
| id | ntu-10356/89722 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:24:38Z |
| publishDate | 2018 |
| record_format | dspace |
| spelling | ntu-10356/897222023-03-04T17:14:41Z Interfacial stability and self-similar rupture of evaporating liquid layers under vapor recoil Wei, Tao Duan, Fei School of Mechanical and Aerospace Engineering Equations Of Fluid Dynamics Linear Stability Analysis DRNTU::Engineering::Mechanical engineering We investigate interfacial stability of an evaporating viscous liquid layer above/below a horizontal heated substrate in the framework of a long-wave model that accounts for surface tension, positive/negative gravity, and evaporation effects of mass loss and vapor recoil. With the time-dependent linear stability analysis, it is found that the interface instability is enhanced by vapor recoil with time using an effective growth rate. The destabilizing mechanism of vapor thrust competes with the stabilizing surface tension, and the effects of the latter are not asymptotically negligible near rupture, reflected by a rescaled effective interfacial pressure. A two-dimensional nonlinear evolution is investigated for the quasi-equilibrium evaporating layers with different evaporative conditions for Rayleigh–Taylor unstable and sessile layers. For weak mass loss and strong vapor recoil, the well-defined capillary ridges emerge around a deepening narrow valley with increasing wavelength under a positive gravity, while, on the basis of initial condition, main and secondary droplets are either coalesced partially or separated by a sharp dry-out point under a negative gravity. The rupture location depends strongly on the characteristics of a given initial condition, except for the random perturbation. For both the cases, an increase in the modified evaporation number tends to reduce the rupture time tr and droplet thickness remarkably. Similarity analysis along with numerical strategy is presented for the final stage of touch-down dynamics, determined by a physical balance between the vapor recoil and capillary force. The evaporation-driven rupture with a significant vapor recoil and negligible mass loss is shown to contain a countably infinite number of similarity solutions whose horizontal and vertical length scales behave as (tr − t)1/2 and (tr − t)1/3. The first similarity solution represents a stable single-point rupture. MOE (Min. of Education, S’pore) Published version 2018-12-20T07:12:33Z 2019-12-06T17:31:58Z 2018-12-20T07:12:33Z 2019-12-06T17:31:58Z 2016 Journal Article Wei, T., & Duan, F. (2016). Interfacial stability and self-similar rupture of evaporating liquid layers under vapor recoil. Physics of Fluids, 28(12), 124106-. doi:10.1063/1.4972179 1070-6631 https://hdl.handle.net/10356/89722 http://hdl.handle.net/10220/47129 10.1063/1.4972179 en Physics of Fluids © 2016 The Author(s) (Published by AIP). This paper was published in Physics of Fluids and is made available as an electronic reprint (preprint) with permission of The Author(s) (Published by AIP). The published version is available at: [http://dx.doi.org/10.1063/1.4972179]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law. 23 p. application/pdf |
| spellingShingle | Equations Of Fluid Dynamics Linear Stability Analysis DRNTU::Engineering::Mechanical engineering Wei, Tao Duan, Fei Interfacial stability and self-similar rupture of evaporating liquid layers under vapor recoil |
| title | Interfacial stability and self-similar rupture of evaporating liquid layers under vapor recoil |
| title_full | Interfacial stability and self-similar rupture of evaporating liquid layers under vapor recoil |
| title_fullStr | Interfacial stability and self-similar rupture of evaporating liquid layers under vapor recoil |
| title_full_unstemmed | Interfacial stability and self-similar rupture of evaporating liquid layers under vapor recoil |
| title_short | Interfacial stability and self-similar rupture of evaporating liquid layers under vapor recoil |
| title_sort | interfacial stability and self similar rupture of evaporating liquid layers under vapor recoil |
| topic | Equations Of Fluid Dynamics Linear Stability Analysis DRNTU::Engineering::Mechanical engineering |
| url | https://hdl.handle.net/10356/89722 http://hdl.handle.net/10220/47129 |
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