Next Article in Journal
Stability and Dynamics of Dark-Bright Soliton Bound States Away from the Integrable Limit
Next Article in Special Issue
The Effect of Temperature Field on Low Amplitude Oscillatory Flow within a Parallel-Plate Heat Exchanger in a Standing Wave Thermoacoustic System
Previous Article in Journal
Mechanically Strong CaSiO3 Scaffolds Incorporating B2O3-ZnO Liquid Phase
Previous Article in Special Issue
Heat Transfer Investigation of the Unsteady Thin Film Flow of Williamson Fluid Past an Inclined and Oscillating Moving Plate
Article Menu
Issue 4 (April) cover image

Export Article

Open AccessArticle
Appl. Sci. 2017, 7(4), 392; doi:10.3390/app7040392

Excitation of Surface Waves Due to Thermocapillary Effects on a Stably Stratified Fluid Layer

1
Department of Chemical and Biological Engineering, Mappin Street, University of Sheffield, Sheffield S1 3JD, UK
2
School of Mathematics and Statistics, Hounsfield Road, University of Sheffield, Sheffield S3 7RH, UK
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Received: 23 February 2017 / Revised: 1 April 2017 / Accepted: 10 April 2017 / Published: 13 April 2017
(This article belongs to the Special Issue Heat Transfer Processes in Oscillatory Flow Conditions)
View Full-Text   |   Download PDF [828 KB, uploaded 14 April 2017]   |  

Abstract

In chemical engineering applications, the operation of condensers and evaporators can be made more efficient by exploiting the transport properties of interfacial waves excited on the interface between a hot vapor overlying a colder liquid. Linear theory for the onset of instabilities due to heating a thin layer from above is computed for the Marangoni–Bénard problem. Symbolic computation in the long wave asymptotic limit shows three stationary, non-growing modes. Intersection of two decaying branches occurs at a crossover long wavelength; two other modes co-exist at the crossover point—propagating modes on nascent, shorter wavelength branches. The dispersion relation is then mapped numerically by Newton continuation methods. A neutral stability method is used to map the space of critical stability for a physically meaningful range of capillary, Prandtl, and Galileo numbers. The existence of a cut-off wavenumber for the long wave instability was verified. It was found that the effect of applying a no-slip lower boundary condition was to render all long waves stationary. This has the implication that any propagating modes, if they exist, must occur at finite wavelengths. The computation of 8000 different parameter sets shows that the group velocity always lies within 1 2 to 2 3 of the longwave phase velocity. View Full-Text
Keywords: thermocapillary; Marangoni number; stability analysis thermocapillary; Marangoni number; stability analysis
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Zimmerman, W.B.; Rees, J.M. Excitation of Surface Waves Due to Thermocapillary Effects on a Stably Stratified Fluid Layer. Appl. Sci. 2017, 7, 392.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Appl. Sci. EISSN 2076-3417 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top