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Surface deformations in dynamic thermocapillary convection under partial slip.
Katarzyna N Kowal1, Stephen H Davis2, Peter W Voorhees3
1Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom, and Trinity College, University of Cambridge, Cambridge CB2 1TQ, United Kingdom.
Physical Review. E
|October 3, 2019
Summary
Surface deformations destabilize hydrothermal waves in liquid layers, favoring two-dimensional waves. Increasing capillary numbers shorten scales and raise critical Marangoni numbers for all instability modes.
Area of Science:
- Fluid dynamics
- Hydrothermal instability
- Thermocapillary effects
Background:
- A horizontal liquid layer with a deformable interface and partial-slip lower surface is subjected to a temperature gradient.
- Thermocapillary forces drive a steady shear flow within the liquid layer.
Purpose of the Study:
- Investigate the onset of various hydrothermal wave instabilities (2D, 3D oblique, longitudinal) in the system.
- Analyze the influence of surface deformation and capillary number on instability modes.
- Examine the impact of surface deformation on longitudinal waves, especially at low Prandtl numbers.
Main Methods:
- Theoretical analysis of a horizontal liquid layer with a deformable interface and partial-slip boundary.
- Low capillary number expansion to study surface deformation effects.
- Analysis of different instability modes: oblique 3D hydrothermal waves, 2D hydrothermal waves, longitudinal traveling waves, and longitudinal rolls.
Main Results:
- Surface deformations are destabilizing for all instability modes at low capillary numbers.
- A preference for two-dimensional hydrothermal waves is observed when surface deformations are present.
- Oblique hydrothermal waves align with flow direction as capillary number increases.
- Surface deformations significantly impact longitudinal waves, particularly at low Prandtl numbers.
- Critical Marangoni numbers increase with capillary number for all modes, while length scales decrease.
Conclusions:
- Surface deformations play a crucial role in destabilizing hydrothermal waves and influencing their selection.
- The system's behavior, particularly the selection of instability modes, is sensitive to capillary number and surface deformability.
- Longitudinal wave selection near a critical Prandtl number is lost with a deformable interface.
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