Thermocapillary and oscillatory-shear instabilities in a layer of liquid with a deformable surface

1998 ◽  
Vol 360 ◽  
pp. 21-39 ◽  
Author(s):  
A. C. OR ◽  
R. E. KELLY
Keyword(s):  
Free Surface ◽  
Marangoni Number ◽  
Thermocapillary Convection ◽  
Oscillatory Shear ◽  
Heated Layer ◽  
Long Wavelength ◽  
Deformable Surface ◽  
Microgravity Conditions ◽  
Shear Instabilities ◽  
Oscillating Plate

The thermocapillary and shear-induced instabilities of a thin heated layer of liquid bounded from the top by a deformable free surface and at the bottom by a horizontally oscillating plate are studied for both Earth-bound and microgravity conditions. Finite-wavelength thermocapillary convection can be stabilized very significantly by the oscillatory shear, whereas shear-induced instabilities are greatly stabilized if the Marangoni number is negative. For long-wavelength thermocapillary convection, oscillatory shear can stabilize or destabilize the basic state, depending primarily on the imposed forcing frequency. With microgravity, significant stabilization of the dominant long-wavelength convection can be achieved by carefully selecting the imposed frequency.

Effect of Marangoni number on thermocapillary convection and free-surface deformation in liquid bridges

2016 ◽  
Vol 25 (2) ◽  
pp. 178-187 ◽  
Author(s):  
Yin Zhang ◽  
Hu-Lin Huang ◽  
Xiao-Ming Zhou ◽  
Gui-Ping Zhu ◽  
Yong Zou
Keyword(s):  
Free Surface ◽  
Marangoni Number ◽  
Thermocapillary Convection ◽  
Surface Deformation ◽  
Liquid Bridges ◽  
Free Surface Deformation

Finite-wavelength instability in a horizontal liquid layer on an oscillating plane

1997 ◽  
Vol 335 ◽  
pp. 213-232 ◽  
Author(s):  
A. C. OR
Keyword(s):  
Free Surface ◽  
Liquid Layer ◽  
Stability Limit ◽  
Physical Parameters ◽  
Long Wavelength ◽  
Subharmonic Solutions ◽  
Neutral Curves ◽  
Free Surface Instability ◽  
Oscillating Plate ◽  
Time Periodic

The linear stability of a thin liquid layer bounded from above by a free surface and from below by an oscillating plate is investigated for disturbances of arbitrary wavenumbers, a range of imposed frequencies and selective physical parameters. The imposed motion of the lower wall occurs in its own plane and is unidirectional and time-periodic. Long-wave instabilities occur only over certain bandwidths of the imposed frequency, as determined by a long-wavelength expansion. A fully numerical method based on Floquet theory is used to investigate solutions with arbitrary wavenumbers, and a new free-surface instability is found that has a finite preferred wavelength. This instability occurs continuously once the imposed frequency exceeds a certain threshold. The neutral curves of this new finite-wavelength instability appear significantly more complex than those for long waves. In a certain parameter regime, folds occur in the finite-wavelength stability limit, giving rise to isolated unstable regions. Only synchronous solutions are found, i.e. subharmonic solutions have not been detected. In Appendix A, we provide an argument for the non-existence of subharmonic solutions.

Marangoni instability of a thin liquid film heated from below by a local heat source

2003 ◽  
Vol 475 ◽  
pp. 377-408 ◽  
Author(s):  
SERAFIM KALLIADASIS ◽  
ALLA KIYASHKO ◽  
E. A. DEMEKHIN
Keyword(s):  
Free Surface ◽  
Liquid Film ◽  
Discrete Spectrum ◽  
Essential Spectrum ◽  
Marangoni Number ◽  
Thin Liquid Film ◽  
Nonlinear Partial Differential Equations ◽  
Spanwise Direction ◽  
Surface Boundary ◽  
Integral Boundary

We consider the motion of a liquid film falling down a heated planar substrate. Using the integral-boundary-layer approximation of the Navier–Stokes/energy equations and free-surface boundary conditions, it is shown that the problem is governed by two coupled nonlinear partial differential equations for the evolution of the local film height and temperature distribution in time and space. Two-dimensional steady-state solutions of these equations are reported for different values of the governing dimensionless groups. Our computations demonstrate that the free surface develops a bump in the region where the wall temperature gradient is positive. We analyse the linear stability of this bump with respect to disturbances in the spanwise direction. We show that the operator of the linearized system has both a discrete and an essential spectrum. The discrete spectrum bifurcates from resonance poles at certain values of the wavenumber for the disturbances in the transverse direction. The essential spectrum is always stable while part of the discrete spectrum becomes unstable for values of the Marangoni number larger than a critical value. Above this critical Marangoni number the growth rate curve as a function of wavenumber has a finite band of unstable modes which increases as the Marangoni number increases.

Thermocapillary Convection With Undeformable Curved Surfaces in Open Cylinders

2001 ◽  
Author(s):  
Bok-Cheol Sim ◽  
Abdelfattah Zebib
Keyword(s):  
Free Surface ◽  
Critical Frequency ◽  
Thermocapillary Convection ◽  
Three Dimensional ◽  
Quantitative Agreement ◽  
Fluid Volume ◽  
Uniform Heat Flux ◽  
Free Surfaces ◽  
Space Experiments ◽  
Steady Convection

Abstract Thermocapillary convection driven by a uniform heat flux in an open cylindrical container of unit aspect ratio is investigated by two- and three-dimensional numerical simulations. The undeformable free surface is either flat or curved as determined by the fluid volume (V ≤ 1) and the Young-Laplace equation. Convection is steady and axisymmetric at sufficiently low values of the Reynolds number (Re) with either flat or curved interfaces. Only steady convection is possible in strictly axisymmetric computations. Transition to oscillatory three-dimensional motions occurs as Re increases beyond a critical value dependent on Pr and V. With a flat free surface (V = 1), two-lobed pulsating waves are found on the free surface and prevail with increasing Re. While the critical Re increases with increasing Pr, the critical frequency decreases. In the case of a concave surface, four azimuthal waves are found rotating clockwise on the surface. The critical Re decreases with increasing fluid volume, and the critical frequency is found to increase. The numerical results with either flat or curved free surfaces are in good quantitative agreement with space experiments.

scholarly journals The effect of uniform magnetic field on spatial-temporal evolution of thermocapillary convection with the silicon oil based ferrofluid

2020 ◽  
Vol 24 (6 Part B) ◽  
pp. 4159-4171
Author(s):  
Shuo Yang ◽  
Rui Ma ◽  
Qiaosheng Deng ◽  
Guofeng Wang ◽  
Yu Gao ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Free Surface ◽  
Transverse Magnetic Field ◽  
Liquid Bridge ◽  
Thermocapillary Convection ◽  
Surface Deformation ◽  
Axial Magnetic Field ◽  
Transverse Magnetic ◽  
Surface Flow ◽  
Silicon Oil

A uniform axial or transverse magnetic field is applied on the silicon oil based ferrofluid of high Prandtl number fluid (Pr ? 111.67), and the effect of magnetic field on the thermocapillary convection is investigated. It is shown that the location of vortex core of thermocapillary convection is mainly near the free surface of liquid bridge due to the inhibition of the axial magnetic field. A velocity stagnation region is formed inside the liquid bridge under the axial magnetic field (B = 0.3-0.5 T). The disturbance of bulk reflux and surface flow is suppressed by the increasing axial magnetic field. There is a dynamic response of free surface deformation to the axial magnetic field, and then the contact angle variation of the free surface at the hot corner is as following, ?hot, B = 0.5 T = 83.34? > ?hot, B = 0.3 T = 72.16? > > ?hot,B = 0.1 T = 54.21? > ?hot, B = 0 T = 43.33?. The results show that temperature distribution near the free surface is less and less affected by thermocapillary convection with the increasing magnetic field, and it presents a characteristic of heat-conduction. In addition, the transverse magnetic field does not realize the fundamental inhibition for thermocapillary convection, but it transfers the influence of thermocapillary convection to the free surface.

Study of the equilibrium free surface of a capillary liquid in a toroidal vessel

2021 ◽  
Author(s):  
Y. Zhaokai ◽  
A.N. Temnov
Keyword(s):  
Free Surface ◽  
Liquid Fuel ◽  
Solid Wall ◽  
Intermolecular Forces ◽  
Bond Number ◽  
Space Technology ◽  
Stationary Potential ◽  
Microgravity Conditions ◽  
Two Phases ◽  
Capillary Liquid

The paper considers an axisymmetric problem of determining the forms of equilibrium of liquid in spacecraft toroidal tanks under conditions close to weightlessness. In the absence of significant mass gravitational forces, the behavior of liquid fuel in tanks begins to be determined by surface tension forces, which are intermolecular forces at the interface of two phases. Relying on the principle of stationary potential, we obtained the conditions of equilibrium of the closed system "liquid - gas - solid wall" under microgravity conditions. The study introduces a system of differential equations that determines the form of equilibrium of a liquid in toroidal tanks, the Young — Dupre equation, the condition for the contact of a free surface with a solid wall, and the condition for the conservation of the volume of the liquid. Furthermore, we quantified the influence of various parameters, such as the contact angle α_0, the Bond number B_0, the ratio of the radii of the circles δ=R_0⁄r_0 and the relative filling volume of liquids V_0, on the form of the equilibrium of the capillary liquid. The study of the forms of equilibrium of liquid fuel makes it possible to develop recommendations for the design of intake devices for fuel tanks in rocket and space technology. Findings of research show that the obtained equilibrium surface is also the unperturbed boundary of the region occupied by liquid fuel, which gives necessary information for further investigation of the spacecraft dynamics.

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