Oscillatory Marangoni instability in a heated layer with insoluble surfactant adsorbed on the free surface

2017 ◽  
Vol 521 ◽  
pp. 161-166 ◽  
Author(s):  
Alexander Mikishev ◽  
Alexander A. Nepomnyashchy
Keyword(s):  
Free Surface ◽  
Heated Layer ◽  
Marangoni Instability ◽  
Insoluble Surfactant

scholarly journals Gravity-driven thin liquid films with insoluble surfactant: smooth traveling waves

2007 ◽  
Vol 18 (6) ◽  
pp. 679-708 ◽  
Author(s):  
RACHEL LEVY ◽  
MICHAEL SHEARER ◽  
THOMAS P. WITELSKI
Keyword(s):  
Free Surface ◽  
Traveling Waves ◽  
Surfactant Concentration ◽  
Piecewise Linear ◽  
Traveling Wave Solutions ◽  
Liquid Films ◽  
Insoluble Surfactant ◽  
Small Parameters ◽  
Gravity Driven ◽  
The One

The flow of a thin layer of fluid down an inclined plane is modified by the presence of insoluble surfactant. For any finite surfactant mass, traveling waves are constructed for a system of lubrication equations describing the evolution of the free-surface fluid height and the surfactant concentration. The one-parameter family of solutions is investigated using perturbation theory with three small parameters: the coefficient of surface tension, the surfactant diffusivity, and the coefficient of the gravity-driven diffusive spreading of the fluid. When all three parameters are zero, the nonlinear PDE system is hyperbolic/degenerate-parabolic, and admits traveling wave solutions in which the free-surface height is piecewise constant, and the surfactant concentration is piecewise linear and continuous. The jumps and corners in the traveling waves are regularized when the small parameters are nonzero; their structure is revealed through a combination of analysis and numerical simulation.

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.

Marangoni instability of two liquids mixing at a free surface

1998 ◽  
Vol 10 (12) ◽  
pp. 3038-3040 ◽  
Author(s):  
E. Tan ◽  
S. T. Thoroddsen
Keyword(s):  
Free Surface ◽  
Marangoni Instability
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