scholarly journals A pinned or free-floating rigid plate on a thin viscous film

2014 ◽  
Vol 760 ◽  
pp. 407-430 ◽  
Author(s):  
Philippe H. Trinh ◽  
Stephen K. Wilson ◽  
Howard A. Stone
Keyword(s):  
Thin Film ◽  
Surface Tension ◽  
Free Surface ◽  
Viscous Fluid ◽  
Substrate Surface ◽  
Rigid Plate ◽  
Viscous Film ◽  
Structure Interaction ◽  
Horizontal Substrate ◽  
The Right

AbstractA pinned or free-floating rigid plate lying on the free surface of a thin film of viscous fluid, which itself lies on top of a horizontal substrate that is moving to the right at a constant speed is considered. The focus of the present work is to describe how the competing effects of the speed of the substrate, surface tension, viscosity, and, in the case of a pinned plate, the prescribed pressure in the reservoir of fluid at its upstream end, determine the possible equilibrium positions of the plate, the free surface, and the flow within the film. The present problems are of interest both in their own right as paradigms for a range of fluid–structure interaction problems in which viscosity and surface tension both play an important role, and as a first step towards the study of elastic effects.

scholarly journals Steady rimming flows with surface tension

2008 ◽  
Vol 597 ◽  
pp. 91-118 ◽  
Author(s):  
E. S. BENILOV ◽  
M. S. BENILOV ◽  
N. KOPTEVA
Keyword(s):  
Thin Film ◽  
Surface Tension ◽  
Viscous Fluid ◽  
Small Parameter ◽  
Outer Region ◽  
Lubrication Approximation ◽  
Steady Flows ◽  
Matched Asymptotics ◽  
Weak Surface ◽  
Rimming Flows

We examine steady flows of a thin film of viscous fluid on the inside of a cylinder with horizontal axis, rotating about this axis. If the amount of fluid in the cylinder is sufficiently small, all of it is entrained by rotation and the film is distributed more or less evenly. For medium amounts, the fluid accumulates on the ‘rising’ side of the cylinder and, for large ones, pools at the cylinder's bottom. The paper examines rimming flows with a pool affected by weak surface tension. Using the lubrication approximation and the method of matched asymptotics, we find a solution describing the pool, the ‘outer’ region, and two transitional regions, one of which includes a variable (depending on the small parameter) number of asymptotic zones.

scholarly journals Dynamics of Thin Film Under a Volatile Solvent Source Driven by a Constant Pressure Gradient Flow

Fluids ◽  
2019 ◽  
Vol 4 (4) ◽  
pp. 198
Author(s):  
Mohammad Irshad Khodabocus ◽  
Mathieu Sellier ◽  
Volker Nock
Keyword(s):  
Thin Film ◽  
Surface Tension ◽  
Free Surface ◽  
Evolution Equation ◽  
Constant Pressure ◽  
Thin Liquid Film ◽  
Gradient Flow ◽  
Surface Tension Gradient ◽  
Nonlinear Parabolic ◽  
Induced Flow

The evolution of a thin liquid film subject to a volatile solvent source and an air-blow effect which modifies locally the surface tension and leads to Marangoni-induced flow is shown to be governed by a degenerate fourth order nonlinear parabolic h-evolution equation of the type given by ∂ t h = − div x M 1 h ∂ x 3 h + M 2 h ∂ x h + M 3 h , where the mobility terms M 1 h and M 2 h result from the presence of the source and M 3 h results from the air-blow effect. Various authors assume M 2 h ≈ 0 and exclude the air-blow effect into M 3 h . In this paper, the authors show that such assumption is not necessarily correct, and the inclusion of such effect does disturb the dynamics of the thin film. These emphasize the importance of the full definition t → · grad γ = grad x γ + ∂ x h grad y γ of the surface tension gradient at the free surface in contrast to the truncated expression t → · grad γ ≈ grad x γ employed by those authors and the effect of the air-blow flowing over the surface.

scholarly journals Onset of Buoyancy and Surface-Tension Driven Instabilities in Presence of Random Vibrations

1990 ◽  
Vol 45 (11-12) ◽  
pp. 1235-1240
Author(s):  
B. S. Dandapat
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Fluid Layer ◽  
Heat Conducting ◽  
Rigid Plate ◽  
Stability Zone ◽  
Random Vibrations ◽  
White Noise Process ◽  
Onset Of Convection ◽  
The Stability

AbstractOnset of thermal convection in an incompressible fluid layer bounded between a perfectly heat conducting lower rigid plate and an upper free surface is analysed when the layer is subject to random vibrations. It is shown that when the vibrations are characterized by a white noise process, they hasten the onset of convection. Further it is shown that the stability zone is demarcated by an inverted parabola in the (R, M) plane.

scholarly journals Coating Flow Near Channel Exit. A Theoretical Perspective

Fluids ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 180
Author(s):  
Roger E. Khayat ◽  
Mohammad Tanvir Hossain
Keyword(s):  
Thin Film ◽  
Surface Tension ◽  
Free Surface ◽  
Theoretical Perspective ◽  
Stress Singularity ◽  
Matched Asymptotic Expansion ◽  
Coating Film ◽  
Moving Wall ◽  
Slot Coating ◽  
Channel Exit

The planar flow of a steady moving-wall free-surface jet is examined theoretically for moderate inertia and surface tension. The method of matched asymptotic expansion and singular perturbation is used to explore the rich dynamics near the stress singularity. A thin-film approach is also proposed to capture the flow further downstream where the flow becomes of the boundary-layer type. We exploit the similarity character of the flow to circumvent the presence of the singularity. The study is of close relevance to slot and blade coating. The jet is found to always contract near the channel exit, but presents a mild expansion further downstream for a thick coating film. We predict that separation occurs upstream of the exit for slot coating, essentially for any coating thickness near the moving substrate, and for a thin film near the die. For capillary number of order one, the jet profile is not affected by surface tension but the normal stress along the free surface exhibits a maximum that strengthens with surface tension. In contrast to existing numerical findings, we predict the existence of upstream influence as indicated by the nonlinear pressure dependence on upstream distance and the pressure undershoot (overshoot) in blade (slot) coating at the exit.

Stability of Hadley Circulations in a Viscoelastic Fluid With Deformable Free Surface

2003 ◽  
Author(s):  
P. N. Kaloni ◽  
J. X. Lou
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Stability Analysis ◽  
Eigenvalue Problem ◽  
Viscoelastic Fluid ◽  
Lower Surface ◽  
Horizontal Layer ◽  
Convective Stability ◽  
Rigid Plate ◽  
Temperature Dependent

This paper deals with liner convective stability analysis of Oldroyd B fluid in a thin horizontal layer with a deformable free surface. The lower surface of the layer is in contact with an adiabatic rigid plate and the upper deformable surface is subject to a temperature dependent surface tension. The eigenvalue problem is solved by the Chebyshev Tau-QZ method and the results for various different forms of upper surfaces are presented.

The instability of uniform viscous flow under rollers and spreaders

1960 ◽  
Vol 7 (4) ◽  
pp. 481-500 ◽  
Author(s):  
J. R. A. Pearson
Keyword(s):  
Thin Film ◽  
Surface Tension ◽  
Viscous Fluid ◽  
Viscous Flow ◽  
Flat Plate ◽  
Secondary Flow ◽  
Lubrication Theory ◽  
Wave Number ◽  
Dimensionless Variable

When a thin film of viscous fluid is produced by passing it through a small gap between a roller or spreader and a flat plate, it often presents a waved, or ribbed, surface. An analysis is given here in terms of lubrication theory to show why in many cases flow leading to a uniform film is unstable. Account is taken of surface tension which proves to be a stabilizing factor. The most unstable values of the wave-number, n (characterizing the disturbance), are calculated as functions of the dimensionless variable T/μU0, and of the geometry of the system; T is the surface tension, μ the viscosity and U0 a representative velocity of the fluid. For the particular case of a spreader in the form of a wide-angled wedge, these predictions are compared with experimental observations. Agreement is obtained for values of T/μU0 between about 10 and 0.1, but for smaller values of T/μU0 it is clear that other considerations, involving only viscous and pressure forces, determine the nature of the secondary flow.

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