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 Process Parameter Identification in Thin Film Flows Driven by a Stretching Surface

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Satyananda Panda ◽  
Mathieu Sellier ◽  
M. C. S. Fernando ◽  
M. K. Abeyratne
Keyword(s):  
Thin Film ◽  
Free Surface ◽  
Temperature Distribution ◽  
Stokes Equations ◽  
Thin Liquid Film ◽  
Algebraic Manipulation ◽  
Navier Stokes ◽  
Surface Tension Gradient ◽  
Test Problems ◽  
Stretching Surface

The flow of a thin liquid film over a heated stretching surface is considered in this study. Due to a potential nonuniform temperature distribution on the stretching sheet, a temperature gradient occurs in the fluid which produces surface tension gradient at the free surface of the thin film. As a result, the free surface deforms and these deformations are advected by the flow in the stretching direction. This work focuses on the inverse problem of reconstructing the sheet temperature distribution and the sheet stretch rate from observed free surface variations. This work builds on the analysis of Santra and Dandapat (2009) who, based on the long-wave expansion of the Navier-Stokes equations, formulate a partial differential equation which describes the evolution of the thickness of a film over a nonisothermal stretched surface. In this work, we show that after algebraic manipulation of a discrete form of the governing equations, it is possible to reconstruct either the unknown temperature field on the sheet and hence the resulting heat transfer or the stretching rate of the underlying surface. We illustrate the proposed methodology and test its applicability on a range of test problems.

scholarly journals The oscillatory longwave Marangoni convection in a thin film heated from below

2021 ◽  
Vol 3 (10) ◽  
Author(s):  
Anna Samoilova ◽  
Alexander Nepomnyashchy
Keyword(s):  
Thin Film ◽  
Free Surface ◽  
Large Scale ◽  
Marangoni Convection ◽  
Thin Liquid Film ◽  
Stationary Regime ◽  
Oscillatory Regime ◽  
Oscillatory Flows ◽  
The Past ◽  
Heating From Below

Abstract A novel type of Marangoni convection was predicted theoretically a decade ago. The thin liquid film atop a substrate of low thermal conductivity was considered. In the case of heating from below, the Marangoni convection emerges not only in a conventional stationary regime, but also as oscillatory flows. Specifically, the oscillatory Marangoni convection emerges if (1) the heat flux from the free surface is small, and (2) the large-scale deformation of the free surface is allowed. During the past decade, this novel Marangoni convection was detected and investigated in several other theoretical works. The review discusses the recent achievements in studying the oscillatory Marangoni convection in a thin film heated from below. The guiding data for observation of the oscillatory regime are also provided.

scholarly journals On the origin of the circular hydraulic jump in a thin liquid film

2018 ◽  
Vol 851 ◽  
Author(s):  
Rajesh K. Bhagat ◽  
N. K. Jha ◽  
P. F. Linden ◽  
D. Ian Wilson
Keyword(s):  
Thin Film ◽  
Surface Tension ◽  
Liquid Film ◽  
Thin Liquid Film ◽  
Capillary Waves ◽  
Hydraulic Jumps ◽  
Planar Surface ◽  
Normal Impact ◽  
Viscous Forces

This study explores the formation of circular thin-film hydraulic jumps caused by the normal impact of a jet on an infinite planar surface. For more than a century, it has been believed that all hydraulic jumps are created due to gravity. However, we show that these thin-film hydraulic jumps result from energy loss due to surface tension and viscous forces alone. We show that, at the jump, surface tension and viscous forces balance the momentum in the liquid film and gravity plays no significant role. Experiments show no dependence on the orientation of the surface and a scaling relation balancing viscous forces and surface tension collapses the experimental data. A theoretical analysis shows that the downstream transport of surface energy is the previously neglected critical ingredient in these flows, and that capillary waves play the role of gravity waves in a traditional jump in demarcating the transition from the supercritical to subcritical flow associated with these jumps.

On cusped interfaces

1998 ◽  
Vol 359 ◽  
pp. 313-328 ◽  
Author(s):  
YULII D. SHIKHMURZAEV
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Reynolds Numbers ◽  
Present Theory ◽  
Similar Process ◽  
Surface Tension Gradient ◽  
Low Reynolds Numbers ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Rate Of Dissipation

An asymptotic analysis of two-dimensional free-surface cusps associated with flows at low Reynolds numbers is presented on the basis of a model which, in agreement with direct experimental observations, considers this phenomenon as a particular case of an interface formation–disappearance process. The model was derived from first principles and earlier applied to another similar process: the moving contact-line problem. As is shown, the capillary force acting on a cusp from the free surface, which in the classical approach can be balanced by viscous stresses only if the associated rate of dissipation of energy is infinite, in the present theory is always balanced by the force from the surface-tension-relaxation ‘tail’, which stretches from the cusp towards the interior of the fluid. The flow field near the cusp is shown to be regular, and the surface-tension gradient in the vicinity of the cusp, caused and maintained by the external flow, induces and is balanced by the shear stress. Existing approaches to the free-surface cusp description and some relevant experimental aspects of the problem are discussed.

Inverse-thermocapillary evaporation in a thin liquid film of self-rewetting fluid

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Elaine Lim ◽  
Tze Cheng Kueh ◽  
Yew Mun Hung
Keyword(s):  
Heat Transfer ◽  
Surface Tension ◽  
Liquid Film ◽  
Temperature Region ◽  
Thin Liquid Film ◽  
Thermocapillary Flow ◽  
Working Fluid ◽  
Surface Tension Gradient ◽  
Thermocapillary Effect ◽  
Content Type

Purpose The present study aims to investigate the inverse-thermocapillary effect in an evaporating thin liquid film of self-rewetting fluid, which is a dilute aqueous solution (DAS) of long-chain alcohol. Design/methodology/approach A long-wave evolution model modified for self-rewetting fluids is used to study the inverse thermocapillary characteristics of an evaporating thin liquid film. The flow attributed to the inverse thermocapillary action is manifested through the streamline plots and the evaporative heat transfer characteristics are quantified and analyzed. Findings The thermocapillary flow induced by the negative surface tension gradient drives the liquid from a low-surface-tension (high temperature) region to a high-surface-tension (low temperature) region, retarding the liquid circulation and the evaporation strength. The positive surface tension gradients of self-rewetting fluids induce inverse-thermocapillary flow. The results of different working fluids, namely, water, heptanol and DAS of heptanol, are examined and compared. The thermocapillary characteristic of a working fluid is significantly affected by the sign of the surface tension gradient and the inverse effect is profound at a high excess temperature. The inverse thermocapillary effect significantly enhances evaporation rates. Originality/value The current investigation on the inverse thermocapillary effect in a self-rewetting evaporating thin film liquid has not been attempted previously. This study provides insights on the hydrodynamic and thermal characteristics of thermocapillary evaporation of self-rewetting liquid, which give rise to significant thermal enhancement of the microscale phase-change heat transfer devices.

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.

Suppression of Thermocapillary Effect in Evaporating Thin Film of Micro Heat Pipes

2015 ◽  
Vol 1101 ◽  
pp. 467-470
Author(s):  
Elaine Lim ◽  
Yew Mun Hung
Keyword(s):  
Surface Tension ◽  
Thin Liquid Film ◽  
Marangoni Effect ◽  
Working Fluid ◽  
Surface Tension Gradient ◽  
Flow Mechanism ◽  
Thermocapillary Effect ◽  
Micro Heat Pipes ◽  
Thermo Physical Properties ◽  
Microelectronics Cooling

This paper presents a theoretical study on the flow mechanism of different types of working fluids incorporated with Marangoni effect in a microelectronics cooling device. It is known that surface tension gradient effect or thermocapillary effect can be induced by temperature gradient which leads to the thermocapillary flow. By adding a small quantity of alcohol into the pure working fluid, the characteristics of surface tension can be altered without changing other thermo physical properties of the working fluid. A theoretical model is employed to focus on the suppression of thermocapillary effect in evaporating thin liquid film. The study reveals the fluid flow mechanism of a working fluid can be altered with thermocapillary effect. Thermal performance of microelectronics cooling devices can also be enhanced by utilizing aqueous solution as the working fluid.

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.

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