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.

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.

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.

Numerical Solution of a Rimming Flow Problem Using a Moving Mesh Method

2003 ◽  
Vol 3 (3) ◽  
pp. 373-386
Author(s):  
Alan F. Hegarty ◽  
Stephen B. G. O'Brien ◽  
Stephen Sikwila
Keyword(s):  
Thin Film ◽  
Surface Tension ◽  
Flow Problem ◽  
Constant Angular Velocity ◽  
Moving Mesh ◽  
Lubrication Approximation ◽  
Moving Mesh Method ◽  
First Order ◽  
Rimming Flow ◽  
Mesh Method

AbstractWe consider the evolution of a thin film of viscous fluid on the inside surface of a cylinder with the horizontal axis, rotating with a constant angular velocity about this axis. We use a lubrication approximation extended to the first order in the dimensionless film thickness (including the small effects of the variation of the film pressure across its thickness and the surface tension) and numerically we compute the time evolution of the film to a steady state.

Surface Ribbing of a Thin Viscous Fluid Film Emerging From a Spreader or Roller

1978 ◽  
Vol 100 (4) ◽  
pp. 462-466 ◽  
Author(s):  
C. Fall
Keyword(s):  
Thin Film ◽  
Surface Tension ◽  
Viscous Fluid ◽  
Flat Plate ◽  
Perturbation Analysis ◽  
Linear Perturbation ◽  
Narrow Gap ◽  
Film Rupture ◽  
Characteristic Distance ◽  
Viscous Fluid Film

The thin film produced by the flow of a viscous fluid through a narrow gap between a spreader (or roller) and a flat plate is often subject to surface ribbing. A linear perturbation analysis, based upon lubrication theory, is used to examine the nature of this ribbed film and, specifically, to explain the large distances over which ribbing is observed to prevail. Taking into account the effects of both surface tension and gravity in smoothing out the film, the analysis predicts a characteristic distance from striated film-rupture to where a uniform film is formed.

scholarly journals An Existence Theory for Gravity–Capillary Solitary Water Waves

Water Waves ◽  
2021 ◽  
Author(s):  
M. D. Groves
Keyword(s):  
Surface Tension ◽  
Water Waves ◽  
Applied Mathematics ◽  
Spatial Dynamics ◽  
Existence Theory ◽  
Water Wave Problem ◽  
Reduction Methods ◽  
Centre Manifold Reduction ◽  
Weak Surface ◽  
The One

AbstractIn the applied mathematics literature solitary gravity–capillary water waves are modelled by approximating the standard governing equations for water waves by a Korteweg-de Vries equation (for strong surface tension) or a nonlinear Schrödinger equation (for weak surface tension). These formal arguments have been justified by sophisticated techniques such as spatial dynamics and centre-manifold reduction methods on the one hand and variational methods on the other. This article presents a complete, self-contained account of an alternative, simpler approach in which one works directly with the Zakharov–Craig–Sulem formulation of the water-wave problem and uses only rudimentary fixed-point arguments and Fourier analysis.

scholarly journals The Effects of Surfactant on the Evolution of a Thin Film under a Moving Liquid Drop

2020 ◽  
Vol 5 (1) ◽  
pp. 75-85
Author(s):  
Kartika Yulianti ◽  
Agus Yodi Gunawan ◽  
Edy Soewono
Keyword(s):  
Thin Film ◽  
Film Thickness ◽  
Solid Surface ◽  
Surfactant Concentration ◽  
Liquid Drop ◽  
Nonlinear Partial Differential Equations ◽  
Normal Pressure ◽  
Lubrication Approximation ◽  
Moving Liquid

The effect of surfactant on the thickness of a thin film bounded by a solid surface and a moving liquid drop was investigated. We proposed a model so that parameters from the liquid drop can be stated in a parameter that acts as normal pressure to the thin film. Using the lubrication approximation, the model was reduced to a set of nonlinear partial differential equations in terms of the film thickness and surfactant concentration. Since we were interested in the role of the surfactant in lifting up the drop, we assumed that the density of the drop is higher than the density of the thin film. Numerically, the results show that the presence of the surfactant tends to delay the decrease of the film thickness insignificantly. However, when the surfactant was added into the system, it tends to significantly increase the film thickness for a certain range value of the normal pressure.

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.

Sign in / Sign up

Export Citation Format

Share Document