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.

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 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 Bursting of Pointed Drops in Slow Viscous Flow

1973 ◽  
Vol 40 (1) ◽  
pp. 18-24 ◽  
Author(s):  
J. Buckmaster
Keyword(s):  
Surface Tension ◽  
Viscous Fluid ◽  
Viscous Flow ◽  
Small Drop ◽  
Shape Preserving ◽  
Slender Body Theory ◽  
Slow Viscous Flow ◽  
Viscous Drops ◽  
Steady Solutions ◽  
Body Theory

Viscous drops, confined by the slow axisymmetric straining motion of a viscous fluid, are considered when the surface tension is weak. The shape of the drops is determined using slender-body theory, and it is found that steady solutions only exist for sufficiently small drop viscosities. Nonuniqueness exists, with bifurcation from a simple quadratic solution. At high drop viscosities, when there are no steady solutions, a description of the unsteady elongation of shape-preserving drops is obtained. This is the bursting phenomenon described experimentally by Taylor [1].

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.

A new Reliable Numerical Algorithm Based on the First Kind of Bessel Functions to Solve Prandtl–Blasius Laminar Viscous Flow over a Semi-Infinite Flat Plate

2012 ◽  
Vol 67 (12) ◽  
pp. 665-673 ◽  
Author(s):  
Kourosh Parand ◽  
Mehran Nikarya ◽  
Jamal Amani Rad ◽  
Fatemeh Baharifard
Keyword(s):  
Viscous Flow ◽  
Flat Plate ◽  
Numerical Algorithm ◽  
Bessel Functions ◽  
Nonlinear Ordinary Differential Equation ◽  
Finite Domain ◽  
Algebraic Equations ◽  
Infinite Domain ◽  
Third Order ◽  
Domain Truncation

In this paper, a new numerical algorithm is introduced to solve the Blasius equation, which is a third-order nonlinear ordinary differential equation arising in the problem of two-dimensional steady state laminar viscous flow over a semi-infinite flat plate. The proposed approach is based on the first kind of Bessel functions collocation method. The first kind of Bessel function is an infinite series, defined on ℝ and is convergent for any x ∊ℝ. In this work, we solve the problem on semi-infinite domain without any domain truncation, variable transformation basis functions or transformation of the domain of the problem to a finite domain. This method reduces the solution of a nonlinear problem to the solution of a system of nonlinear algebraic equations. To illustrate the reliability of this method, we compare the numerical results of the present method with some well-known results in order to show the applicability and efficiency of our method.

On a sphere performing linear and torsional oscillations in a viscous fluid

1988 ◽  
Vol 66 (7) ◽  
pp. 576-579
Author(s):  
G. T. Karahalios ◽  
C. Sfetsos
Keyword(s):  
Boundary Layer ◽  
Viscous Fluid ◽  
Secondary Flow ◽  
Small Amplitude ◽  
Equations Of Motion ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Time Varying ◽  
Torsional Oscillations

A sphere executes small-amplitude linear and torsional oscillations in a fluid at rest. The equations of motion of the fluid are solved by the method of successive approximations. Outside the boundary layer, a steady secondary flow is induced in addition to the time-varying motion.

The Motion of a Flat-Plate Pendulum in a Viscous Fluid

1969 ◽  
Vol 91 (4) ◽  
pp. 1100-1104
Author(s):  
J. P. Ries ◽  
W. G. Harrach
Keyword(s):  
Viscous Fluid ◽  
Flat Plate ◽  
Amplitude Ratio ◽  
Harmonic Oscillation ◽  
Oscillation Period ◽  
Velocity Amplitude ◽  
Boundary Layer Equations ◽  
Light Oil ◽  
Damped Oscillation ◽  
Predicted Values

The motion of an infinite, flat plate undergoing free oscillations as a submerged pendulum in a viscous fluid is analyzed. An analytical solution has been obtained through a simultaneous solution of the equation of motion for the plate, the drag force relationship, and the boundary-layer equations for the case of laminar, incompressible, unsteady flow. Expressions for the displacement and velocity of the plate appear as the sum of a damped harmonic oscillation and a particular solution which decays asymptotically to zero with increasing time. The period and logarithmic decrement are expressed as functions of a single parameter which contains the physical properties of the fluid and dimensions of the system. Predicted values of plate displacement, plate velocity, amplitude ratio, and damped oscillation period are compared to the results of an experimental investigation performed in water and a light oil.

Sign in / Sign up

Export Citation Format

Share Document