Journal ArticleDOI
Film flow on a rotating disk
TLDR
In this article, the authors analyzed how a film of uniform thickness thins when the disk is set in steady rotation and showed that the leading order term in the long-time-scale solution for the transient film thickness is a lower bound for film thickness for all time.Abstract:
Unsteady liquid film flow on a rotating disk is analyzed by asymptotic methods for low and high Reynolds numbers. The analysis elucidates how a film of uniform thickness thins when the disk is set in steady rotation. In the low Reynolds number analysis two time scales for the thinning film are identified. The long‐time‐scale analysis ignores the initial acceleration of the fluid layer and hence is singular at the onset of rotation. The singularity is removed by matching the long‐time‐scale expansion for the transient film thickness with a short‐time‐scale expansion that accounts for fluid acceleration during spinup. The leading order term in the long‐time‐scale solution for the transient film thickness is shown to be a lower bound for film thickness for all time. A short‐time analysis that accounts for boundary layer growth at the disk surface is also presented for arbitrary Reynolds number. The analysis becomes invalid either when the boundary layer has a thickness comparable to that of the thinning film, or when nonlinear effects become important.read more
Citations
More filters
Journal ArticleDOI
Stochastic simulation of the flow of a thin liquid film over a rough rotating disk
TL;DR: In this paper, a stochastic model of surface roughness is used, and the equation describing the flow of a thin viscous film over a rough rotating disk is solved by Monte Carlo techniques.
Journal ArticleDOI
On the flow of a thin liquid film over a rotating disk
TL;DR: In this article, the authors investigated the effect of disjoining pressure on the retention of a thin film flowing on a rotating disk and found that the disjoining term has a small but still appreciable effect on the asymptotic limits of lubricant retention.
Journal ArticleDOI
Asymptotic study of film thinning process on a spinning annular disk
TL;DR: In this paper, an axisymmetric flow of a thin liquid film on a rotating annular disk is considered, and an asymptotic solution for the free surface of the thin film is found using an expansion for the film thickness in powers of a small parameter characterizing the thickness in comparison to the inner disk radius.
Journal ArticleDOI
Numerical study of film cooling on a rotating disk
R. Usha,R. Ravindran +1 more
TL;DR: In this article, the development of a heat conducting fluid film on a rotating disk has been analyzed numerically under the planar interface assumption and the film thickness, the flow characteristics, the temperature distribution and the rate of heat transfer are determined.
Journal ArticleDOI
Flow of a thin liquid film over a cold hot rotating disk
B.S. Ddandapat,P. C. Ray +1 more
TL;DR: In this article, the unsteady flow of a liquid film on a cold hot rotating disk is analyzed by means of matched asymptotic expansion under the assumptions of radially uniform film thickness that varies with time.
References
More filters
Book
Introduction to perturbation techniques
TL;DR: In this paper, the authors introduce the notion of forced Oscillations of the Duffing Equation and the Mathieu Equation for weakly nonlinear systems with quadratic and cubic nonlinearities.
Journal ArticleDOI
Über laminare und turbulente Reibung
Journal ArticleDOI
Flow of a Viscous Liquid on a Rotating Disk
TL;DR: In this paper, it was shown that initially irregular fluid distributions tend toward uniformity under centrifugation, and means of computing times required to produce uniform layers of given thickness at given angular velocity and fluid viscosity are demonstrated.
Journal ArticleDOI
Characteristics of resist films produced by spinning
TL;DR: In this article, a model for the description of thin films prepared from solution by spinning is presented, and the thickness of the film and the time of drying can be calculated as functions of various processing parameters.