Flow of thin liquid film over a rough rotating disk in the presence of a transverse magnetic field

doi:10.1007/PL00001574

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Flow of thin liquid film over a rough rotating disk in the presence of a transverse magnetic field

Journal Article•DOI•

Flow of thin liquid film over a rough rotating disk in the presence of a transverse magnetic field

R. Usha¹, B. Uma¹•Institutions (1)

Indian Institute of Technology Madras¹

01 Sep 2001-Zeitschrift für Angewandte Mathematik und Physik (Birkhauser Verlag)-Vol. 52, Iss: 5, pp 793-809

TL;DR: In this paper, the development of a viscous conducting fluid over a rough spinning disk in the presence of a transverse magnetic field has been analyzed for different patterns of surface roughness of the disk and different initial distributions of the height of the liquid lubricant.

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Abstract: The development of a flow of a viscous conducting fluid over a rough spinning disk in the presence of a transverse magnetic field has been analysed for different patterns of surface roughness of the disk and different initial distributions of the height of the liquid lubricant. The numerical solution of the governing equation of motion subject to initial and boundary conditions has been obtained by a finite-difference method. The temporal evolution of the free surface of the fluid and the rate of retention of the liquid lubricant on the spinning disk have been obtained for different values of the two parameters M , the Hartmann number and Nratio, the ratio of the surface tension effect to the centrifugation effect. In the absence of the magnetic field, the results have been observed to agree with those of [6]. It has been observed that the effect of surface roughness is to enhance the relative volume of the fluid retained on the spinning disk and this is further enhanced by the presence of the magnetic field.

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Journal Article•DOI•

Analysis of cooling of a conducting fluid film of non-uniform thickness on a rotating disk

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R. Usha¹, R. Ravindran¹•Institutions (1)

Indian Institutes of Technology¹

01 Jan 2004-International Journal of Non-linear Mechanics

TL;DR: In this paper, the evolution equation of the free surface of a rotating disk has been solved numerically by solving the evolution equations of the non-uniform thickness of conducting liquid films.

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Abstract: The unsteady thin conducting liquid film of non-uniform thickness on a rotating disk which is cooled axisymmetrically from below has been analysed numerically by solving the evolution equation of the free surface. Transient film profiles for different initial liquid film distributions have been obtained. The results reveal that the thinning process and film planarisation are markedly influenced by the heat dissipating or cooling parameter β, Prandtl number σ and Reynolds number Re.

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5 citations

Journal Article•DOI•

A Thin Conducting Liquid Film on a Spinning Disk in the Presence of a Magnetic Field: Dynamics and Stability

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B. Uma¹, R. Usha²•Institutions (2)

University of California, Santa Barbara¹, Indian Institute of Technology Madras²

01 Jul 2009-Journal of Applied Mechanics

TL;DR: In this paper, the effects of a magnetic field on the dynamics of a thin nonuniform conducting film of an incompressible viscous fluid on a rotating disk has been considered, and a nonlinear evolution equation describing the shape of the film interface has been derived as a function of space and time and solved numerically.

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Abstract: A theoretical analysis of the effects of a magnetic field on the dynamics of a thin nonuniform conducting film of an incompressible viscous fluid on a rotating disk has been considered A nonlinear evolution equation describing the shape of the film interface has been derived as a function of space and time and has been solved numerically The temporal evolution of the free surface of the fluid and the rate of retention of the liquid film on the spinning disk have been obtained for different values of Hartmann number M, evaporative mass flux parameter E, and Reynolds number Re The results show that the relative volume of the fluid retained on the spinning disk is enhanced by the presence of the magnetic field The stability characteristics of the evolution equation have been examined using linear theory For both zero and nonzero values of the nondimensional parameter describing the magnetic field, the results show that (a) the infinitesimal disturbances decay for small wave numbers and are transiently stable for larger wave numbers when there is either no mass transfer or there is evaporation from the film surface, and although the magnitude of the disturbance amplitude is larger when the magnetic field is present, it decays to zero earlier than for the case when the magnetic field is absent, and (b) when absorption is present at the film surface, the film exhibits three different domains of stability: disturbances of small wave numbers decay, disturbances of intermediate wave numbers grow transiently, and those of large wave numbers grow exponentially The range of stable wave numbers increases with increase in Hartmann number

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3 citations

References

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Journal Article•DOI•

Flow of a Viscous Liquid on a Rotating Disk

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Alfred G. Emslie, Francis T. Bonner, Leslie G. Peck

01 May 1958-Journal of Applied Physics

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.

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Abstract: Equations describing the flow of a Newtonian liquid on a rotating disk have been solved so that characteristic curves and surface contours at successive times for any assumed initial fluid distribution may be constructed. It is shown that centrifugation of a fluid layer that is initially uniform does not disturb the uniformity as the height of the layer is reduced. It is also 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. Contour surfaces for a number of exemplary initial distributions (Gaussian, slowly falling, Gaussian plus uniform, sinusoidal) have been constructed. Edge effects on rotating planes with rising rims, and fluid flow on rotating nonplanar surfaces, are considered.

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696 citations

"Flow of thin liquid film over a rou..." refers background or result in this paper

...Several theoretical and experimental investigations have been considered by taking into account different aspects of this process ([3], [5], [6], [8], [9], [11], [12], [14], [15]) and these have been sparked by the importance of the study of the detailed mechanism that retains the lubricant onto the surface of the rotating disk....
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...When the initial height of the lubricant is constant, it is observed from Figure 2 that the uniform distribution of lubricant height remains uniform with time for different values of M and when M = 0 the results agree with those of [3]....
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...Case i: smooth disk surface (h(r) = 0) and negligible liquid surface tension (γ = 0) This case addresses the effect of magnetic field on the retention of conducting fluid on the smooth spinning disk and hence is an extension of the work done by [3]....
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...Different initial distributions of the height of the lubricant [3] lead to different relative volume ( Q/Q0 ) of the conducting fluid retained on the spinning disk (Figure 4), where Q0 is the initial fluid volume on the disk....
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Journal Article•DOI•

Film flow on a rotating disk

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Brian G. Higgins

01 Nov 1986-Physics of Fluids

TL;DR: 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.

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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 moreread less

109 citations

"Flow of thin liquid film over a rou..." refers background in this paper

...Several theoretical and experimental investigations have been considered by taking into account different aspects of this process ([3], [5], [6], [8], [9], [11], [12], [14], [15]) and these have been sparked by the importance of the study of the detailed mechanism that retains the lubricant onto the surface of the rotating disk....
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...The radius of the disk is large compared with the thickness of the film so that the edge effect is neglected ([5], [6], [11], [14])....
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Journal Article•DOI•

The effect of induced air‐flow on the spin coating of viscous liquids

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Stanley Middleman

15 Sep 1987-Journal of Applied Physics

TL;DR: In this paper, an approximate analysis using Cochran's classical solution for the induced air flow is presented, and regions where air flow significantly enhances thinning are delineated. But, as film thickness becomes very small, the external air flow dominates the centrifugal effect and controls the final rate of thinning, but not to the degree predicted.

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Abstract: In the spin‐coating process for producing thin films, air flow induced by disk rotation provides a shear stress at the liquid‐air interface which enhances the rate of thinning of the liquid film on the disk. An approximate analysis using Cochran’s classical solution [Proc. Cambridge Philos. Soc. 30, 365 (1934)] for the induced air flow is presented. Regions wherein air flow significantly enhances thinning are delineated. As film thickness becomes very small, in accordance with a dimensionless criterion developed as part of the analysis, the external air flow dominates the centrifugal effect and controls the final rate of thinning. A set of data obtained under conditions appropriate to application of this new theory shows enhanced thinning, but not to the degree predicted.

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102 citations

"Flow of thin liquid film over a rou..." refers background in this paper

...Several theoretical and experimental investigations have been considered by taking into account different aspects of this process ([3], [5], [6], [8], [9], [11], [12], [14], [15]) and these have been sparked by the importance of the study of the detailed mechanism that retains the lubricant onto the surface of the rotating disk....
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Journal Article•DOI•

On the flow of a thin liquid film over a rough rotating disk

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J. H. Hwang

01 Jul 1989-Journal of Applied Physics

TL;DR: In this paper, the depletion of thin viscous films due to centrifugation was studied and the depletion histories of the film were given for cases involving regular patterns of surface asperities.

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Abstract: This study addresses the depletion of thin liquid films due to centrifugation. Equations describing the flow of a thin viscous film over a rough rotating disk are solved by either an analytical or numerical method. Depletion histories of the film are given for cases involving regular patterns of surface asperities. It is found that surface roughness markedly enhances the retention of a thin liquid film on a rotating disk. Moreover, different topographic structures of the surface roughness lead to different asymptotic limits of liquid retention.

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53 citations

Journal Article•DOI•

Depletion and Retention of Fluid on a Rotating Disk

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Yih-O Tu¹•Institutions (1)

IBM¹

01 Oct 1983-Journal of Lubrication Technology

28 citations

"Flow of thin liquid film over a rou..." refers background or methods or result in this paper

...As has been pointed out by Tu [ 14 ] and Hwang and Ma [6], the boundary conditions at the edge of a flnite disk cannot be prescribed in a simple mathematical form due to the complicated edge efiect known as ‘tea-pot efiect’....
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...This case is an extension of the results presented by [6] and [ 14 ] and considers the magnetic efiects on the rate of retention of the liquid lubricant....
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...It is of interest to compute the total volume Q(T) of the lubricant that remains on the rough rotating disk and it is given by [ 14 ]...
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...Using Laplace formula that relates the ∞uid pressure „ p , the surface tension ∞ and the mean curvature 1 according to ([7] and [ 14 ]) „ p = ∞...
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...Several theoretical and experimental investigations have been considered by taking into account difierent aspects of this process ([3], [5], [6], [8], [9], [11], [12], [ 14 ], [15]) and these have been sparked by the importance of the study of the detailed mechanism that retains the lubricant onto the surface of the rotating disk....
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