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

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

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.

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

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

Flow of a Viscous Liquid on a Rotating Disk

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.

Film flow on a rotating disk

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.

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

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.

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

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.