A Thin Conducting Liquid Film on a Spinning Disk in the Presence of a Magnetic Field: Dynamics and Stability
01 Jul 2009-Journal of Applied Mechanics (American Society of Mechanical Engineers)-Vol. 76, Iss: 4, pp 041002
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.
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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TL;DR: In this paper, the effects of rotation and inertia on the thin-film flow formed by a circular jet impinging on a rotating disk is analyzed theoretically and the location and height of the hydraulic jump are determined subject to the value of the thickness at the edge of the disk, which is established first for a stationary disk based on the capillary length, and then for a rotating disks using existing analyses and measurements in spin coating.
Abstract: The free-surface flow formed by a circular jet impinging on a rotating disk is analysed theoretically. The study explores the effects of rotation and inertia on the thin-film flow. Both boundary-layer height and film thickness are found to diminish with rotation speed. A maximum film thickness develops in the supercritical region, which reflects the competition between the convective and centrifugal effects. Unlike the flow on a stationary disk, an increase in the wall shear stress along the radial direction is predicted, at a rate that strengthens with rotating speed. Our results corroborate well existing measurements. The location and height of the hydraulic jump are determined subject to the value of the thickness at the edge of the disk, which is established first for a stationary disk based on the capillary length, and then for a rotating disk using existing analyses and measurements in spin coating. The case of a stationary is revisited in an effort to predict the location and height of the jump uniquely. The formulated value of the height at the edge of the disk seems to give excellent results for a jet at moderately high flow rate (or low viscosity) where the jump structure is well identifiable in reality.
26 citations
Cites background from "A Thin Conducting Liquid Film on a ..."
...The flow of a thin film over a rotating disk is important in numerous industrial applications such as the spinning disk reactor, spin coating, jet cooling of rotating devices, spray and atomization and powder production (Lawley 1992; Uma & Usha 2009)....
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TL;DR: This article reviews experimental and modeling methods for determining the critical roles played by the various factors that control nanocarrier drug delivery to vascular endothelial cells.
Abstract: This article reviews experimental and modeling methods for determining the critical roles played by the various factors that control nanocarrier drug delivery to vascular endothelial cells.
19 citations
Cites background from "A Thin Conducting Liquid Film on a ..."
...Magnetic nanofilms or nanosheets (also called polymeric ultra thin films) produced using a spin-coating process (43) are also used for delivering drug loaded patches on inner organ walls or on ulcers....
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TL;DR: In this article, a dynamic model of the atomizing disc as a spinning Kirchhoff plate is established with moving melt film treated as a moving load on the disc and as an unstable growing wave interacting with the surrounding air outside the disc.
Abstract: Spinning discs with liquid film on the surface have numerous applications in many industrial processes and have attracted a lot of investigations. Centrifugal atomization of metallic melts using a spinning disc is an efficient process for powder production and spray deposition, which is a typical example of a spinning disc interacting with a liquid film. In this paper, the vibration of an atomizing disc excited by a moving melt is analysed and the role of vibration in the disintegration of the melt film on atomizing discs is then investigated. A dynamic model of the atomizing disc as a spinning Kirchhoff plate is established with moving melt film treated as a moving load on the disc and as an unstable growing wave interacting with the surrounding air outside the disc. The powder size is analysed theoretically and then compared with experimental results. It is found that the predicted results agree with the experimental results very well in the film disintegration mode. Furthermore, the influences of the atomizer parameters on the melt break up and powder size are discussed. The control parameters in the centrifugal atomization are identified, which can provide guidance for atomizer designs.
12 citations
Cites background from "A Thin Conducting Liquid Film on a ..."
...A spinning disc interacting with a thin liquid film on the surface has attracted numerous investigations in science and engineering because of its various applications in many industrial processes that range from chemical reactors to powder production in metallurgy (Uma & Usha 2009)....
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845 citations
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.
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.
696 citations
TL;DR: In this article, the authors consider horizontal static liquid layers on planar solid boundaries and analyse their instabilities, including the effects of mass loss (or gain) and non-equilibrium thermodynamic effects.
Abstract: We consider horizontal static liquid layers on planar solid boundaries and analyse their instabilities. The layers are either evaporating, when the plates are heated, or condensing, when the plates are cooled. Vapour recoil, thermocapillary, and rupture instabilities are discussed, along with the effects of mass loss (or gain) and non-equilibrium thermodynamic effects. Particular attention is paid to the development of dryout. We derive long-wave evolution equations for the interface shapes that govern the two-dimensional nonlinear stability of the layers subject to the above coupled mechanisms. These equations are analysed and their predictions discussed. Previous theoretical and experimental results are reviewed and compared with the present results. Finally, we discuss limitations of the modelling and extend our derivation to the case of three-dimensional disturbances.
648 citations
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.
Abstract: A model is presented for the description of thin films prepared from solution by spinning. Using only the centrifugal force, linear shear forces, and uniform evaporation of the solvent, the thickness of the film and the time of drying can be calculated as functions of the various processing parameters. The model is compared with experimental results obtained on positive photoresists and excellent agreement is obtained. When adequate care are is taken, the liquid forms a level surface during spinning, and the film thickness becomes uniform and independent of the size of the substrate. The film thickness h shows the following dependence on spin speed f, initial viscosity ν0, and evaporation rate e:h∝f−2/3νo1/3e1/3, and e is proportional to f1/2.
628 citations
01 Nov 1982
TL;DR: In this article, a nonlinear evolution equation is derived for h ( x, t ), the film thickness, and this strongly nonlinear partial differential equation is solved by numerical methods as part of an initial value problem for periodic boundary conditions in x, the lateral space dimension.
Abstract: The present work aims at examining nonlinear effects on film rupture by investigating the stability of thin films to finite amplitude disturbances. The dynamics of the liquid film is formulated using the Navier-Stokes equations augmented by a body force describing the London/van der Waals attractions. The liquid film is assumed to be charge neutralized, nondraining, and laterally unbounded. A nonlinear evolution equation is derived for h ( x , t ), the film thickness. This strongly nonlinear partial differential equation is solved by numerical methods as part of an initial-value problem for periodic boundary conditions in x , the lateral space dimension. Given this model, one obtains true rupture in the sense that the film thickness becomes zero in a finite time. The results reveal rupture characteristics and effects of nonlinearities on the rupture properties.
426 citations