Summary
A numerical solution is obtained for the development of a conducting fluid film on the surface of a spinning disc, in the presence of a magnetic field applied perpendicular to the disc. A finite-difference method is employed to obtain the solution of Navier-Stokes equations modified to include magnetic forces due to MHD interactions. The combined effects of film inertia, acceleration of the disc and magnetic forces are analysed. The numerical results reveal that the rate of thinning of the fluid film is strongly influenced by the inertial and magnetic forces when the Reynolds number is large and that the existing asymptotic theory by Ray and Dandapat [24] is inadequate for predicting transient film thickness. When the disc has a finite acceleration at the start-up, the magnetic and inertia effects are important even at low Reynolds numbers and the thinning rate is reduced. It is observed that for both low and high Reynolds number flows, the film thickness increases with Hartmann numberM for a fixed time and the rate of depletion is less for largeM than for smallM.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ghandi, S. K.: VLSI fabrication principles. New York: Wiley 1983.
Weiss, R. D.: Perpendicular orientation of aeicularr-Fe2O3 on recording discs. IEEE Transactions of Magnetics.19, 1677–1679 (1983).
Emslie, A. G., Bonner, F. T., Peck, L. G.: Flow of a viscous liquid on a rotating disk. J. Appl. Phys.29, 858–862 (1958).
Thomas, I. M.: High Laser Damage threshold porous silica antireflective coating. Applied Optics.25, 1481–1483 (1986).
Acrivos, A., Shah, M. J., Petersen, E. E.: On the flow of a non-Newtonian liquid on a rotating disk. J. Appl. Phys.31, 963–968 (1960).
McConnell, W. H.: On the rate of thinning of thin liquid films on a rotating disk. J. Appl. Phys.64, 2232–2233 (1988).
Flack, W. W., Soong, D. S., Bell, A. T., Hess, D. W.: A mathematical model for spin coating of polymer resists. J. Appl. Phys.56, 1199–1206 (1984).
Bornside, D. E., Macosko, C. W., Scriven, L. E.: On the modeling of spin coating. J. Imag. Tech.13, 122–128 (1987).
Jenekhe, S. A., Schuldt, S. B.: Coating flow of non-Newtonian fluids on a flat rotating disk. Ind. Eng. Chem. Fund.23, 432–436 (1984).
Tu, O. Y.: Depletion and retention of fluid on a rotating disk. J. Lub. Tech.105, 625–629 (1983).
Chun, B. T.: Investigation of the solvent-evaporation effect on spin coating of thin films. Polym. Eng. Sci.23, 399–403 (1983).
Lawrence, C. J.: The mechanics of spin coating of polymer films. Phys. Fluids.31, 2786–2795 (1988).
Yanagisawa, M.: Slip effect for thin liquid film on a rotating disk. J. Appl. Phys.61, 1034–1037 (1987).
Middleman, S.: The effect of induced air-flow on the spin-coating of viscous liquids. J. Appl. Phys.62, 2530–2532 (1987).
Meyerhofer, D.: Characteristics of resist films produced by spinning. J. Appl. Phys.49, 3993–3997 (1978).
Jenekhe, S. C.: Effects of solvent mass transfer on flow of polymer solutions on a flat rotating disk. Ind. Eng. Chem. Fund.23, 425–432 (1984).
Hwang, J. H., Ma, F.: On the flow of a thin liquid film over a rough rotating disk. J. Appl. Phys.66, 388–394 (1989).
Dandapat, B. S., Ray, P. C.: Film cooling on a rotating disk. Int. J. Nonlinear Mech.25, 569–582 (1990).
Dandapat, B. S., Ray, P. C.: Flow of a thin liquid film over a cold/hot rotating disk. Int. J. Nonlinear Mech.28, 489–496 (1993).
Dandapat, B. S., Ray, P. C.: The effect of thermocapillarity on the flow of a thin liquid film on a rotating disk. J. Appl. Phys.27, 2041–2045 (1994).
Higgins, B. G.: Flow on a rotating disk. Phys. Fluids.29, 3522–3529 (1986).
Regh, T. J., Higgins, B. G.: The effect of inertia and interfacial shear on film flow of a rotating disk. Phys. Fluids.31, 1360–1371 (1988).
Wang, C. Y., Watson, L. T., Alexander, K. A.: Spinning of a liquid film from an accelerating disk. IMA J. Appl. Math.46, 201–210 (1991).
Ray, P. C., Dandapat, P. S.: Flow of thin liquid film on a rotating disk in the presence of a transverse magnetic field. Quart. J. Mech. Appl. Math.47, 297–304 (1994).
Roberts, G. O.: Lecture Notes in Physics. New York: Springer, No.8, pp. 171–175 (1971).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Usha, R., Götz, T. Spinning of a liquid film from a rotating disc in the presence of a magnetic field — a numerical solution. Acta Mechanica 147, 137–151 (2001). https://doi.org/10.1007/BF01182358
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01182358