Journal ArticleDOI
Film flow on a rotating disk
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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
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Journal ArticleDOI
On the spin coating of viscoplastic fluids
TL;DR: In this paper, a finite element/Newton-Raphson method is presented for solving the moving boundary problem after mapping the deforming domain onto a fixed one, assuming axial symmetry, the effect of the Bingham, Reynolds, Capillary and gravitational Bond numbers is examined.
Journal ArticleDOI
Investigation of the effect of the Coriolis force on a thin fluid film on a rotating disk
Ebrahim Momoniat,D.P. Mason +1 more
TL;DR: The effect of the Coriolis force on the evolution of a thin film of Newtonian fluid on a rotating disk is investigated in this article, in which inertia terms in the Navier-Stokes equation are neglected.
Journal ArticleDOI
Film/substrate/vacuum-chuck interactions during spin-coating
Dunbar P. Birnie,Brian J.J. Zelinski,Stuart P. Marvel,Sharon Marilyn Melpolder,Ronald L. Roncone +4 more
TL;DR: In this paper, the thickness variations associated with the vacuum chuck were observed in wet-chemical-derived dielectric films applied by the spin-coating technique, and these thickness variations are controlled by factors such as the thermal properties of the substrate material, the evaporation behavior of the coating solution, and the physical design of the vacuum CH.
Journal ArticleDOI
Spin coating of viscoelastic and nonvolatile fluids over a planar disk
TL;DR: In this article, a theoretical analysis of spin coating of two commercially used polymer solutions is studied both theoretically and experimentally, and the amplitude of these oscillations increases with the ratio of the retardation parameter to Deborah number, whereas their damping rate gets smaller as De increases.
Journal ArticleDOI
Suspension mechanics for particle contamination control
TL;DR: In this article, a review is intended to bridge the gap between research in particle contamination control for the electronics industry and research in the fluid mechanics of small-particle motions; these two subjects are clearly closely related, but there seems to have been a lack of communication in the past.
References
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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.
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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.
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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.