The Flow Between Two Parallel Circular Disks, One of Which is Subject to a Normal Sinusoidal Oscillation
01 Jan 1969-Journal of Lubrication Technology (American Society of Mechanical Engineers)-Vol. 91, Iss: 1, pp 126-131
About: This article is published in Journal of Lubrication Technology.The article was published on 1969-01-01. It has received 27 citations till now. The article focuses on the topics: Flow (mathematics).
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TL;DR: In this article, a theoretical study of the flow behavior of thin Newtonian liquid films being squeezed between two flat plates is made, and solutions to the problem are obtained by using a numerical method, which is found to be stable for all Reynolds numbers, aspect ratios, and grid sizes tested.
Abstract: A theoretical study is made of the flow behavior of thin Newtonian liquid films being “squeezed” between two flat plates. Solutions to the problem are obtained by using a numerical method, which is found to be stable for all Reynolds numbers, aspect ratios, and grid sizes tested. Particular emphasis is placed on including in the analysis the inertial terms in the Navier-Stokes equations. Comparison of results from the numerical calculation with those from Ishizawa's perturbation solution is made. For the conditions considered here, it is found that the perturbation series is divergent, and that in general one must use a numerical technique to solve this problem.
110 citations
TL;DR: In this paper, the authors show that the complete parameter range is covered by three classes of models: the standard wave equation model, the low reduced frequency model and the full linearized Navier-Stokes model.
82 citations
TL;DR: In this article, the authors deal with pressure wave propagation in a gas trapped in thin layers or narrow tubes, where viscous and thermal effects can have a significant effect on the propagation of waves.
Abstract: This research deals with pressure waves in a gas trapped in thin layers or narrow tubes. In these cases viscous and thermal effects can have a significant effect on the propagation of waves. This so-called viscothermal wave propagation is governed by a number of dimensionless parameters. The two most important parameters are the shear wave number and the reduced frequency.
75 citations
Cites background from "The Flow Between Two Parallel Circu..."
...Increasing machine speeds and the use of gas bearings initiated research on the role of inertia [7, 8, 9, 10, 11, 12, 13, 14, 15]....
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TL;DR: In this paper, the authors studied the special case where one surface is fixed and the other is rapidly accelerated from a state of rest to a uniform motion, based in part on linear theory and in substance on a finite difference analysis of the full nonlinear equations of motion.
Abstract: We study the motion which results when a fluid film is squeezed between two parallel plane surfaces in relative motion. Particular attention is given to the special case where one surface is fixed and the other is rapidly accelerated from a state of rest to a state of uniform motion. The analysis is based in part on linear theory and in substance on a finite-difference analysis of the full nonlinear equations of motion.
61 citations
Cites background or methods from "The Flow Between Two Parallel Circu..."
...Equation (3) is the same equation given by Terrill (1969). The transformed boundary conditions are F = 0, F = 0, y = 0; F = cos t/2, F = 0, y = 1....
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...Terrill (1969) obtained an analytic solution that depends on two parameters, the nondimensional amplitude of the oscillation of the surface and a Reynolds number that is related to the maximum velocity of the vibrating surface....
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...The nondimensionalization used by Terrill (1969) will be employed here....
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...(3) Equation (3) is the same equation given by Terrill (1969)....
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...Terrill (1969), correctly obtained f0 , f1 , g1 and g2 through using a perturbation scheme....
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TL;DR: In this paper, the exact solution of the Navier-Stokes equation is obtained as a multifold series of an infinite set of time-dependent nondimensional parameters, for small values of the parameters, and applied to the case when the walls perform harmonic oscillations with finite amplitude.
49 citations