Author
R. M. Terrill
Bio: R. M. Terrill is an academic researcher from University of Liverpool. The author has contributed to research in topics: Flow (mathematics). The author has an hindex of 1, co-authored 1 publications receiving 27 citations.
Topics: Flow (mathematics)
Papers
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27 citations
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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
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
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