Open AccessA Fluid Film Squeezed Between Two Parallel Plane Surfaces Subject to Normal Oscillations
Author(s) -
E. A. Hamza
Publication year - 2002
Publication title -
maǧallaẗ ǧāmiʿaẗ al-sulṭān qābūs li-l-ʿulūm/sultan qaboos university journal for science
Language(s) - English
Resource type - Journals
eISSN - 2414-536X
pISSN - 2308-3921
DOI - 10.24200/squjs.vol7iss2pp283-294
Subject(s) - perturbation (astronomy) , nonlinear system , plane (geometry) , mathematical analysis , motion (physics) , physics , rest (music) , classical mechanics , equations of motion , differential equation , inclined plane , partial differential equation , mathematics , mechanics , geometry , quantum mechanics , acoustics
We study the motion which results when a fluid film is squeezed between two parallel surfaces in relative motion. Particular attention is given to the special case where one surface is fixed and the other is impulsively accelerated from a state of rest to a state of sinusoidal oscillations in a direction normal to its plane. In addition to the presentation of analytic solutions which are based on the regular perturbation technique and on the linearised analysis of the resulting nonlinear partial differential equation, a numerical solution of the full nonlinear equation based on a finite-difference scheme is obtained. The effects of the sinusoidal motion on the velocity profiles and on the normal forces which the fluid exerts on the surfaces are investigated.