NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2013, 4 (5), P. 592–604
RESPONSE OF A STRATIFIED VISCOUS HALF-SPACE TO A PERTURBATION OF THE FREE SURFACE
S. A. Chivilikhin – St. Petersburg National Research University of Information Technologies, Mechanics and Optics, St. Petersburg, Russia; firstname.lastname@example.org
A. S. Amosov – Corning Incorporated, Corning, USA; email@example.com
I. F. Melikhov – St. Petersburg National Research University of Information Technologies, Mechanics and Optics, St. Petersburg, Russia; firstname.lastname@example.org
The flow of a highly viscous liquid in a half-space due to the deformation of the free surface is investigated. The viscosity of the layer adjoining to the free surface is different from the viscosity of the remaining half-space. In the framework of small perturbation theory, the relationship between the deformation of the free surface and the deformation of the layer/half-space interface is obtained. It was demonstrated that the volume and geometrical center of the perturbation on the interface and on the free surface are the same. The dependence of the perturbation’s amplitude and width on layer thickness was investigated. The results of numerical and analytical calculations are close, even for moderate free surface perturbations.
Keywords: quasisteady-state Stokes approximation, free surface, linear approximation, evolution of perturbation.