Slow Motion and Viscometric Motion. Part V. The Free Surface on a Simple Fluid Flowing Down a Tilted Trough.

摘要

This paper is a contribution to the theory of viscometry of slow steady motions of a simple fluid and is presented as Part V of the work on slow motion and viscometric motion which formed the subject of the paper in four parts of Joseph (1974). The tilted trough viscometer, studied here, exploits the fact that the free surface on a viscoelastic fluid flowing down an open channel which is inclined to the horizontal will deform under the action of normal stresses induced by flow. The trough is a companion to the rotating rod viscometer (Joseph, Beavers and Fosdick, 1974: Beavers and Joseph, 1975). Both the rod and the trough utilize the idea that the shape of the free surface depends on material parameters. By using the two instruments one can, at a minimum, determine the values of the two Rivlin-Ericksen constants of the 2nd order approximation relating stress to deformation in the slow steady motion of simple fluid. A proposal is made to use the formulas derived here as the guiding theory for the experimental determination of the special combinations of RE constants which arise in the study of flow down a tilted trough. The solution is calculated, in a series of powers, of the tilt angle beta and it is shown that secondary motions do not appear until sixth order when the trough is infinitely deep or has a semicircular cross-section. For these troughs simple formulas are given relating the shape of the free surface to the RE constants of the first, second, third and fourth-order fluids. (Author)