Flow of a Viscoelastic Fluid between Eccentric Cylinders. I. Rectilinear Shearing Flow.

摘要

The longitudinal flow of a viscoelastic fluid in the annular region between two cylinders of circular cross-section with parallel, but not coincident, axes is considered. Instead of considering the flow resulting from the application of a constant longitudinal pressure gradient (i.e. Poiseuille flow), the somewhat simpler problem of the flow resulting from the motion of the inner cylinder, parallel to its axis, with constant velocity is considered, the outer cylinder being held fixed. The resulting flow is called longitudinal shearing flow. It is found that the resultant forces, per unit length, which are exerted on the inner cylinder by the fluid, consist of a longitudinal force opposing the motion of the inner cylinder, a transverse force, the line of action of which intersects the axes of the cylinders, and a couple about a line intersecting the axis of the inner cylinder and perpendicular to the plane containing the axes of the two cylinders. These resultant forces are calculated as functions of the radii of the cylinders and the distance between their centers. The longitudinal force and couple are, of course, precisely the same as those for a Newtonian fluid, whose viscosity is the same as that of the second-order fluid. However, the transver force is, of course, zero in the case of a Newtonian fluid. Simpler approximate formulate are obtained for the following cases: (1) the radius of the inner cylinder is small compared with that of the outer cylinder, (2) the radii of the two cylinders are nearly equal, (3) the cylinders are nearly coaxial, (4) the cylinders are nearly touching. (Author)