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The Stokes drag and couple acting on a disc moving through incompressible Newtonian fluid are investigated for the case when the fluid obeys a Navier slip condition, with slip length b, on the surface of the disc. The fluid is bounded by an infinite plane wall on which there is no slip. The disc, of zero thickness and radius a, is parallel to the wall and distance h from it. Analyses are presented for the limits h ≫a and h ≪a; results for intermediate values of the separation h are obtained numerically by means of Tranter's method. The resistance coefficients for translation normal to the disc surface, and for rotation about a diameter, are unaffected by slip when the disc lies in unbounded fluid, but all resistance coefficients depend upon the slip length b when the disc is close to the wall. Their dependence on h becomes weak when b≫a. [ABSTRACT FROM AUTHOR]

The container shape that minimizes the volume of draining fluid remaining on the walls of the container after it has been emptied from its base is determined. The film of draining fluid is assumed to wet the walls of the container, and is sufficiently thin so that its curvature may be neglected. Surface tension is ignored. The initial value problem for the thickness of a film of Newtonian fluid is studied, and is shown to lead asymptotically to a similarity solution. From this, and from equivalent solutions for power-law fluids, the volume of the residual film is determined. The optimal container shape is not far from hemispherical, to minimize the surface area, but has a conical base to promote draining. The optimal shape for an axisymmetric mixing vessel, with a hole at the center of its base for draining, is also optimal when inverted in the manner of a washed wine glass inverted and left to drain. [ABSTRACT FROM AUTHOR]

A wellbore (radius b) filled with Newtonian fluid (viscosity η), contains a cylindrical drill string [radius a=b(1-ε)] that touches the wall of the wellbore. Lubrication theory is applied to the fluid-filled annular gap between cylinder and wall, while Darcy’s law is assumed valid within the rock surrounding the wellbore. The force required to lift the cylinder away from the wall with velocity U is F=bBπA-3/5, where B=12ηU/bε3 and A=12k/b2ε3<1. The couple required to rotate the cylinder (in a rolling motion) with angular velocity ω is T=0.75Db2πA-1/5, where D=12ηωε-3. The effect of a filter cake of permeability kc and thickness g