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The stability of viscous rotating liquid columns and their application to rotating viscous liquid jets aligned under gravity is reviewed. Experiments on stable viscous fluid flow discharged from rotating vertical pipes exhibit very weak contraction. We present an elementary liquid jet analysis to understand this phenomenon. Indeed, our inviscid model of a slender rotating inviscid liquid jet shows that rotation suppresses contraction. Next we study the comparable problem for granular flow. Our model for noncohesive granular flow emanating from a vertical pipe rotating about its central axis, valid for sufficiently large rotation rate, shows that the granular profiles blossom rather than contract. The profiles of both the liquid and granular jets depend on the same dimensionless parameters—an exit Froude number Fr0 and an exit swirl parameter χ0. The limitations of both models are discussed. Experimental data for granular jet profiles compare well with the collision-free granular flow model in its range of applicability. A criterion for the rotation rate at which particles adjacent to the inner wall of the rotating pipe cease to flow is also given and compared to experiment. [ABSTRACT FROM AUTHOR]

An experimental study of the drag on hollow cylinders and conglomerates falling in a viscous fluid under Stokes flow conditions is described. The experiments were carried out in a tank of square cross section using silicone oil as the Newtonian fluid. Settling velocities of the free falling objects were measured and corrected to conditions of zero Reynolds number flow in an unbounded fluid. The results reveal that all objects tested have Stokes settling velocities smaller than that of a sphere of equal mass and volume. Measurements are reported in terms of the settling speed ratio defined as the ratio of the Stokes settling speed to that of a sphere of equal mass and volume. For the hollow cylinders two parameters are varied: the aspect ratio (length to outside diameter) and the radius ratio (inner to outer radius). Measurements show that the settling speed ratio decreases markedly as the hollowness of the cylinder increases. Each fixed radius ratio data set exhibits a maximum settling speed ratio near an aspect ratio of 1.65. For conglomerates composed of n spheres two trends appear: one for planar configurations and the other for globular clusters. Experimental data for two spheres and three spheres in point contact are in good agreement with recent theoretical results. [ABSTRACT FROM AUTHOR]

An experimental study has been made of the hydrodynamic stability of viscous fluid flow contained between the differentially heated walls of a tall vertical annulus. Tests were conducted using different glycerol solutions spanning a range of Rayleigh numbers (104–106) and moderately high Prandtl numbers (15–150) for a height/gap ratio of 64 and a radius ratio equal to 0.62. Visualization studies show that the unstable flow consists of two separate progressive wave systems, one ascending the hot inner wall and the other descending the cold outer wall. The approximate Rayleigh number, phase speed, and wavelength at the onset of instability for each wave system were determined for several Prandtl numbers. The regular wave patterns observed near the stability boundary persist over only a very limited range of supercritical Rayleigh numbers above which flow dislocations set in. At higher Rayleigh numbers these random dislocations appear in increasing numbers and ultimately render the flow turbulent. [ABSTRACT FROM AUTHOR]