An experimental study of the motion of a viscous liquid contained between two coaxial cylinders

Abstract The stability of a viscous liquid contained between two coaxial cylinders which are capable of independent rotation has been investigated by G. I. Taylor. At low speeds of rotation the motion of the liquid is two-dimensional, each particle of liquid rotating in a circle concentric with the cylinders. This type of motion is possible whether the cylinders rotate in the same or in opposite directions, and is stable for velocities of the inner cylinder not exceeding a certain critical value. At the critical speed the laminar motion is succeeded by a three-dimensional motion, such that the circulation of the liquid is confined to a scries of annular compartments, one above the other. When both cylinders rotate in the same direction, the height of each compartment equals the distance between the cylinders, and the motion in an axial plane appears to consist of a series of vortices in square compartments, adjacent vortices rotating in opposite directions. For cylinders rotating in opposite directions there are, at a given horizontal level, two annular compartments side by side and concentric with the cylinders. In this case, the circulation in an axial plane appears to consist of two series of vortices, adjacent vortices both vertically and horizontally rotating in opposite directions. By using coloured liquid filaments to follow the motion, Taylor verified experimentally, within a limited range, the expression for the critical velocity at which the stream-line motion becomes unstable and certain other points. The apparatus used was large and robust, the length of the cylinders being 90 cm., and it was unsuitable for investigating the motion under varying conditions, such as with inner cylinders of different diameters and with liquids giving a wide range in viscosity.