Oscillatory motion of an elastico-viscous liquid contained in a cylindrical cup: I. Theoretical

Abstract

The theory of an oscillatory motion of a liquid and its containing cylindrical cup (when the motion of the latter is constrained by a torsion wire) is developed; the liquid is one the viscous and elastic properties of which are assumed to be characterized by three constants, namely a viscosity and two relaxation times. When the amplitude of the oscillation is sufficiently small (i.e. small enough for no secondary flow to set in), it is shown that the values of the elastic constants of such a liquid can be deduced from calculations of two very easily and accurately measurable quantities, namely the time period of the oscillation and the logarithmic decrement in the amplitude of the oscillation.