Unsteady measurement of dynamic viscosity

The paper describes a rotating coaxial cylinder rheometer based on unsteady flow, and its technique of operation which, unlike that of conventional devices working in steady regime, dispenses with the need of measuring the resulting torque that arises from the viscous forces on the inner cylinder surface. The equation for calculating the dynamic viscosity has a very simple form; it was derived from a rather difficult theoretical solution of unsteady flow of a Newtonian liquid in the gap between coaxial cylinders and is thus based solely on the knowledge of kinematics of the flow in the instrument. The process of measurement consists in establishing the number of voltage pulses recorded by an electronic counter; the measurement of torque, the other required quantity, is replaced by simple and exact measurement of time. The technique of the dynamic viscosity determination and the resulting equation have been tested using various Newtonian liquids. As an analysis of the exactness of the equation shows, the method is capable of measuring, absolutely, the viscosity with an accuracy better than 1%.List of symbols a radius of the inner cylinder - b radius of the outer cylinder - (t) transient angular velocity of the inner cylinder - ₀ constant angular velocity of the inner cylinder - N number of horizontal holes in the inner cylinder - elevation of the inner cylinder above the bottom of the outer one - r z cylindrical coordinates - r* dimensionless radial coordinate r/b - t* dimensionless time vt/b ² - dynamic viscosity - v kinematic viscosity - * dimensionless transient angular velocity of the liquid / ₀ - A _n constants - _n eigenvalues of the characteristic equation - J _p Bessel function of the first kind of order p - Y _p Bessel function of the second kind of order p - Z _p linear combination of Bessel functions of the first and second kind of order p in Nielsen's sense - ratio of the radii of inner and outer cylinder - dimensionless parameter - density of the liquid - h height of the overflow hole above the outer cylinder bottom - I _z moment of inertia of the rotating system - T _n ^* dimensionless half-time - t time interval - K instrument constant - n _i averave number of voltage pulses at equidistant time intervals - n _i+1 =t _i –t _i–1=t _i+1–t _i - p average value of the ratios n _i/n _i+1 - n(t) instantaneous number of pulses - shear stress - D rate of shear - V volume - Ta Taylor criterion