SOLUTION FOR THE OSCILLATION OF A NEWTONIAN FLUID IN A CO-AXIAL VISCOMETER

When one cup of a co-axial viscometer oscillates,the measured moment on theother(stationary)cup shows a phase lag,partly due to the inertial effect of the fluidwithin the gap between the cups.In this paper such an effect is illustrated by a newexact solution of the Navier-Stokes equation,which is derived herein by a scheme ofreducing it to a two-point boundary value problem for ODEs,Our numerical resultsindicate that,as the Womersley number a or the dimensionless gap widthδincreases,the fluid velocity profile within the gap gradually deviates from the linear one andtransits to that of the boundary layer type,with the result that the moment decreasesin the magnitude and lags behind in the phase.With the advantage of high accuracyand excellent stability,the scheme proposed herein can readily be extended to solveother linear periodic problems.