When one cup of a co-axial viscometer oscillates, the measured moment on the another (stationary) cup shows a phase lag, partly due to the inertial effect of the fluid within the gap between the two cups. Such an effe...When one cup of a co-axial viscometer oscillates, the measured moment on the another (stationary) cup shows a phase lag, partly due to the inertial effect of the fluid within the gap between the two cups. Such an effect was illustrated by a new exact solution of Navier-Stokes equation, which was derived herein by a scheme of reducing it to a two-point boundary value problem for ordinary differential equations. The numerical results indicate that, as the Womersley number or the dimensionless gap width increases, the fluid velocity profile within the gap gradually deviates from the linear one and transits to that of the boundary layer type, with the result that the moment decreases in the magnitude and lags behind in the phase. With the advantage of high accuracy and excellent stability, the scheme proposed here can be easily extended to solve other linear periodic problems.展开更多
文摘When one cup of a co-axial viscometer oscillates, the measured moment on the another (stationary) cup shows a phase lag, partly due to the inertial effect of the fluid within the gap between the two cups. Such an effect was illustrated by a new exact solution of Navier-Stokes equation, which was derived herein by a scheme of reducing it to a two-point boundary value problem for ordinary differential equations. The numerical results indicate that, as the Womersley number or the dimensionless gap width increases, the fluid velocity profile within the gap gradually deviates from the linear one and transits to that of the boundary layer type, with the result that the moment decreases in the magnitude and lags behind in the phase. With the advantage of high accuracy and excellent stability, the scheme proposed here can be easily extended to solve other linear periodic problems.
