Fluid mode spectroscopy for measuring kinematic viscosity of fluids in open cylindrical containers

Abstract

On a daily basis, we stir tea or coffee with a spoon and leave it to rest. We know empirically the larger the stickiness, viscosity, of the fluid, the more rapidly its velocity slows down. It is surprising, therefore, that the variation, the decay rate of the velocity, has not been utilized for measuring (kinematic) viscosity of fluids. This study shows that a spectroscopy decomposing a velocity field into fluid modes (Stokes eigenmodes) allows us to accurately measure the kinematic viscosity. The method, fluid mode spectroscopy (FMS), is based on the fact that each Stokes eigenmode has its inherent decay rate of eigenvalue, and the dimensionless rate of the slowest decaying mode is constant, dependent only on the normalized shape of a fluid container, obtained analytically for some shapes including cylindrical containers. The FMS supplements major conventional measuring methods with each other, which is particularly useful for measuring relatively low kinematic viscosity and for a direct measurement of viscosity at zero shear rate without extrapolation. The method is validated by the experiments of water poured into an open cylindrical container, as well as by the corresponding numerical simulations.