Intermediate viscosity in a gravity-driven flow and its application to simple viscometry

In a capillary tube flow, if the wall shear stress τw and apparent shear rate 4V/R are given, the viscosity reduces to the viscosity τw/(4V/R) at a dimensionless intermediate radius ra* (≡ra/R) of approximately 0.8, where the shear rate is ra* × 4V/R. This known result is extended to the quasi-steady gravity-driven flow in a capillary tube, where the fluid head decreases from Hmax to H over a period of T seconds. Using a Carreau and power-law model, the intermediate viscosity for a gravity-driven flow is derived for the logarithmic middle fluid head between Hmax and H. This intermediate viscosity and its shear rate can be obtained from a single measurement of T using a flow setup like an Ubbelohde viscometer. The experimental results validate the proposed method and show its potential for an easy and inexpensive viscometry oriented toward practical applications, like the viscosity measurement of a liquid diet for dysphagia.