Method for measurement of viscosity and density of liquid with a slowly rotating column

Abstract

The locus of a fine spherical particle in a slowly rotating column filled with liquid is investigated in detail with a fundamental equation of motion, and a method for measurements of viscosity η and density ρ′ of the liquid is proposed. With a particle having the radius a=10−3–10−2 cm from the restriction Re≲1, (Re, Reynolds number) and the density ρ within 1.5ρ′≲ρ<4ρ′ in a column rotating at the angular velocity ω0 within 1.5≲Aω0/V0<2, the particle locus becomes almost a circle with a diameter D that sensitively correlates with η and ρ′ to be measured, where A=A0−a (A0, column radius) and V0 is the speed at free fall. For one particle (a one-particle system), η is universally measurable for almost any kind of liquid with a known ρ′. A two-particle system is also proposed for the continuous measurement of both η and ρ′, and would be applied, for example, at varying temperatures or in the course of a chemical reaction.