Experimental Study on the Effect of Bubble Concentration on the Effective Viscosity of Liquids

It is widely accepted that the volatile gas in magma plays an important role in volcanic eruptions. With the ascent of magma, pressure gradually decreases and increases the degree of supersaturation of volatile components and consequently, nucleation of the gas phase is initiated. Though the dynamical process of magma in a volcanic conduit is very complicated, the viscosity of magma is known to be a fundamentally important factor. As for the effective viscosity of a liquid containing small concentration of bubbles, Taylor, Batchelor and Shimozuru derived theoretically the following formula, ηe/η0 = (1 + φ), where φ is the volume concentration of bubbles. But if violent nucleation happens, the concentration of bubbles will increase rapidly and the interaction of bubbles will not be ignored. The author tried to examine experimentally how the effective viscosity varies when bubble concentration is large. The viscosity was measured using a specially deviced rotation viscometer in which air bubbles were injected from the bottom into silicon oil. The torque of the inner cylinder was measured for various bubble concentration. The results of experiments show that the change of the effective viscosity coincides with the theoretical predicted curve within the bubble concentration below 30%, above which, the experimental value tends to increase. The empirical formula which is written below is the best fit curve of the change of the effective viscosity of liquid which contains bubbles with volume fraction less than 40%. ηe/η0=(1-1.5φ)-0.55 (O.O<φ