Dynamics of rising bubbles in gradually mixing fluids due to the effect of Rayleigh–Taylor instability

Abstract

Three dimensional dynamics of rising bubbles in gradually mixing fluids due to the effect of Rayleigh-Taylor instability have been numerically investigated. The effect of various parameters such as Eotvos (Eo) number and Morton (M) number for three different cases represented as single bubble rising, inline bubbles rising and offset bubbles rising are comprehensively investigated. It is observed that, two raising bubbles either inline or offset exhibits higher terminal Reynolds number (ReT) in quiescent liquids when compared with single rising bubble. They enhances ReT by 120.22% for Eo = 38.8 and M = 9.71 × 10−4. Moreover, in gradually mixing fluids due to the presence of Rayleigh-Taylor instability, single rising bubble also exhibits higher ReT and at earlier time. In fluids with low Eo and high M values, mixing effect is very slow because of the presence of higher value of fluids internal resistance as well as high cohesive forces. This causes a delay in the formation of bubble behind the rising pre-defined bubbles. Whereas, in the opposite case, this bubble forms much quicker. But the rising pre-defined bubble breaks up and gradually vanishes off with time. Due to significant decrement in the fluids internal resistance, it is also observed that; at same Eo = 10, by decreasing the value of M from 9.71 × 10−4 to 9.71 × 10−8, the ReT value is increased by 48.84% for inline and offset bubbles. Furthermore, at same M = 9.71 × 10−4, by increasing the value of Eo from 10 to 38.8, 18.3% lower time is required for single bubble to attain higher velocity. This is due to the presence of low cohesive forces and high fluids internal resistance.