Buoyancy-Driven Path Instabilities of Bubble Rising in Simple and Polymer Solutions of Hele–Shaw Cell

Abstract

The buoyancy-driven path instabilities of an air bubble rising in a Hele–Shaw cell are examined as a function of the ratio of the gravitational and the capillary forces, i.e., the Eötvös number ( Eo ) of the bubble, for pure water, aqueous isopropyl alcohol (IPA) solutions, and aqueous hydroxypropyl methyl cellulose (HPMC) solutions. In the simple solutions, when Eo exceeds a threshold value, the motion of the bubble center can be categorized into three regimes: (1) a zigzag path for small Eo , (2) a straight path for intermediate Eo , and (3) another zigzag path accompanied by changes in the bubble for larger Eo ; these transitions occur irrespective of the fluid we examined. For HPMC solutions with concentrations lower than 0.001 g/100 mL, three different trajectories–a damped vibrational motion without changes in the bubble shape, a straight trajectory, and another damped vibrational motion accompanied by changes in the bubble shape–are observed as Eo increases. However, such path instabilities are suppressed for HPMC solutions with concentrations higher than 0.005 g/100 mL. Moreover, path instabilities occur when the Strouhal number exceeds a threshold of 0.2, which leads to the oscillation of the periphery length of the bubble for any of the solutions we studied.