The onset conditions of oscillatory motion of single gas bubbles rising in various liquids.

Abstract

Manystudies have been made about the behaviors of single gas bubbles ascending in various liquids, that is, the rising velocities or the shapes of single bubbles2'4'8)9). Single bubbles rise in a straight line when the bubble diameter is very small, and with increase of the bubble diameter, the path of the gas bubble turns to be zigzag or spiral. On the condition of onset of zigzag or spiral motion, Saffman6) and Hartunian and Sears3) carried out experimental and theoretical work. Saffman6) suggested that the zigzag motion was caused by the interaction between a periodic oscillation of the wake and the instability of the motion near the front of the bubble, and deduced that the value of the critical Weber number WeGat which instability appeared was 1.03. But this criterion does not agree with experimental results. Hartunian and Sears3) suggested that the interaction between surface tension and hydrodynamic pressure could result in instability of the bubble motion, and on a basis of the existing data and their ownexperimental results, they proposed that there

Paths and wakes of deformable nearly spheroidal rising bubbles close to the transition to path instability

“…[23]; dash-dotted and dashed lines, critical curves obtained in Ref. [24] using the LSA approach with a freely moving and a fixed bubble, respectively; and symbols, experimental data corresponding to incipient path instability observed in various liquids (+ [12], × [13], • [4], [14], [9], [10], and ◮ [11]). …”

“…The transition from a rectilinear to an oscillatory path was specifically examined in Refs. [4,5,[7][8][9][10][11][12][13][14]. Some of the corresponding results are displayed in Fig.…”

Bubble Rise Phenomena in Non-Newtonian Crystal Suspensions

“…Under the same experimental conditions, Yoshida and Manasseh (1997) reported that the bubbles can also follow a spiral trajectory without vortex shedding. Tsuge and Hibino (1997) reported that the trajectories of rising spherical and ellipsoidal gas bubbles at higher Reynolds numbers are identical.…”

“…Duineveld (1994) . The onset of path instability is generally assumed to occur at a critical Weber number (Duineveld, 1994;Maxworthy, 1996 andTsuge andHibino, 1997). Tsuge and Hibino (1997) proposed an empirical relation for determining cr We which is presented in equation (11).…”

“…Deane and Stokes (2002) indicated that 4.7 cr We  must be exceeded for the deformation of the bubble to occur, and they found the critical Reynolds number Re (450) cr that must be exceeded for bubble shape oscillations and elongation and subsequent deformation to occur in water. Tsuge and Hibino (1997) proposed an empirical relation for determining …”