Mechanics and mass transfer of single bubbles in free rise through some Newtonian and non-Newtonian liquids

New Approaches for Theoretical Estimation of Mass Transfer Parameters in Both Gas-Liquid and Slurry Bubble Columns

“…Calderbank (1967) argue that the eccentricity decreases with increasing viscosity accompanied by the appearance of "tails" behind small bubbles and of spherical indentations in the rear surfaces. Calderbank et al (1970) developed a new theory for mass transfer in the bubble wake. Their work with aqueous solutions of glycerol covers the bubble size range 0.2-6.0×10 -2 m and includes the various bubble shapes as determined by the bubble size and the viscosity of the Newtonian liquid.…”

“…Astarita and Apuzzo (1965) presented experimental results on the rising velocity and shapes of bubbles in both purely viscous and viscoeleastic non-Newtonian pseudoplastic liquids. According to Calderbank et al (1970) bubble shapes observed in distilled water vary from spherical to oblate spheroidal (0.42-1.81×10 -2 m) to spherical cap (1.81-3.79×10 -2 m) with increasing bubble size. Over the size range (4.2-70×10 -3 m) the bubbles rise with a zigzag or spiral motion and between bubble diameters of 7×10 -3 m (Re=1800) and 18×10 -3 m (Re=5900) an irregular ellipsoid shape is adopted and the bubble pulsates about its mean shape.…”

“…These spherical cap bubbles rise rectilinearly. Calderbank et al (1970) developed theory of mass transfer from the rear of spherical-cap bubbles. The authors argue that the overall mass transfer coefficients enhance by hydrodynamic instabilities in the liquid flow round bubbles near the bubble shape transition from spherical cap to oblate spheroid.…”

“…The authors argue that the overall mass transfer coefficients enhance by hydrodynamic instabilities in the liquid flow round bubbles near the bubble shape transition from spherical cap to oblate spheroid. Calderbank et al (1970) reported that for bubble sizes 1-1.8×10 -2 m a shape transition occurs, the bubble rear surface is gradually flattening and becoming slightly concave as the bubble size is increased. The onset of skirting is accompanied by a flattening of the bubble rear surface.…”

“…Behind the sphericalcap bubble is formed a torroidal vortex. Calderbank et al (1970) reported that a maximum value of k L occurs shortly before the onset of creeping flow conditions and corresponds to a bubble shape transition from spherical cap to oblate spheroid. This shape transition and the impending flow regime transition results in instabilities in the liquid flow around the bubble resulting in k L enhancement.…”