Motion of singles bubbles moving under a slightly inclined surface through stationary liquids

Effect of disjoining pressure on terminal velocity of a bubble sliding along an inclined wall

“…This is because the buoyancy force acting parallel to the motion of the bubble sliding under an inclined surface is dependent on the sine of the angle. This trend has been observed by several researchers [23,25–28,31,37,52,54,55] from their experiments using a wide range of bubble radius from the smallest of ∼0.85 mm by Masliyah and his co-workers [28] to elongated bubbles with equivalent radius of ∼2.4 cm by Zukoski [23] and by Maxworthy [27] . In their independent studies, both Zukoski [23] and Maxworthy [27] observed a maximum velocity at an inclination angle of 45°.…”

“…The body of literature on bubbles sliding along inclined surfaces in liquid mostly reports on effects of bubble size [27,31,33,37,40] , bubble shape [25] , size of liquid channel [24–26,30] , angle of inclination [23–28,30,31,33,36–38,41] , surfactants [33,34,40] , gas type [40] , liquid temperature [26,40,52] , and other liquid properties [23,24,26,28,30,31,52] such as viscosity, density, and surface tension on the dynamics of the sliding bubble. However, salt concentrations of liquid media, to our knowledge, have not yet been a parameter of any study in bubbles sliding along inclined surfaces.…”

Morphology of Two-Phase Layers with Large Bubbles

“…They found that the terminal velocity increases monotonously with the inclination angle. This is not in agreement with Maxworthy's [8] and Perron et al's [10,11] observations. Perron et al made a wide range of experimental and theoretical studies on small bubbles rising in liquids under a slightly inclined plate.…”

Between inertia and viscous effects: Sliding bubbles beneath an inclined plane

“…The present article takes place in the context of a bubble sliding beneath an inclined plane. This subject has already been explored experimentally [16,[20][21][22][23][24][25], numerically [26] θ v 2 mm and theoretically [27,28]. The question of the bubble terminal velocity has been solved in terms of scaling laws for small Reynolds number and low inclination angles [22].…”

“…The question of the bubble terminal velocity has been solved in terms of scaling laws for small Reynolds number and low inclination angles [22]. This question has also received a lot of attention in the case of large bubbles (large in comparison to the capillary length) [20,23,24,27]. The case of bubbles sliding beneath a plane with a Reynolds number larger than one and for bubbles diameters of the order of the capillary length c (detailed further) remains only partially treated by Masliyah et al and Tsao et al [16,21], who respectively interpreted the bubble motion in terms of drag coefficient and answered only qualitatively the problem.…”