Effects of fine particles on terminal velocities of single bubbles in a narrow channel between parallel flat plates

Shapes and Rise Velocities of Single Bubbles in a Confined Annular Channel: Experiments and Numerical Simulations

“…For small bubble size (3-4 mm), the aspect ratio decreases with the increasing Weber or Tadaki number. This agrees with the trend for an unconfined rise: in fact, the prediction methods in Equations ( 12) and (13) indicate that, when the bubbles are rising through unconfined liquids, the aspect ratio decreases as the Weber or Tadaki number increase. On the other hand, for larger bubbles (4.5 mm and above) the aspect ratio levels off and then increases with the increasing Weber or Tadaki number, which is the opposite of what happens during unconfined rise.…”

“…Wall effects were investigated rather extensively for bubbles rising through circular tubes [4][5][6] and through narrow rectangular channels [7][8][9][10][11][12][13]. For circular tubes, wall effects typically cause the elongation of the bubbles in the vertical direction and the alteration of the wake structure behind the rising bubble, resulting in milder bubble deformation and a reduced rise velocity in comparison with the unconfined case.…”

Bubble rise in a Hele-Shaw cell: bridging the gap between viscous and inertial regimes

“…2015; Hashida et al. 2019, 2020). At dynamic equilibrium, the drag force equals the driving force due to buoyancy and so, the model developed in gives where the second term resembles the expression of the drag coefficient for an isolated spherical bubble in three dimensions, i.e , where .…”

“…From a dynamical point of view, the bubble's motion is characterised by its drag force F D . It can be computed from the drag coefficient C D = F D /(ρv 2 b S/2), where S = πd 2 3 /4 the equivalent spherical surface and not the true projected area 2bh as often considered (Filella et al 2015;Hashida et al 2019Hashida et al , 2020. At dynamic equilibrium, the drag force F D equals the driving force due to buoyancy F B = ρg(πabh) and so, the model developed in (3.1) gives…”

“…While this result is analogous to isolated spherical cap bubbles in an unbounded liquid (Davies & Taylor 1950), the physical origin of the constant is still not clear. By studying air bubbles in various glycerol/water solutions and colloidal suspensions of fine silica particles in water, respectively, Hashida, Hayashi & Tomiyama (2019, 2020) proposed that the factor should depend on liquid characteristics such as , and (its surface tension). Regarding the bubble shape, Roig et al.…”