Collision and Attachment Interactions of Single Air Bubbles with Flat Surfaces in Aqueous Solutions - Drops and Bubbles in Contact with Solid Surfaces - page 219

Figure 5. Perpendicular position the centroid of a bubble with 0.85 mm radius ( Re = 522 and

We = 0 . 866) rising toward and oscillating at a horizontal solid surface [59].

The energy balance for the deformable bubbles bouncing from the solid sur-
face has also been analysed [19, 29, 38, 81]. A few convenient locations (or times)
on the bubble trajectory can be considered in assessing the energy components,
namely, (1) the bubble position at its terminal velocity at a sufficient distance from
the wall so that the effect of the solid surface on the bubble shape and liquid velocity
can be neglected, (2) the position bubble arrested upon collision with the surface,
and (3) the lowest position of the bubble bounce. The bubble velocity is equal to
zero at the last two positions. The experimental data [71] show that 95% of the ki-
netic and surface energy of bubbles colliding with the solid surface at their closest
proximity is stored as surface energy and only 41% of the initial energy is con-
verted into the gravitational and surface energy at the lowest bubble position on its
bounce trajectory. Furthermore, the energy dissipated during the rebound is signifi-
cantly larger than the energy loss predicted based on the drag on a spherical bubble
in an unbounded fluid with the same initial energy. The shape of bubbles is nearly
spherical after the rebound. The additional energy losses may be due to the acoustic
radiation by the bubble oscillation and the energy dissipation into the thinning of
the intervening liquid films. The interchange between the kinetic and surface en-
ergies during the bubble-surface interaction has been quantitatively analysed [82].
The collision-rebound process is also analysed by considering the restitution co-
efficient (defined as the ratio of rebound to impact velocity) in a similar way to
analysing the solid particle-solid surface collision [51] which predicts the collision
and rebound distance as a function of the Stokes number. There is a critical Stokes
number below which the viscous effect on the bubble collision overcomes the iner-
tial effect and no bubble rebound at the solid surface occurs [19, 29, 38]. However,
the bubble-surface interaction is significantly different from that of the solid par-
ticle in one aspect, that is, the bubble approach distance and velocity are similar