This paper presents a numerical modeling of the collision between a small bubble -of a few hundred microns, initially moving at terminal velocity, and an inclined wall, with relevance to drag reduction schemes. The theoretical model uses the lubrication theory to describe the film drainage as the bubble approaches the wall, and compute the force exerted by the wall as the integral of the excess pressure due to the bubble deformation. The model is solved using finite differences. The trajectory of the bubble is then determined using equations of classical mechanics. This study is an extension of previous work by Moraga, Cancelos and Lahey, [Multiphase Science and Technology, 18,(2),2006] where the simulation and comparison with experiments was carried out for a horizontal wall. In the present study where the wall is inclined, the bubble trajectory is no longer onedimensional and axisymmetry around the vertical axis is lost, allowing for more complex behavior. The influence of various parameters (Reynolds number, Weber number) is examined. Numerical results are compared with the experimental data from Tsao and Koch [Physics Fluids 9, 44, 1997]

1.
Lumley J.L. and Kubo Y. Turbulent drag reduction by polymer additives: a survey. In The Influence of Polymer Additives on Velocity and Temperature Fields, ed. B. Gampert, pp. 3–24. New York: Springer-Verlag.
2.
Kodama, Y., Takahashi, T., Makino, M., Ueda, T., and Hori, T., “Possibility of Net Energy Saving of Microbubbles as a Drag Reduction Device for Ships”, 2nd Asia-Pacific Workshop on Marine Hydrodynamics, Busan, June 2004.
3.
”,
van den Berg
T. H.
,
Luther
S.
,
Lathrop
D. P.
, and
Phys
D. Lohse
Drag reduction in bubbly Couette-Taylor turbulence
.
Rev. Lett.
94
,
044501
044501
(
2005
)
4.
Antal
S. P.
,
Lahey
R. T.
and
Flaherty
J. E.
Analysis of phase Distribution in Fully Developed Laminar Bubbly Two-Phase Flow
Int. J. Multiphase Flow
17
, (
5)
,
635
652
.
1991
5.
Moraga
F. J.
,
Larreteguy
A.
,
Drew
D.
,
Lahey
R. T.
, “
A center-averaged two-fluid model for wall-bounded bubbly flows
”.
2006
Computers & Fluids
,
35
,
429
461
.
6.
Klaseboer, E., Chevaillier, J.P., Mate´, A., Masbernat, O.m and Gourdon, C. “Models and experiments of a drop impinging on an immersed wall” Physics of Fluids 2001, 13 (1).
7.
Moraga
F. J.
,
Cancelos
S.
,
Lahey
R. T.
, “
Modeling wall-induced forces on bubbles for inclined walls
”,
Multiphase Science and Technology
,
2006
,
18
(
2)
111
133
8.
Lin
C. Y.
and
Slattery
J. C
, “
Thinning of a liquid film as a small drop or bubble approahces a solid plane
”,
AIChE J.
1982
,
28
,
147
147
9.
Clift, R., Grace, J.R., and Weber, M.E. “Bubbles, drops, and Particles” Academic Press 1978
10.
Van der Geld
C. W. M. Geld
,
On the motion of a spherical bubble deforming near a plane wall
,
J. Eng. Math.
,
42
(
1)
,
91
118
, (
2002
)
11.
Moore
D. W.
The Velocity of Rise of Distorted Gas Bubbles in a Liquid of Small Viscosity
”,
Journal of Fluid Mechanics
,
1965
,
23
, (
4)
,
749
766
12.
Khoja, S. and Attinger, D. A. “High-speed vizualizations of bubbles interacting with a solid surface” submitted to ASME 2006
13.
Brennen, C. “Cavitation and Bubble Dynamics”, Oxford University Press, 1995
14.
Tsao
H. K.
and
Koch
Observations of high Reynolds number bubbles interacting with a rigid wall
Physics of Fluids
1997
,
9
,
44
44
This content is only available via PDF.
You do not currently have access to this content.