Bubble Bouncing on Solid/Free SurfacesM.R. Brady, D.P. Telionis – Engineering Science and Mechanics

P.P. Vlachos – Mechanical EngineeringR.-H. Yoon, S.B. Yazgan – Mining Engineering

Virginia Tech

The rise of a buoyant bubble and its interaction with solid and free surfaces was experimentally investigated using a combination of shadowgraphs and Laser Induced Fluorescence (LIF). These optical techniques were used to track the bubble position, and measure the velocity field around the bubble

in a time resolved manner. The results are quantified as a function of bubble size and surfactant concentration of the fluid medium.

Forces on a particle or bubble/added mass system1. Lubrication Forces

Squeeze film lubrication (Panton) (viscous adhesion)

Pad finds very large repulsive pressures if pushed against plate; but very large attractive forces if pulled up and away

2. Stokes drag

3. Added mass (ideal flow)

4. Bubble Elasticity (Barnocky & Davis)

3R2U/2h = C3U/h

22

0 3

6 21

L dh xp p

h dt L

0 if 0, dh

p pdt

0 if 0,

dhp p

dt

L

h

16 RU CU

32

3 f

aUF R

dt

IntroductionEquation of Motion• General case of a particle or bubble 0 in a flow (without lubrication or

elasticity)

• To include lubrication, integrate pressure relation

note:

With lubrication and for the case of a bubble (M0 = 0):

Stokes and lubrication forces are always opposing motion. They are dissipative effects.

0 0 1

Stoke draggravitybuoyancymass acceleration added mass

1

2f f

dU dUM M g M g M CU

dt dt

dhU

dt2

lubr. 3

CF U

h

2

1 3

Stokesbuoyancylubricationdragadded mass

acceleration

1

2 f f

CdUM M g CU U

dt h

Experimental Technique: Laser Induced FluorescenceLaser Induced Fluorescence is the effect of seeding a flow with fluorescent particles, and tracking their movement with high speed video. The incident laser light is subtracted out the image with a filter, leaving only the fluorescent particles. The resulting velocity field around the bubble

is then calculated through a cross correlation based software.

Images and corresponding velocity fields (zoomed in) for 1.5mm bubble in pure water hitting a free surface

Experimental Technique: Shadowgraph

High-speed images (1000fps) were recorded for the buoyancy-driven bouncing bubble. The independent quantities were bubble size, ionic concentration and hydrophobicity of the contact surface. A sample time

series of shadowgraphs is shown below for a 1.5mm bubble. The substrate had a 75 degree contact angle with a water droplet in a fluid medium of pure water,

Bubble Trajectories

The vertical component of the center of mass of the bubbles were tracked and their distance from the origin is shown

below. The first case shows the behavior for a 5e-4 M Sodium Silicate solution and the second case for pure water.

Terminal Bubble Velocity vs. We

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.01 0.1 1 10 100

We

Te

rmin

al B

ub

ble

Ve

loc

ity

Uo, m

/s 5e-4 M sodium silicatePure Water

Log Trendline

Terminal Bubble Velocity vs. Bubble Re

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

10 60 110 160 210 260 310 360 410

Bubble Re

Te

rmin

al

Bu

bb

le V

elo

cit

y U

o,

m/s

Pure Water

5e-4 M sodium silicate

Poly Trendline (order 2)

CR vs. Approach Velocity

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.00 0.10 0.20 0.30 0.40

Approach Velocity, m/s

CR

first bounce

second bounce

Linear (secondbounce)

Results and ConclusionsThe three figures below show how the terminal velocity and the Coefficient of Restitution (ratio of

post-bounce momentum to pre-bounce momentum) scale with relevant nondimensional quantities. The significant increase in velocity in pure water compared to a surfactant

concentration can be attributed to surfactant molecules attaching to the bubble, as shown in the drawing. The surfactant molecules create a no-slip condition in the region around the wake of the

bubble and increase the dissipative viscous drag on the bubble.

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