SELF-ORGANIZATION of a GROUP of LARGE RISING BUBBLES

Kamil WichterlePavel Raška

Marek VečeřM.C. Ruzicka

VŠB-Technical University of Ostrava, Faculty of Metallurgy and Material

EngineeringDepartment of Chemistry, 70833 Ostrava Poruba, CR

Institut of Chemical Process Fundamentals, v.v.i.

AS CR,16502 Prague 6 Suchdol, CR

RISING BUBBLESRISING BUBBLES

QUESTIONS ?

MACROSCALE : Bubble plume

Boiling Chemical processes (gas absorption in liquids, chemical reactions, evolution of gases) Bioreactors (fermentation, water treatment, sugar saturation) Geology (oceanology, volcanology) Metallurgy (liquid steel oxidation, removal of slag particles, aloys mixing, molten metals

homogenization)

RISING BUBBLESRISING BUBBLES

SIMPLEST ANSWERSMICROSCALE :

Single bubble Two bubbles

ContentsContents

Experience related to the bubble shape Experience related to the bubble shape and risingand rising

Theoretical models of bubble Theoretical models of bubble interactionsinteractions

Experiments with two bubbles of Experiments with two bubbles of identical sizeidentical size

Probability of relative position of the Probability of relative position of the bubblesbubbles

SHAPE AND SHAPE AND MOVEMENT MOVEMENT OF SINGLE OF SINGLE

RISING RISING BUBBLEBUBBLE

LOWER DRAG (hypothetical)

Why not during rising ??

Sometimes immediately after detaching the bubble from a capillary

Hydrostatics

Surface tension

BUBBLE SHAPE

REAL RISING BUBBLES

increasing volume

gd

Eo B

2

gV

Eo B3/2

6

Buoyancy forces .

Surface forces

Eötvös (or Bond) number

SYMMETRIC OBLATE BUBBLE

Drag

Buoyancy

Drag

Drag

ASYMMETRIC BUBBLE

Hydrostatic pressure lower

Buoyancy

Radius higher

Radius lower

Hydrostaticpressure

higher

Surface forces

Resulting force

CENTRE OF MASS

Force proportional to angle

results in harmonic oxcillation

Other authors suppose that it is vortex shedding, which is reponsible for the oscillations

We are convinced that it is the shape oscillation, which is reponsible for the vortex shedding

RISING BUBBLERISING BUBBLE horizontal velocity

rising velocity

amplitude

Oscillatory Oscillatory movement of a movement of a

bubble bubble sinusoidal sinusoidal (zig-zag)(zig-zag)

oror

helicalhelicalTypical frequency Typical frequency

5-10 Hz5-10 Hz

TWO BUBBLESTWO BUBBLES

THEORETICAL THEORETICAL MODELSMODELS

Liq

uid

flo

w f

rom

vie

wp

oin

t o

f o

bse

rver

TWO BUBBLES (FROM VIEWPOINT OF THE OBSERVER MOVING

WITH ONE BUBBLE)

•or collision ?

EQUILIBRIUM POSITION :

•either horizontally parallel position ?

Liq

uid

flo

w f

rom

vie

wp

oin

t o

f th

e u

pp

er b

ub

ble

wake

Lower bubble in the wake should rise faster than the upper one.

It results in collision of the bubbles

WRONG !!!

TWO BUBBLES(FROM VIEWPOINT OF THE OBSERVER MOVING

WITH THE UPPER BUBBLE)

WHAT ACTUALLY TAKES PLACE IN THE SYSTEM ???

Liq

uid

flo

w

DRIFT

Spherical (smaller) bubbles(FROM VIEWPOINT OF THE OBSERVER MOVING

WITH THE UPPER ONE)

wake

Liq

uid

flo

w

DRIFT

Ellipsoidalal (larger) bubbles (FROM VIEWPOINT OF THE OBSERVER MOVING

WITH THE UPPER ONE)

wake

LIFT

uL

DRIFT

Mathematical models of

LIFT and DRIFT

LIFT

LLBTD urotuuCt

u

d

d

uB

uD

uL

2/1d

d

Eo

d

x

uu LD

TWO BUBBLESTWO BUBBLES

EXPERIMENTEXPERIMENT

OBSERVER – STATIONARYOBSERVER – STATIONARY LIQUID FLOWING DOWNWARDSLIQUID FLOWING DOWNWARDS RISING BUBBLES STATIONARY RISING BUBBLES STATIONARY

WITH RESPECT TO THE WITH RESPECT TO THE OBSERVEROBSERVER

„„LEVITATING BUBBLES“LEVITATING BUBBLES“

LEVITATING BUBBLESLEVITATING BUBBLESDivergent downstream flow

MIRROR FRONT

y x

zx

y

LIQ

UID

FLO

W

Overall view

LEVITATING BUBBLES

VB = 250 mm3 in glycerol 70%

5 x slower

0 10 20 30 40

0

10

20

30

40

50

r , mm

zmm

13-14.3

11.7-13

10.4-11.7

9.1-10.4

7.8-9.1

6.5-7.8

5.2-6.5

3.9-5.2

2.6-3.9

1.3-2.6

0-1.3

Bubbles 250 mm3,in glycerol 70%

PROBABILITY of RELATIVE POSITION

of TWO ELLIPSOIDAL BUBBLES ( volumes 250 mm3 = equivalent diameters dB= 7.82 mm).

Coordinates in milimeters are related to the centre of mass of the upper bubble.

Size and typical position of the bubbles are drawn by ellipsoids)

wake

Ve

rtic

al d

ista

nc

e

Horizontal distance

Wake = forbidden space

Conclusions• Bubble position in downstream divergent liquid flow were

recorded by high speed camera. Ellipsoidal bubbles of volumes 50 – 400 mm3 in water, calcium chloride solutions (electrolytes), glycerol solutions (viscosity), butyl alcohol (surface tension), polyacrylamide solutions (viscoelasticity) are studied.

• Particular bubbles (which in ideal case should assume identical position) move in fact quite independently (frequency and amplitude). These oscillations are not synchronous.1. Statistical analysis of the mutual positions indicates

that the most probable is horizontal allignement with a narrow gape

2. Wake behind the upper rising bubble is a forbidden space. Collision of the bubbles does not occur regularly

• Our simple hydrodynamics theory can explain such a behavior

Generous support of the Grant Agency of the Czech Republic

through the project 104/07/1110is acknowledged.

coworkers:coworkers:

Pavel RaškaPavel RaškaKateřina Smutná Kateřina Smutná

Lenka Kulhánková Lenka Kulhánková VŠB-Technical University of Ostrava Jana Wichterlová VŠB-Technical University of Ostrava Jana Wichterlová

Marek VečeřMarek Večeř

Marek C. Růžička Marek C. Růžička Jiří Drahoš Jiří Drahoš

InstitutInstitutee of Chemical Process Fundamentals, of Chemical Process Fundamentals, PraguePrague

Thank you for the attentionThank you for the attention

VŠB – Technical University of Ostrava

InstitutInstitutee of of Chemical Process Chemical Process

FundamentalsFundamentalsPraguePrague