# rising bubble

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16. Rising Bubble. Kamila Soukov. Task. A vertical tube is filled with a viscous fluid. On the bottom of the tube, there is a large air bubble. Study the bubble rising from the bottom to the surface. Understanding the Task. - PowerPoint PPT Presentation

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Rising BubbleKamila Soukov16TaskA vertical tube is filled with a viscous fluid. On the bottom of the tube, there is a large air bubble. Study the bubble rising from the bottom to the surface.2

Understanding the TaskA vertical tube is filled with a viscous fluid. On the bottom of the tube, there is a large air bubble. Study the bubble rising from the bottom to the surface.3large = length > widthUnderstanding the TaskA vertical tube is filled with a viscous fluid. On the bottom of the tube, there is a large air bubble. Study the bubble rising from the bottom to the surface.4large = length > width

= stable flowUnderstanding the TaskA vertical tube is filled with a viscous fluid. On the bottom of the tube, there is a large air bubble. Study the bubble rising from the bottom to the surface.5large = radius comparable to radius of tube(length > width)

= stable flowUnderstanding the TaskWhat to Study:motionshape of bubbleDepending on:volume of bubble Vdiameter of tube Dproperties of liquid6Study the bubble6Analysis of the SYstemProperties of Liquiddensityviscositysurface tension= resistance to flow dynamic kinematic result of cohesive intermolecular forces

minimizes surface areawater1000 kg/m31.0 kg/(sm) (at 20C)71.97 mN/moil890 kg/m343.7 kg/(sm)32 mN/methanol789 kg/m30.9 kg/(sm)22.27 mN/msoap1020 kg/m35 kg/(sm)3 mN/m8

8Forces in the System

9gravity acting on liquidgravity acting on bubble liquid will flow down,pushing bubble up

water needs to flow around9

Forces in the System10gravity acting on liquidgravity acting on bubble

resistance due to viscositypressure inside bubblestresses due to surface tensionand pressure in the liquidwater needs to flow around liquid will flow down,pushing bubble up10Motion of the bubbleSpeed of risingstabilized soon due to viscous forceswater,D = 1.4cm12Speed of risingdoes not depend on bubble volume:oil,D = 1.4cmwater,D = 0.9cm13Speed of Rising: Different Liquids, Tubes14density dynamic viscosity surface tension water1000 kg/m31.0 kg/(sm)71.97 mN/moil890 kg/m343.7 kg/(sm)32 mN/methanol789 kg/m30.9 kg/(sm)22.27 mN/msoap1020 kg/m35kg/(sm)3mN/mvidime ze pre rozne kvapaliny s roznymi vlastnostami su rozne rychlosti, je to cele zlozite podme to popisat!14

Description of Bubble Risingvu(z)wzStarting withunknowns:velocity profile of the thin layer flowing around the bubble u(z)

velocity of bubble vwidth of layer flowing around bubble w

16

vu(z)wStarting withunknowns:velocity profile of the thin layer flowing around the bubble u(z)

velocity of bubble vwidth of layer flowing around bubble w

17gravity + shear force

vu(z)w wok, mam u(z) (medzera) teraz podme rozmyslat nad tym, ako dostat hentie 2 ciselka

nemam popisane veliciny17unknowns:velocity profile of the thin layer flowing around the bubble u(z)gravity + shear force

velocity of bubble vwidth of layer flowing around bubble w

Starting with18continuity (liquid = air )

vu(z)w18Starting withunknowns:velocity profile of the thin layer flowing around the bubble u(z)gravity + shear force

velocity of bubble vwidth of layer flowing around bubble w

19continuity (liquid = air )

vu(z)h3rd equation19Combine the equations20

velocity profilecontinuitytried to find 3rd equation no analytical solution; very difficult to solve numerically20Bubble Rising:Experimentally Prove Expected v/h3need to find h measure change in bubble length21

Lcylindrical bodyBubble Rising:Experimentally Prove Expected v/h322

expectation:

L = 1.15L0 + 1.06

Bubble Rising:Experimentally Prove Expected v/h3Prolonging of the cylindrical part:

23

Bubble Rising:Experimentally Prove Expected v/h3Pluding experimental velocity:24

Bubble Rising:Experimentally Prove Expected v/h325

Theory correlates with experiment

25Speed of Rising: More ExperimentsIsolate Parameter: Viscosityhot water: viscosity changes with temperature much more than density, surface tension27http://www.engineeringtoolbox.com/water-dynamic-kinematic-viscosity-d_596.html27Shape of Bubbles28Characterizing the SystemReynolds number: viscous vs inertial forces

Etvs (Bond) number: surface tension vs gravitational forces29

velky eotvos znamena male sigmy bude to negulate29Shapes of BubbleReEo510205102030

honeyshampoowateroil?

petrolShapes of Bubble: Comparison with Literature (no tubes)

31source: Jinsong Hua, Jing Lou, 2007, Numerical simulation of bubble rising in viscous liquid31Mystery: Tailshampoo has a clearly visible tailsometimes a small tail can be observed in honey too (esp. when not exactly vertical)not mentioned in literatureour explanation: very viscous does not fill the bottom fast enough32

Conclusion

gravity acting on liquidgravity acting on bubblepressure inside bubblestresses due to surface tension liquid will flow down, pushing bubble up

resistance due to viscosityConclusionforce analysis34 wConclusionforce analysis (gravity, viscosity, pressure, surface tension)

flow in the tube35

Conclusionforce analysis (gravity, viscosity, pressure, surface tension)

flow in the tube (velocity profile)

speed of rising36

theory correlates with experimentConclusionforce analysis (gravity, viscosity, pressure, surface tension)

flow in the tube (velocity profile)

speed of rising (theory + correlating exp for various parameters)

shapes of bubbles37

Conclusionforce analysis (gravity, viscosity, pressure, surface tension)

flow in the tube (velocity profile)

speed of rising (theory+correlating exp for various parameters)

shapes of bubbles (depending on Re, Eo)38study the bubbleThank you for your attention!force analysis (gravity, viscosity, pressure, surface tension)

flow in the tube (velocity profile)

speed of rising (theory+correlating exp for various parameters)

shapes of bubbles (depending on Re, Eo)39study the bubble16. Rising BubbleKamila Soukovfor your attention!Thank youAppendixCharacteristics of the System: FlowReynolds number: defines relative importance of viscous and inertial forces

in our case always flow is laminar42

42Refound in articles =

Reussualy expected =

Estimations from continuity equation:

Reynolds number43

v velocity of bubbleu velocity of liquidR- radius of bubble- density of liquid - viscosity of liquidw- thickness of layerRwvu= Refound in articles Velocity Profilevelocity profile of the thin layer flowing around the bubble u(z)

gravity + shear force44

(holds for laminar flow and sufficiently long bubbles) wsource: Zbierka FX (collection of solved physics problems)44Velocity of Rising, Width of Layervelocity of bubble vwidth of layer flowing around bubble h

continuityamount of liquid going down = amount of air going up

45

integrating + simplifying *velocity profile=

* simplification: thin layer(approximation:cylinder)

Description of Bubble Rising46

velocity profilecontinuity(const for a given liquid & tube)Beyond the Ratio

experiment: v depending on R47

??Beyond the Ratio

experiment: v depending on R48

??21