the influence of gravity on physicochemical systems · 2011. 2. 8. · effect of gravity on...

March 2-4, 2004 MEIT-2004 / Section 5 /

The Influence of Gravity on Physicochemical Systems


J. Iwan D. Alexander

National Center for Microgravity Research Case Western Reserve University

• Introduction: acceleration- terrestrial and planetary gravity, weightlessness, ‘effective gravity’, microgravity,

• Buoyancy: common processes affected by gravity• Effects of ‘steady acceleration’ on fluid motion:

• Density variations in liquids and gases – thermal and solutal buoyancy

• Free surfaces and interfaces of liquidsResidual acceleration or g-jitter effects on fluid motion and transport

• Instantaneous system responses• Mean flow generation

• Summary



SymbolsG ~ gravitational constantg0 ~ 9.8 m/s2

Me ~ mass of the earthGr ~ Grashof number: ratio of buoyant to viscous forces = β= coefficient of thermal expansion [K-1]∆Τ = characteristic temperature difference [K]L = characteristic length scale [m]ν= kinematics viscosity [m/s2]κ = thermal diffusivity [m/s2]D = diffusivity [m/s2 ]

3 2TgL / ,β ν∆

Pr ~ Prandtl number = kinematics viscosity / thermal diffusivity = ratio of thermal and momentum diffusion timescales, Pr = ν/κRa ~ Rayleigh number: ratio of conductive heat transfer and convection timescales, Ra = GrPrRav = vibrational Rayleigh number characterizes ratio of conductive heat transfer and mean convective flow time scales, Rav = (β∆TbωL)2/2κνSt = dimensionless frequency, St = ωL2/νΩ= dimensionless frequency, Ω = ωL2/κ

Sc ~ Schmidt number = ratio of species and momentum diffusion timescales, Sc = ν/DB = Bond number = ratio of gravity forces and surface tension forces, B = ρgL2/σσ = surface tensionPe = Peclet Number = ratio of crystal growth velocity and characteristic diffusion speed, Pe = VgL/DVg = crystal growth velocityNu = Nusselt Number = ratio of convective heat transfer and conductive heat transfer



Gravitational acceleration

2eGMF

r=−

11 3 1 26 673 10G . m kg s− − −= ×245 976 10eM . kg= ×

altitude km

acceleration [m/s2]

Earth 0 9.80308 100.00%1 9.80001 99.97%5 9.78773 99.84%

8.85 9.77593 99.72%10 9.77548 99.72%

Spacelab 325 8.87551 90.54%ISS 425 8.61650 87.90%

Moon 0 1.62592

ag = -



‘Effective gravity in low earth orbit’

Isoacceleration Surfaces [µg]

z1

z2

0.5 m

0.6

0.20.4

z2

X2

X3

X1

z1

z3

OS

r0(t)

OG

Reference Frames

The gravity gradient stabilized type attitude motion will yield a quasi-steady acceleration that varies in orientation and magnitude with distance from the spacecraft mass center



BuoyancyGravity affects the state of fluid matter and exerts a major influence over mass, heat and momentum transfer in systems where fluids are prevalent

The degree to which gravity, or any similar body force affects fluid processes will depend whether the density distribution is uniform or not and how the density gradient is oriented with respect to the gravity vector. In this tutorial I will discuss how gravity as experienced at the earth (or other planetary surfaces) can affect transport and on the nature of the microgravity environment and how it can generate fluid motions (even under near weightless conditions) and, thus, influence transport of heat and mass



Effects of ‘steady acceleration’ on fluid motion: isothermal density stratification

1 2

Two immiscible fluids initially separated by a partition

liquid 1 has a large density than liquid 2

g

1 2ρ ρ>

1

2

When the partition is removed the liquids will reorient so that the interface is level and the denser liquid lies below the interface

In an isothermal stratified fluid, surfaces of equal density will generally orient themselves to be perpendicular to gravity and with density decreasing upward.

Near the walls surface tension may cause deviations from the horizontal surface…

g



1

2Surface tension generally bends the interface near walls. The direction of bending depends on the interfacial tension and which liquid prefers to wet the container wallsg

1

2gHere fluid 2 prefers to wet the walls and displaces fluid 1 downward near the walls

In both cases the surface is nearly perpendicular to the gravity vector away from the walls and the denser liquid always lies below the interface



Rayleigh-Taylor instability in miscible liquids

gg1

2

1 2ρ ρ> Images after Olson, 1999U. Chicago



Effects of sudden acceleration on motion: Richtmeyer-Meshkov instability

• Richtmyer-Meshkov (RM) instability occurs when two fluids of different densities are impulsively accelerated normal to their nearly planar interface.

• A fundamental fluid instability and is importance in fields ranging from astrophysics to material processing.

• RM instability normally carried out in shock tubes using gases, & generation of a sharp well-controlled interface is difficult → scarcity of good experimental visualizations

Niederhaus & Jacobs (1998)



g

Effects of ‘steady acceleration’: nonisothermal density stratification

0-g

TCOLD THOT

Insulated top and bottom boundaries

Isotherms (here = density contours) attempt to reorient perpendicular to gravity vector with lighter fluid below

Fluid density is a linearly decreasing function of temperature

Hotter, less dense fluid rises at the hot wall

cooler, denser fluid sinks at the

cold wall

Distortion of isotherms from vertical straight lines is a function of Rayleigh number:

( ) 3HOT COLDT T gL

Raβ

κν−

= → Characteristic time for conductive heat transferCharacteristic time for momentum transfer



Effects of ‘steady acceleration’ on fluid motion: Liquid interfaces and free surfaces- liquid bridges

B > 0 B < 0

Vact = volume/π* r2hK = ratio of the small disk to the largest gradientΛ = h/2* rr = mean radius and B = Bond number



Surface tension-driven flows• Near corners interfaces are forced to

curve

• The pressure difference p1 - p2 is inversely proportional to surface mean curvature

Zero gravity - pressure gradient not hydrostatically balanced -⇒ narrow columns of liquid pumped up the corners by surface-tension forces

time

1-g low-g



Normal Gravity Horizontal

Stratified Smooth

Stratified Wavy

Elongated bubble

Annular

Slug flow

Wavy Annular

BubbleBubble Slug Churn Annular

Normal Gravity Vertical

Increasing Gas Velocity

Incr

easi

ng G

as V

eloc

ity

Effect of Gravity on Gas-Liquid flow



Slug-Annular Flow

Stratified Flow

Stratified Wavy FlowSlug Flow

Reduced Gravity

Bubble Flow

Annular Flow

1 g

Effect of Gravity on Gas-Liquid flow



Detrimental effects of sedimentation and convection are eliminated in microgravity

µg µg µgdisordered fluid

random particle motionNucleation Crystallization

• Results from PHASE surprised the condensed matter physics community. Large dendritic crystals were produced that were previously undetected in ground-based studies.

• Industrial relevance: semiconductors, electro-optics, ceramics, and composites leading to progress toward development of new materials



Steady acceleration: effects on directional solidification

• Newtonian fluid, linear dependence of density on temperature differentially heated cavity

• Two component melt• Ampoule is translated through a furnace at a fixed rate• If convective effects are negligible- lines of equal composition will be

parallel to the (flat) crystal melt interface and the longitudinal profile will change exponentially with distance away form the interface

MELTT

HOTT

Crystal-melt interface

Heat flux through ampoule sidewalls proportional to difference between wall temperature and heater temperature

1

2

Tm T

1 Fixed Furnace2 Moving Furnace



Steady acceleration: effects on directional solidification

1.00.50-0.5

log

GrS

c

1

2

3

4

5

6

7

8

ConvectiveTransport

DiffusiveTransport

(0.43)(1.4)

(4.8)(6.1)

(0.05)(0.19)

(0.39)(0.93)

(1.6)(2.5)

log Pe

CRYSTAL

CRYSTAL

(0.43)Sc = 10

(0.05)Sc = 10

CRYSTAL

CRYSTAL

(6.1)Sc = 100

(2.5)Sc = 100

g



g-jitter effects: The MEPHISTO g-jitter Experiments on USMP-3

0

-2

-4

-6

-8

-10

-12

-14

-16

-18

Burn 1

V

Actu

alSe

ebec

k[µ

V]

V

Burn 2

0 20000 40000 60000

(a)

Time [seconds]

Burn 1Burn 2

0 20000 40000 60000-14

-12

-10

-8

-6

-4

-2

Sim

ulat

edSe

ebec

k[µ

V]

(b)

Response of solute transport to impulsive g-jitter in a tin-bismuth alloy



g-jitter effects: The MEPHISTO Experiments on USMP-3

Time [seconds]

-6

-4

-2

2

4

0

6

55 60 65 70 75 80 85 90acce

lera

tion

[10-

3 g]

net z+y acceleration

Time [seconds]

-8

-6

-4

-2

2

4

0

55 60 65 70 75 80 85 90acce

lera

tion

[10-

3 g]

x-acceleration

SAMS Acceleration DataMET: 7/00:25



g-jitter effects on directional solidification: periodic acceleration

0 1000 2000 3000 4000 50000

5

10

15

20

25

TIME [sec]

0 100 200 300 4000

0.5

1.0

1.52.0

2.5

3.0ξ[%

]

ξ[%

]

TIME [sec]

Sc = 1

1

60

50

20

Interfacial composition nonuniformity as a function of time for a 1 Hz acceleration oriented parallel to the melt-crystal interface

ζ = Interfacial non-uniformity, Cmax - Cmin / Cav

C = composition



0Tn

∂ =∂

0Tn

∂ =∂

( )2 Pr cosRav tΩ Ω

1T = 0T = 0Tn

∂ =∂

0Tn

∂ =∂

1T =

0T =No steady acceleration Ra = 0

Horizontal vibration

Insulated top andbottom walls

flow

Mean flows generated by periodic g-jitter acceleration

The vibrational Rayleigh number, Rav, is the ratio of the characteristic time for heat transfer by conduction to the characteristic time for convective heat transfer



Rav = 103 Rav = 104 Rav = 105

Mean flows and temperature profilesgenerated by periodic g-jitter acceleration



1

1.5

2

2.5

3

0 10 20 30 40 50

Rav × 10-3

Nus

selt

Num

ber

1

2

3

4

Dependence of heat transfer on Rav and Aspect Ratio

Aspect Ratio = h/w



Rav = 1500 Rav = 104 Rav = 105

Effect of cavity Geometry and Rav



Ra = 11Rav = 500Pr =0.153 (Sn-Bi)Ω= 2000

Vibration parallelto the crystal-meltinterface

Ra = 11

3.38 Hz

Mean Transport due to g-jitter during Directional Solidification



Ra = 11Rav = 500Pr =0.153 (Sn-Bi)Ω= 2000

Ra = 11Rav = 104

Pr =0.153 (Sn-Bi)Ω= 2000

Vibration parallelto the crystal-meltinterface

Ra = 11

3.38 Hz

Mean Transport due to g-jitter during Directional Solidification



Natural convectionVertical temperature gradient Ra=104, Pr = 6.96 (water)

C H

gg + vibration

Rav = 104

Ω = 8000Rav = 105

Ω = 2x104

Flow Suppression by vibrational flow



Rav = 105

Ω = 2x104

10Periods

50 100 200 500 750 1000

g + vibration

Flow Suppression by vibrational flow



g

3 mm

30m

m

0.33m

Sample

∆T = 0.1 K

∆Tz = 0 or 2 K“stabilizing”

c/c0

8.5 × 10-3

6.4 × 10-3

g ∆Tz = 0

∆Tz = 2 K

Dax0DaxDaxπ

Dinput = 1.48 × 10-5 cm2/s

Daxπ = 8.43 × 10-5

cm2/s

lnc

0z2 [cm2]

2 4 6 8

Dax0 = 6.18 × 10-5

cm2/s

-6.0

-5.5

-5.0

-6.5

Dax = 7.87 × 10-5

cm2/s

r = 0.75 R

t = 175 min t = 350 min

Ra = 3Pr = 10-2

Contamination of diffusion measurements by convection

C = concentration



1

10

100

1000

0.01 0.1 1 10 100

( )220

1 15 1

GrScD AD Stπ

⎛ ⎞⎜ ⎟ ⎛ ⎞⎝ ⎠

⎜ ⎟⎝ ⎠

= ++

0.75

1.00

1.25

1.50

1.75

2.00

2.25

0.01 0.1 1 10 100 1000

GrSc = 7.5π/A

GrSc = 15π/A

GrSc = 0.75π/A

Pe[A GrSc/(15/π)] St = ωR2/ν

D/D

01

2

3

4

5

0 1 2

Gravity effects on diffusive processes

Ratio of measured diffusion coefficient D to actual coefficient depends on the ratio of the characteristic time for diffusive transport to the characteristic time for convective transport-GrSc, the aspect ratio, A of the container, and the dimensionless frequency St which is the ratio of the viscous response time to the period of the g-jitter.

D/D

0



• Significant progress has been made toward the understanding of g-jitter effects on microgravity experiments

• Most of this understanding is based on theory and simulation• Recent work on mean flows driven by oscillatory g-jitter shows that even if the time-

dependent response of the fluid is small in amplitude, a mean flow may still be generated that can lead to significant compositional distortion.

• Convection driven by compositional gradients may be more sensitive to oscillatory g-jitter at high frequencies. More work is needed to clarify this

• More experimental evidence of on-orbit g-jitter effects would be useful • Free surfaces and fluid interfaces are particularly sensitive to changes in gravitational

environment. Liquid configurations generally take on very different characteristics in weightlessness

• Gas-liquid and two –phase flows have very different flow regime characteristics under 1-g as compared to zero-g or partial-g. This needs to be better understood

• Lack of effective buoyant transport can lead to problems with bubble accumulation

Summary

the influence of gravity on physicochemical systems · 2011. 2. 8. · effect of gravity on...

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