Mass Confusion About Air-Water Mass Transfer Damon Turney

Mass Confusion About Air-Water Mass Transfer

Damon Turney

Bren School of Environmental Science and Management

Committee Members:Jeff Dozier, Sanjoy Banerjee, Sally MacIntyre, Jordan

Clark

Fate and Transport

- Carbon- Toxins (DDT, Hg, Dieldrin, PCBs, many more)- Aeration of Hypoxic Water- DeAeration of Water Below Dam Spillways- Industrial Cleaning of Water in Air Spargers- Bioreactors and Other Reactors in Industry- Steam Condensation in Power Plants

from Wanninkhof et al. 1992

from Rosso 2006

from Kelly 1997

Convection + Diffusion

Convection + Diffusion = Confusion

€

∂[c]

∂t+

r v ⋅

r ∇[c] = D

r ∇2[c]

€

rF =

r v [c] + D

r ∇[c]

advection diffusion

€

∂[c]

∂t+

r v ⋅

r ∇[c] = D

r ∇2[c]

€

rF =

r v [c] + D

r ∇[c]

advection diffusion

€

rF ∝ ΔCr F = kΔC

Air

Water

Advection into thewater is not possible

Air

Water

Advection into thewater is not possible

Diffusion

Air

Water

Diffusion is ~10-9 m2/s

Diffusion is ~10-5 m2/sAdvection into thewater is not possible

Diffusion

Air

Water

Surface Renewal Theory

€

F =D

tNo unambiguous way of

determining a value for average t€

F = Δ[c]D

π t

Surface Divergence Theory

Surface Divergence Theory

1 mm

€

F = D∂[c]

∂y

Surface Divergence Theory

100 μm

€

∂w

∂z+

∂u

∂x ⎛ ⎝

⎞ ⎠i

= β

Surface Divergence Theory

1 mm

€

v =∂w

∂z+

∂u

∂x ⎛ ⎝

⎞ ⎠y = βy

€

∂w

∂z+

∂u

∂x ⎛ ⎝

⎞ ⎠i

= β

Surface Divergence Theory

€

∂[c]

∂t+

r v ⋅

r ∇[c] = D

r ∇2[c]

€

rF =

r v [c] + D

r ∇[c]

€

β

€

t

€

F

€

t

Surface Divergence Theory

€

∂[c]

∂t+

r v ⋅

r ∇[c] = D

r ∇2[c]

€

rF =

r v [c] + D

r ∇[c]

€

F = kΔC = 0.5 β 'D

How do we visualize (or measure) the velocities in the top ~100 microns of the water column accurately?

Surface Divergence Theory

from Turney et al. 2005

from McKenna & McGillis 2004

Surface Divergence Theory

from Xu et al. 2006

from Turney et al. 2005

Experimental Conditions

No Wind, Channel Flow (Straight Channelized River) 4 water heights 3 water velocities

Reynolds numbers ranging from 5000 to 30,000

Wind Waves, Microscale Wave Breaking10 wind speeds

fetch constant ~9 meters

Measurements

No Wind, Channel Flow- Mean Velocity, Depth, Temperature,- PIV Turbulence in Middle of Water Column- Friction of Water on Channel Bottom - PIV of Surface Divergence Motions- Oxygen Transfer Measurements

Wind Waves- Mean Velocity, Depth, Temperature,- PIV Turbulence in Middle of Water Column- Friction of Water on Channel Bottom- Wind Speeds (~1mm apart) at Locations Above Interface- Friction of Wind on Air-Water Interface- Stereo PIV of Surface Divergence Motions- Oxygen Transfer Measurements- Standard Water Height Measurements and Shadowgraphs

u* (cm/s)

k 1

0-5

(cm

/s)

€

β 'D

k=3.3 x 10-5 m/s

F=3.3 x 10-5 ΔC

Conclusions:

• It’s possible that the Surface Divergence Models is too simple, i.e., it ignores organized flows such as waves. Perhaps it is time for a new theory.

•Time-history effects are necessary for an adequate understanding of how the chemical is transported away from the interface.

• Accurate knowledge of velocity near the interface is very valuable. These measurement techniques should be pushed forward.

The Bigger Picture and Future Work

Pg C: 3.2 (+/-0.2) = 6.3 (+/-0.4) + 2.2(+/-1.3) - 2.4(+/-1.2) – 2.9 atmosphere fossil fuel terrestrial oceanic error

from Sabine et al. 2004

from Woods Hole Website

1 cmAir

Water

from Herlina & Jirka 2004

Air

Water

1 cm

from Tokoro et al 2007

from Belanger 1991

Surface Divergence Theory

1 mm

€

v = v i + y∂v

∂yi

+ y 2 ∂ 2v

∂y 2

i

+ y 3 ∂ 3v

∂y 3

i

+ H.O.T.

Surface Divergence Theory

1 mm€

v − v i = y∂v

∂yi

+ y 2 ∂ 2v

∂y 2

i

+ y 3 ∂ 3v

∂y 3

i

+ H.O.T.€

v = v i + y∂v

∂yi

+ y 2 ∂ 2v

∂y 2

i

+ y 3 ∂ 3v

∂y 3

i

+ H.O.T.

Surface Divergence Theory

1 mm€

v − v i = y∂v

∂yi

+ y 2 ∂ 2v

∂y 2

i

+ y 3 ∂ 3v

∂y 3

i

+ H.O.T.€

v = v i + y∂v

∂yi

+ y 2 ∂ 2v

∂y 2

i

+ y 3 ∂ 3v

∂y 3

i

+ H.O.T.

€

u − u i = y∂u

∂yi

+ y 2 ∂ 2u

∂y 2

i

+ y 3 ∂ 3u

∂y 3

i

+ H.O.T.

Surface Divergence Theory

1 mm€

v − v i = y∂v

∂yi

+ y 2 ∂ 2v

∂y 2

i

+ y 3 ∂ 3v

∂y 3

i

+ H.O.T.€

v = v i + y∂v

∂yi

+ y 2 ∂ 2v

∂y 2

i

+ y 3 ∂ 3v

∂y 3

i

+ H.O.T.

€

∂w

∂z+

∂u

∂x= −

∂v

∂y

Surface Divergence Theory

1 mm€

v − v i = −y∂w

∂z+

∂u

∂x ⎛ ⎝

⎞ ⎠i

+ y 2 ∂ 2v

∂y 2

i

+ y 3 ∂ 3v

∂y 3

i

+ H.O.T.€

v = v i + y∂v

∂yi

+ y 2 ∂ 2v

∂y 2

i

+ y 3 ∂ 3v

∂y 3

i

+ H.O.T.

€

∂w

∂z+

∂u

∂x= −

∂v

∂y

Surface Divergence Theory

1 mm

€

v = v i + y∂v

∂yi

+ y 2 ∂ 2v

∂y 2

i

+ y 3 ∂ 3v

∂y 3

i

+ H.O.T.

€

v − v i ≈ −y∂w

∂z+

∂u

∂x ⎛ ⎝

⎞ ⎠i

€

∂w

∂z+

∂u

∂x= −

∂v

∂y

Surface Divergence Theory

1 mm

€

v = v i + y∂v

∂yi

+ y 2 ∂ 2v

∂y 2

i

+ y 3 ∂ 3v

∂y 3

i

+ H.O.T.

€

v − v i ≈ −y∂w

∂z+

∂u

∂x ⎛ ⎝

⎞ ⎠i

= −yβ

€

∂w

∂z+

∂u

∂x ⎛ ⎝

⎞ ⎠i

=∂v

∂yi

= β

Surface Divergence Theory

1 mm

€

v = v i + y∂v

∂yi

+ y 2 ∂ 2v

∂y 2

i

+ y 3 ∂ 3v

∂y 3

i

+ H.O.T.

€

v − v i ≈ −y∂w

∂z+

∂u

∂x ⎛ ⎝

⎞ ⎠i

= −yβ

€

∂w

∂z+

∂u

∂x ⎛ ⎝

⎞ ⎠i

=∂v

∂yi

= β€

u − u i ≈ 0

Depth (cm) Flow Speed (cm/s) Macro Re Turbulent Re

5 2.3 1150 5 3.0 1510 5 10.0 5000 100 5 24.0 12000 170 5 54.5 30000 310 7 7.1 5000 100 7 17.1 12000 170 7 42.9 30000 280 9 5.6 5000 80 9 13.3 12000 140 9 33.3 30000 250 10 5.8 5800 10 10.7 10700 13 3.8 5000 50 13 9.2 12000 100 13 23.1 30000 190

No Wind

Depth (cm) Wind Speed (cm/s) Wave Height (cm)

5 75 - 5 75 - 5 165 - 5 224 - 5 291 - 10 319 - 10 410 0.2 10 499 0.4 10 599 0.6 10 712 0.7 10 706 0.7 10 799 0.9 10 894 1.1

Windy

from Takahashi et al. 2008

from Richey et al. 2002

Chemical Budgets

Change in Amount per Unit Time = Flux In - Flux Out

Surface Renewal Theory

Surface Divergence Theory

1 mm

€

F = D∂[c]

∂y

€

Δy = DΔ[c]

F

Surface Divergence Theory

100 μm

€

∂w

∂z+

∂u

∂x ⎛ ⎝

⎞ ⎠i

= β

Surface Divergence Theory

1 mm

€

v =∂w

∂z+

∂u

∂x ⎛ ⎝

⎞ ⎠y = βy

€

∂w

∂z+

∂u

∂x ⎛ ⎝

⎞ ⎠i

= β

Surface Divergence Theory

1 mm

Surface Divergence Theory

€

∂[c]

∂t+

r v ⋅

r ∇[c] = D

r ∇2[c]

€

rF =

r v [c] + D

r ∇[c]

Surface Divergence Theory

€

∂[c]

∂t+

r v ⋅

r ∇[c] = D

r ∇2[c]

€

rF =

r v [c] + D

r ∇[c]

€

β

€

t

€

F

€

t

Pg C: 3.2 (+/-0.2) = 6.3 (+/-0.4) + 2.2(+/-1.3) - 2.4(+/-1.2) – 2.9 atmosphere fossil fuel terrestrial oceanic error

Chemical Budgets

Change in Amount per Unit Time = Flux In - Flux Out

from Blais et al. 2001

from Schimpf et al. 2004

from Herlina & Jirka 2004

Surface Renewal Theory

Surface Renewal Theory

“Renewed” Spot

Surface Renewal Theory

“Renewed” Spot

Surface Renewal Theory

€

F = Δ[c]D

π t

Surface Renewal Theory

€

F = Δ[c]D

π t

Surface Renewal Theory

€

F =D

t€

F = Δ[c]D

π t