Grain size-dependent viscosity convection

Slava SolomatovWashington University in St. Louis

Acknowledgements: Rifa El-Khozondar

Boulder CO, June 23

Outline

• Mantle rheology

• What controls the grain size?

• How does grain size affect mantle convection?

Rheology

Dislocation creep

Dislocation creep

RT

Qnexp

11−∝

τη

τ - stressn ~ 3

Diffusion creep

Diffusion creep

RT

Qd grm exp∝η

Diffusion creep

RT

Qd grm exp∝η

m ~ 2-3

Superplasticity

RT

Qdn

m

exp1−∝

τη

What controls the grain size?

Grain growth

Grain growth: Example from Dresen et al. (2001), one phase, calcite

Ostwald ripening: Example from Yamazaki et al. (1996) two phases, perovskite+magesiowustite

Ostwald ripening in two-phase systems (from El-Khozondar’s thesis)

Ostwald ripening

⎟⎟⎠

⎞⎜⎜⎝

⎛−∝∝pRT

QtDtd grpp exp)( /1/1

p ~ 3-4

Phase transformations

Polymorphic phase transformations(410, 520, 2600)

Grain size reductioninduced by a phase transformation

Grain growth aftergrain size reduction(from El-Khozondar’sthesis, 2002)

Eutectoid phase transformations(660)

From Yamazaki et al. (1996):

Why is n so high in Yamazaki’s experiments?(~11 rather than 3 or 4)

Degeneration of lamellar eutectic(from El-Khozondar’s thesis, 2002)

Degeneration of Al-Cu lamellar eutectic (from Martin et al., 1997)

Elastic coupling between grains (from Su and Voorhees, 1996)

How does grain size affect mantle convection?

Simple example (from Solomatov, 1996)

RT

Qd exp2∝η ⎟⎟

⎠

⎞⎜⎜⎝

⎛−∝RT

Qtd gr

3exp3/1

RT

QQt gr 3/2exp3/2 −

∝η

660 km

ColdHot (but can have higher viscosity if Qgr > 1.5Q)

Simple example (from Solomatov, 1996)

RT

Qd exp2∝η ⎟⎟

⎠

⎞⎜⎜⎝

⎛−∝RT

Qtd gr

3exp3/1

RT

QQt gr 3/2exp3/2 −

∝η

660 km

ColdHot (but can have higher viscosity if Qgr > 1.5Q)

Qeff

Implications for thermal evolution

Earth’s heat flux

Time, b. y.

H

eat

flu

x, m

W/m

2

Earth’s heat flux

Time, b. y.

H

eat

flu

x, m

W/m

2

F ~ (tin / tr) Fr

Earth’s heat flux

Time, b. y.

H

eat

flu

x, m

W/m

2

F ~ (tin / tr) Fr

tin ~ 1/Q

Possible explanations

• Mantle has more U, Th and K than geochemistry suggests (by as much as 50%)

Possible explanations

• Mantle has more U, Th and K than geochemistry suggests (by as much as 50%)

• Viscous bending controls plate velocity (Christensen and others)

Possible explanations

• Mantle has more U, Th and K than geochemistry suggests (by as much as 50%)

• Viscous bending controls plate velocity (Christensen and others)

• Decreasing convective layering (Peltier and others)

Possible explanations

• Mantle has more U, Th and K than geochemistry suggests (by as much as 50%)

• Viscous bending controls plate velocity (Christensen and others)

• Decreasing convective layering (Peltier and others)

• Larger heat flux from the core than we used to believe

The role of grain size dependent viscosity

Assumptions

• Lower mantle is in the grain size sensitive creep regime (seismically isotropic = diffusion creep/superplasticity).

• Slab buoyancy is mainly balanced by viscous resistance in the lower mantle (so that plate velocity is controlled by lower mantle viscosity).

Parameterized convection calculations from Solomatov (2001)

Observed

Implications for plumes

Montelli et al (2004)

Firm plumes from Korenaga (2005)

Qeff=Q-2Qgr/3

Qeff > 0 Qeff < 0

From Korenaga (2005)

Implications for sublithosphericsmall-scale instabilities

Hall and Parmentier (2003) included grain size evolution as well as grain size reduction in a numerical convection model.

From Hall and Parmentier (2003)

From Hall and Parmentier (2003)

Implications for chemical mixing

Models of mantle reservoirs(from Tackley, 2000)

Layeredmantle

Primitive blobs

Primitivepiles

Well stirred except forprimitive/enrichedbottom

Recycled lithosphere+crust

Deep primitivelayer

d~0.01 cmd~1 cm

Viscosity contrast ~ d2-d3 ~ 104-106

Initial grain size

Implications for other planets

The absence of spinel-perovskite transition is an issue for Mars and Mercury – grains (and viscosity) keep growing without recrystallization (to ~1, maybe 10 cm).

Mars and Mercury

Conclusion

Grain size is important for mantle convection:

• Planetary evolution• Plumes• Sublithospheric small-scale instabilities• Chemical mixing

(well, it’s not the size that matters but how muchit changes)

Future directions

• Better constraints on grain size evolution.

• Implementation in mantle convection models. • Addressing the problems of planetary evolution, plumes, chemical mixing, instabilities, etc. numerically.