Fluid dynamics of magma oceans Slava Solomatov

1
Fluid dynamics of magma oceansSlava Solomatov
2
Outline

• The terrestrial magma ocean hypothesis
• Crystallization of the magma ocean
• Some thoughts on Mars

3
Old view Soft accretion
4
New view Hard accretion
5
Simulation of giant impact, Canup (2004)
6

• Factors contributing to the formation of
• a terrestrial magma ocean

• Impact heating (Safronov 1964 Kaula 1979
• Benz and Cameron 1990 Melosh 1990 Canup
  2004).
• Gravitational energy release due to core
  formation
• (Flasar and Birch 1973).
• Blanketing effect of the atmosphere (Hayashi et
  al.
• 1979 Abe and Matsui 1986 Zahnle et al. 1988).

7

How did the magma ocean crystallize?
8
Fractional crystallization?

9
Fractional crystallization?

10
Equilibrium crystallization?

11

• Geochemical constraints

• Core segregated within 30-50 Myr (Kleine et al.
  2002, 2004 Yin et al. 2002). The Earth had to be
  at least partially molten at that time.

12

• Geochemical constraints

• The pattern of siderophile elements is
  consistent with metal-silicate equilibrium around
  28 GPa and 2200 K (Righter and Drake 2003
  however, see Rubie et al. 2003).

13

• Geochemical constraints

• The degree of fractionation in the lower mantle
  has to be less than 10-20 based on minor
  element ratios (Corgne and Wood 2002 Walter et
  al. 2004 Ito et al. 2004).

14

• Geochemical constraints

• Element abundances seem to be best explained by
  melt differentiation at small melt fractions, 5
  (Gasparik and Drake 1995 Caro et al. 2005).

15

• One of the major uncertainties

Do crystals sink of float? Interpretation of
geochemical data depends on Dr(P,T)! (e.g. Agee
1988 Ohtani and Maeda 2001).
16

Can convection prevent differentiation?
17
Early criteria for suspension

Vcrystals lt Vconvection
Barlett (1969), Huppert and Spark (1980),
Marsh and Maxey (1985) The predicted
critical crystal size is 10-100 m!
18
Martin and Nokes experiments (1989)
Even when Vparticles ltlt Vconvection sedimentation
occurs almost as fast as in the absence of
convection! Their explanation Vconvection 0 at
the bottom.

19
Tonks and Meloshs (1990) criterion

Vparticles lt V
V - friction velocity The predicted critical
crystal size is 1-10 m!
20
(No Transcript)
21
Experiments on entrainment
critical convective stress
22
Criterion for entrainment
tc dominant convective stress (buoyancy
stresses for laminar and soft turbulence
convection and Reynolds stresses for hard
turbulence)
23
How much solid fraction can be suspendedby
convection?
Rate of change of gravitational energy due to
particle settling
Total mechanical work done by convection per
unit time
24
Suspended solid fraction
e lt 1 efficiency factor
25
Experimental constraints on the efficiency
factor e
26
Formation of solid bonds can prevent entrainment
in magma oceans
27
A criterion for sedimentation (perhaps more
useful)
or
28
Equilibrium crystallization can happen
independently of whether or not entrainment
occurs if
Crystallization time ltlt Crystal settling time
Critical crystal size
29
The 1 mm boundary
Equilibrium crystallization is inevitable when
Fractional crystallization is inevitable when
30
How large are the crystals in the magma
ocean? Can they reach 1 mm? Can easily
exceed 1 m?

31
(No Transcript)
32
Liquidus and solidus for a simple 3-component
lower mantle model
33
Nucleation in the downgoing flow
34
(No Transcript)
35
(No Transcript)
36
Crystal size controlled by nucleationin the
descending flow (Solomatov 2000)
- derivatives of the phase diagram
- a transcendental equation for q
37
Nucleation in the magma ocean and in
continuous cooling experiments is described by
similar equations
38
Typical parameters of a magma ocean(hard
turbulence regime rotation)
Convective velocities 10 m s-1
Heat flux
106 W m-2 Thermal boundary layer 1
cm Surface temperature 2000 K
39
Continuous cooling experiments and magma ocean
40
Ostwald ripening after nucleation
Early stages Late stages
41
Estimates of crystal sizes
d 0.1-1 mm after nucleation d 0.1-1 mm
Ostwald ripening for weeks
(early stages of crystallization) d 1-10
cm Ostwald ripening for 100s years
(late stages of
crystallization) d meters Ostwald
ripening on geological
time scales
42
Critical crystal size for suspension and the
actual crystal size in the magma ocean
43
Crystallization beyond the rheological
transition (f50)
44
The rheological transition
m 1015 Pa s
m 1 Pa s
Suspension
Partially molten solid
45
Does melt percolation cause differentiation
after magma becomes solid-like (beyond the
rheological transition)?

46
Crystallization beyond the rheological
transition (f50)
Temperature
liquidus
adiabat
f50
Depth
solidus
liquid-like
solid-like
47
Crystallization beyond the rheological
transition (f50)
Temperature
Mantle overturn 10 years Crystallization
103 years Melt percolation 108 years
f50
Depth
adiabat
48
Crytallization at low pressures
49
Adiabats at low pressures
50
Onset of fractional crystallization

• The cycle nucleation-growth-dissolution changes
  to growth. Crystals reach 1 cm and cannot be
  suspended by convection.
• 2. Crystal settling generates a stable density
  gradient which supresses convection.
• 3. Silicate atmosphere changes to steam
  atmosphere and the heat flux drops
• Fractional crystallization begins at low
  pressures and
• low melt fractions.

51
Three major time scales
Crystallization of deep layers lt 103
years Crystallization of shallow layers gt 107
years Planetary accretion
108 years

There is an apparent bottom of the magma
oceanwhere Fe can accumulate and equilibrate
with silicates (controlled by pressure rather
than depth)
52
Metal-silicate equilibration boundary?
53
Martian magma oceans

• Smaller planet (1/2 Earth size,
• 1/10 Earth mass)
• Less energetic impacts
• Lower resulting temperatures
• Lower pressures
• Differentiation is stronger
• A global magma ocean may
• or may not form

54
Martian magma ocean evolution scenarios
(from Reese and Solomatov, 2006)
55
Conclusions

• Deep terrestrial magma ocean crystallized
  quickly
• (lt1000 years) and could have avoided
  substantial
• chemical differentiation.
• Differentiation occurred largely in a shallow
  magma
• ocean which remained partially molten for a
  long time
• (perhaps the Earth never fully crystallized).
• Mars may not necessarily form a global magma
  ocean.
• Melting and crystallization could be local
  (origin of
• crustal dichotomy? Tharsis?).