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Is there a stressed equilibrium?

Dag Kristian Dysthe

Physics of Geological Processes

University of Oslo

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The November (wet & stressed) Earth

• Plate tectonics => horizontal stresses

• Overburden => vertical stresses

• Most rocks are wet (mineral grains+water)

• Influensa: weakening of the crust by water and stress

• Viscosity of rocks

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Compaction by pressure solution creep

• Dissolution of stressed surface of solid

• Diffusion of dissolved mass

• Precipitation on less stressed surface of solid

Same process active in deformation under stress

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Pressure solution creep: ”primitive processes”

Pressure solution creep (PSC) in contact

Crack healing in contact

Dissolution – precipitation waves on stressed, free surfaces

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The stressed and his solution

NaClO3(s)s=eq

H2O+NaClO3

saturated solutionl=eq

hexadecane

NaClO3(s)s()>eq

F, p,T=const

Towards new equilibriuml=s() ?s(surface)=eq ?- linear transport process?

p=patm

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Asaro-Tiller-Grinfeld (ATG) instability

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Asaro-Tiller-Grinfeld (ATG) instability + fluid and gravity

• Driving force: =(1-2)(nn-tt)2/2E+• Kinetics:

– Dissolution: vs=/– Mass and heat transport: j~Dc~, q~(+)j, (T=0)– Navier-Stokes: 2v~-p~-grc~ez=0

• Dispersion relation~ 2Dk2(G-i)/(+k+Dk2-iG/4)• G=crg, r=(1/)∂/∂c, =D/(1-c), =(k,,E,,)• Fluid motion coupled with solid must be solved to find

effect of gravity. Finally: advection negligible (no )

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Wave motion

• Gravity driven waves• Experimental

v = 20 m/h• Theoretical: Numbers

are difficult!

=KTd/dc|p,T-Td/dT|p,c

=/vs

• Critical angle to vertical for waves?

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Coarsening of pattern

• Experimental: ~t• Simulation (outside

linear stability analysis, no diffusion): ~t1/2

• Confined (exp): ~t1/3

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Coarsening

From simulation

From experiment

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Pattern formation &non-linear systems

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Which new equilibrium?

NaClO3(s)s()>eq

F, p,T=const

Towards new equilibriums(surface)=eq ?l=s() ?

Mach-Zehnder interferometer to measure concentration of NaClO3 in liquid

After passing of grooves:• Phase change?• Crystal surface very stable

How stable and accurate are conductivity measurementsof concentration?

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Extrapolation to geological conditions

1mmFluid cell for microscope or AFM with• fluid inlet/outlet• temperature sensor• conductivity electrodes?

calcite

• Calcite, CaCO3

• Abundant in Nature: Limestone, chalk, marble…• Perfect cleavage => suitable for AFM => well studied molecular scale dissolution properties• Lower (higher) solubility, slower (faster) dissolution kinetics than NaClO3 (quartz)• Theoretically at 25C, =100MPa:

• = 7 m• diff= 40 hours• diss = 5 years

• Observe molecular onset of instability

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Conclusions

• 100 years of discussion on what is important for non-hydrostatically stressed solids

• Non-linear effects a test bed of real theory– Which approximations are correct?

• Only experiments could renew the field!

• A stressed equilibrium? Still an open question