1. Is there a stressed equilibrium?
Dag Kristian Dysthe
Physics of Geological Processes
University of Oslo

2. 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

3. 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

4. Pressure solution creep: ”primitive processes”
Pressure solution creep (PSC) in contact
Dissolution – precipitation waves on stressed, free surfaces
Crack healing in contact

5. The stressed and his solution
NaClO3(s)
ms(s)>meq
F, p,T=const
hexadecane
p=patm
NaClO3(s)
ms=meq
Towards new equilibrium
-ml=ms(s) ?
ms(surface)=meq ?
- linear transport process?
H2O+NaClO3
saturated solution
ml=meq

6. 3-4 mm high, 2mm thick NaClO_3-crystals in saturated solution (9
3-4 mm high, 2mm thick NaClO_3-crystals in saturated solution (9.4 mol/l) at 24C.
Double T-control (water + Peltier), T-fluct in metal next to cuvette: 2mK.
High resolution time lapse photography at transmitted or reflected light.
Frictionless loading system and capacitance measurement of crystal shortening

7. This experiment:
8MPa. 1hour between frames (whole movie=5 days), 3mm high crystal, inhomogenous stress field at bottom (no glue, glass-crystal contact).
Image enhancement by subtracting average intensity. Semicircular structure on top is an air bubble that distorts the view of the surface
General:
Stresses: 8 (2 exp.), 4 and 0 MPa, after 1-2 hours the surface roughens and develops grooves
24 hours with no stress, no measurable change of crystal surface.
Initial distance between grooves:
8MPa: ~50 mm (Asaro-Tiller Grinfeld instab., linear stab anal: ~40 mm)
4MPa: ~180 mm (Asaro-Tiller Grinfeld instab., linear stab anal: ~150 mm)
Travel speed upwards ~20 mm for both stresses
Crystal shortening stopped during onset and travelling of grooves.

8. This experiment:
8MPa, 4mm high crystal, hours between frames, total movie 13 days. Crystal glued to bottom.
Crystal shortening stopped during onset and travelling of grooves.
Transmitted light, changes in intensity due to picked pictures from sets with rotating polarizer
General:
24 hours with no stress, no measurable change of crystal surface.
Stresses: 8 (2 exp.), 4 and 0 MPa, after 1-2 hours the surface roughens and develops grooves
Initial distance between grooves:
8MPa: ~50 mm (Asaro-Tiller Grinfeld instab., linear stab anal: ~40 mm)
4MPa: ~180 mm (Asaro-Tiller Grinfeld instab., linear stab anal: ~150 mm)
Travel speed upwards ~20 mm for both stresses

10. Asaro-Tiller-Grinfeld (ATG) instability

11. Asaro-Tiller-Grinfeld (ATG) instability + fluid and gravity
Driving force: Dm=(1-n2)(snn-stt)2/2E+gk
Kinetics:
Dissolution: vs=Dm/d
Mass and heat transport: j~rDc~, q~(m+a)j, (T=0)
Navier-Stokes: 2v~-p~-grrc~ez=0
Dispersion relation
(k) ~ 2rDk2(G-iG)/(G+ak+Dk2-iG/4)
G=crg, r=(1/r)∂r/∂c, D=rDd/(1-c), G=G(k,,E,s,g)
Fluid motion coupled with solid must be solved to find effect of gravity. Finally: advection negligible (no )

12. Wave motion Gravity driven waves Experimental v = 20 mm/h
Theoretical: Numbers are difficult!
a=KTdm/dc|p,T-Tdm/dT|p,c
d=Dm/vs
Critical angle to vertical for waves?

13. Coarsening of pattern Experimental: l~t
Simulation (outside linear stability analysis, no diffusion): l~t1/2
Confined (exp): l~t1/3

14. Coarsening
From experiment
From simulation l l

15. Pattern formation &
non-linear systems

16. Which new equilibrium? After passing of grooves: Phase change?
Crystal surface very stable
F, p,T=const
NaClO3(s)
ms(s)>meq
Mach-Zehnder interferometer to measure
concentration of NaClO3 in liquid
Towards new equilibrium
ms(surface)=meq ?
-ml=ms(s) ?
How stable and accurate are conductivity measurements
of concentration?

17. Extrapolation to geological conditions
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, s=100MPa:
l = 7 mm
tdiff = 40 hours
tdiss = 5 years
Observe molecular onset of instability
1mm
Fluid cell for microscope or AFM with
fluid inlet/outlet
temperature sensor
conductivity electrodes?
calcite s

18. 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