Transcript Transient dissolution patterns on stressed crystal surfaces

Is there a stressed equilibrium?
Dag Kristian Dysthe
Physics of Geological Processes
University of Oslo
www.fys.uio.no/pgp
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
www.fys.uio.no/pgp
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
www.fys.uio.no/pgp
Pressure solution creep:
”primitive processes”
Pressure
solution
creep (PSC)
in contact
Crack
healing in
contact
Dissolution –
precipitation
waves on
stressed, free
surfaces
www.fys.uio.no/pgp
The stressed and his solution
hexadecane
p=patm
NaClO3(s)
ms=meq
H2O+NaClO3
saturated solution
ml=meq
F, p,T=const
NaClO3(s)
ms(s)>meq
Towards new equilibrium
-ml=ms(s) ?
-ms(surface)=meq ?
- linear transport process?
www.fys.uio.no/pgp
www.fys.uio.no/pgp
www.fys.uio.no/pgp
www.fys.uio.no/pgp
www.fys.uio.no/pgp
Asaro-Tiller-Grinfeld (ATG)
instability
www.fys.uio.no/pgp
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,n,E,s,g)
• Fluid motion coupled with solid must be solved to find
effect of gravity. Finally: advection negligible (no )
www.fys.uio.no/pgp
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?
www.fys.uio.no/pgp
Coarsening of pattern
l
• Experimental: l~t
• Simulation (outside
linear stability
analysis, no
diffusion): l~t1/2
• Confined (exp): l~t1/3
www.fys.uio.no/pgp
Coarsening
From experiment
From simulation
l
l
www.fys.uio.no/pgp
Pattern formation &
non-linear systems
www.fys.uio.no/pgp
Which new equilibrium?
F, p,T=const
After passing of grooves:
• Phase change?
• Crystal surface very stable
Mach-Zehnder interferometer to measure
concentration of NaClO3 in liquid
NaClO3(s)
ms(s)>meq
Towards new equilibrium
-ms(surface)=meq ?
-ml=ms(s) ?
How stable and accurate are conductivity measurements
of concentration?
www.fys.uio.no/pgp
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
s
calcite
Fluid cell for microscope or AFM with
• fluid inlet/outlet
• temperature sensor
• conductivity electrodes? www.fys.uio.no/pgp
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
www.fys.uio.no/pgp