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

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

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

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

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

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

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.

This experiment: 8MPa, 4mm high crystal, 2.5-5 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

Asaro-Tiller-Grinfeld (ATG) instability

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 )

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?

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

Coarsening From experiment From simulation l l

Pattern formation & non-linear systems

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?

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

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