1. Trailing Behind the Bandwagon: Transition from Pervasive to Segregated Melt Flow in Ductile Rocks James Connolly and Yuri Podladchikov Sowaddahamigonnadoaboutit? Flog a dead hypothesis: reexamine mechanical flow instabilities in light of a rheological model for plastic decompaction Review steady flow instabilities in viscous matrix Consider the influence of plastic decompaction General analysis of the compaction equations for disaggregation conditions

2. Review of the Blob, an Old Movie Porosity, t=0  /  0 ~10 t=3.3   /  0 ~50 5  next slide

3. A differential compaction model: Death of the Blob? What’s wrong with the Blob? Compaction and decompaction are asymmetric processes

4. Channelized flow, characteristic spacing ~  c Domains carry more than the excess flux? Flow channeling instability in a matrix with differential yielding next slide

5. Numerical Problem A traveling wave with gradients on drastically different spatial scales A variable resolution grid that propagates with the center of mass

6. Intrinisic flow instability in viscoplastic media Waves nucleate spontaneously from vanishingly small heterogeneities and grow by drawing melt from the matrix next slide

7. Constant Viscosity vs. Differential Yielding next slide

8. Return of the Blob R=1/125R=1/10000 Porosity Pressure Low Pressure next slide

9. Scaling? 1D analytic R = 1/156 R = 1/625 R = 1/2500 R = 1/10,000 R = 1/40,000 R = 1/160,000 next slide

10. Is there a dominant instability? R = 1/156 R = 1/625 R = 1/2500 R = 1/10,000 R = 1/40,000 R = 1/160,000 next slide

11. Wave growth rate ~R  3/8 /t c * For R ~ 10 -3 an instability grows from  = 10 -3 to disaggregation in ~10 3 y with v ~ 10-500 m/y over a distance of 30 km Yes and Maybe Yes, the mechanism is capable of segregating lower asthenospheric melts on a plausible time scale If the waves survive the transition to the more voluminous melting regime of the upper asthenosphere, total transport times of ~1 ky are feasible. Alternatively, waves could be the agent for scavenging Actinide excesses that are transported by a different mechanism, e.g., RII or dikes. So does it work for the McKenzie MORB Actinide Hypothesis? next slide

12. Conclusions I Pipe-like waves are the ultimate in porosity-wave fashion: nucleate from essentially nothing suck melt out of the matrix grow inexorably toward disaggregation Growth/dissipation rate considerations suggest R~10 -4, mechanistic arguments would relate R to the viscosity of the suspension

13. Toward a Complete Classification of Melt Flow Regimes Transition from Darcyian (pervasive) to Stokes (segregated “magmatic”) regime

14. Balancing ball

15. Wave Solutions as a Function of Flux

16. Phase diagram / x

17. Sensitivity to Constituitive Relationships

18. Conclusions II

19. Objectives Review steady flow instabilities => birth of the blob Consider the influence of differential yielding => return of the blob Analysis of the compaction equations for dissagregation conditions

20. So dike-like waves are the ultimate in porosity-wave fashion: They nucleate out of essentially nothing They suck melt out of the matrix They seem to grow inexorably toward disaggregation But Do they really grow inexorably, what about 1  ? Can we predict the conditions (fluxes) for disaggregation? Simple 1D analysis

21. Wave growth rate ~R  3/8 /t c * For R ~ 10 -4 (10 -8 ) an instability grows from  = 10 -3 to disaggregation in ~10 4 y with v ~ 1-50 m/y over a distance of 30 (1) km Adequate to preserve actinide secular disequilibria? Excuses: McKenzie/Barcilon assumptions give higher velocities and might be justified at large porosity The waves are dike precursors? So does it work for MORB transport?

22. Conclusions I Pipe-like waves are the ultimate in porosity-wave fashion: nucleate from essentially nothing suck melt out of the matrix grow inexorably toward disaggregation Growth/dissipation rate considerations suggest R~10 -4, mechanistic arguments would relate R to the viscosity of the suspension Velocities are too low to explain MORB actinide signatures, but the waves could be precursors to a more efficient mechanism

23. Problem: Geochemical constraints suggest a variety of melting processes produce minute quantities of melt, yet that this melt segregates and is transported to the surface on extraordinarily short time scales Hypotheses: dikes (Nicolas ‘89, Rubin ‘98), reactive transport (Daines & Kohlstedt ‘94, Aharanov et al. ‘95) and shear-induced instability (Holtzman et al. ‘03, Spiegelman ‘03) partial explanations Flog a dead hypothesis: reexamine mechanical flow instabilities in light of a rheological model for plastic decompaction Review steady flow instabilities => birth of the blob Consider the influence of differential yielding => return of the blob Analysis of the compaction equations for disaggregation conditions Sowaddahamigonnadoaboutit?

24. A Pet Peeve: Use and Abuse of the Viscous Compaction Length, Part II

25. Good News for Blob Fans Soliton-like behavior allows propagation over large distances Bad News for Blob Fans Stringent nucleation conditions Soliton-like behavior prevents melt accumulation Small amplification, low velocities Dissipative transient effects

26. Is there a dominant instability? R = 1/156 R = 1/625 R = 1/2500 R = 1/10,000 R = 1/40,000 R = 1/160,000 SS stage 1 SS stage 2 transient

27. Conclusions I Pipe-like waves are the ultimate in porosity-wave fashion: nucleate from essentially nothing suck melt out of the matrix grow inexorably toward disaggregation Growth/dissipation rate considerations suggest R~10 -4, mechanistic arguments would relate R to the viscosity of the suspension Velocities are too low to explain MORB actinide signatures, but the waves could be precursors to a more efficient mechanism