Trailing Behind the Bandwagon:

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. Porosity, t=0 f/f0~10 t=3.3 t f/f0~50 5 d 5 d Review of the Blob, an Old Movie next slide

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

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

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

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

7. Constant Viscosity vs. Differential Yielding next slide

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

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

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

11. So does it work for the McKenzie MORB Actinide Hypothesis? Wave growth rate ~R-3/8/tc* For R ~ 10-3an instability grows from f = 10-3 to disaggregation in ~103 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. next slide

12. Conclusions I Pipe-like waves are the ultimate in porosity-wave fashion:nucleate from essentially nothingsuck melt out of the matrixgrow 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-f? Can we predict the conditions (fluxes) for disaggregation? Simple 1D analysis

21. So does it work for MORB transport? Wave growth rate ~R-3/8/tc* For R ~ 10-4 (10-8) an instability grows from f = 10-3 to disaggregation in ~104 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?

22. Conclusions I Pipe-like waves are the ultimate in porosity-wave fashion:nucleate from essentially nothingsuck melt out of the matrixgrow 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 Sowaddahamigonnadoaboutit? • 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

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

27. Conclusions I Pipe-like waves are the ultimate in porosity-wave fashion:nucleate from essentially nothingsuck melt out of the matrixgrow 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