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## Trailing Behind the Bandwagon:

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**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**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**Compaction and decompaction are asymmetric processes**What’s wrong with the Blob? A differential compaction model: Death of the Blob?**Flow channeling instability in a matrix with differential**yielding next slide Channelized flow, characteristic spacing ~ dc Domains carry more than the excess flux?**A traveling wave with gradients on drastically different**spatial scales A variable resolution grid that propagates with the center of mass Numerical Problem**Intrinisic flow instability in viscoplastic media**next slide Waves nucleate spontaneously from vanishingly small heterogeneities and grow by drawing melt from the matrix**Constant Viscosity vs. Differential Yielding**next slide**Return of the Blob**R=1/125 R=1/10000 Porosity Pressure LowPressure next slide**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**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**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**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**Toward a Complete Classification of Melt Flow Regimes**Transition from Darcyian (pervasive) to Stokes (segregated “magmatic”) regime**Phase diagram**x /**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**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**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?**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**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**A Pet Peeve:Use and Abuse of the Viscous Compaction Length,**Part II**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**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**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