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
Review of the Blob, an Old Movie
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3
Whats wrong with the Blob?
A differential compaction model Death of the
Blob?
4
Flow channeling instability in a matrix with
differential yielding
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Channelized flow, characteristic spacing
dc Domains carry more than the excess flux?
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Numerical Problem
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Intrinisic flow instability in viscoplastic media
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Waves nucleate spontaneously from vanishingly
small heterogeneities and grow by drawing melt
from the matrix
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Constant Viscosity vs. Differential Yielding
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Return of the Blob
R1/125
R1/10000
Porosity
Pressure
LowPressure
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Scaling?
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Is there a dominant instability?
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So does it work for the McKenzie MORB Actinide
Hypothesis?
Wave growth rate R-3/8/tc For R 10-3 an
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.
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12
Conclusions I
Pipe-like waves are the ultimate in porosity-wave
fashionnucleate from essentially nothingsuck
melt out of the matrixgrow inexorably toward
disaggregation
Growth/dissipation rate considerations suggest
R10-4, mechanistic arguments would relate R to
the viscosity of the suspension
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Toward a Complete Classification of Melt Flow
Regimes
Transition from Darcyian (pervasive) to Stokes
(segregated magmatic) regime
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Balancing ball
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Wave Solutions as a Function of Flux
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Phase diagram
x
/
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Sensitivity to Constituitive Relationships
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Conclusions II
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Objectives

• Review steady flow instabilities gt birth of the
  blob
• Consider the influence of differential yielding
  gt 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
fashionnucleate from essentially nothingsuck
melt out of the matrixgrow inexorably toward
disaggregation
Growth/dissipation rate considerations suggest
R10-4, 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 gt birth of the
  blob
• Consider the influence of differential yielding
  gt return of the blob
• Analysis of the compaction equations for
  disaggregation conditions

24
A Pet PeeveUse 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?
SS stage 2
SS stage 1
transient
27
Conclusions I
Pipe-like waves are the ultimate in porosity-wave
fashionnucleate from essentially nothingsuck
melt out of the matrixgrow inexorably toward
disaggregation
Growth/dissipation rate considerations suggest
R10-4, 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