Here are papers and movies illustrating the behaviour of the reaction infiltration instability (Aharonov et al 1995, Spiegelman et al 2001,Spiegelman and Kelemen, 2003), a coupled physical/chemical instability proposed for developing spontaneous localization of melt flow into channels during magma migration.
| Some movies showing the time-dependent evolution of high porosity
channels in a compactible reactive porous medium for a problem with
Da=40, Pe=40. These boxes are 4x5 compaction lengths.
(see paper for details and
Panel A shows porosity with a color map such that the minimum porosity is 0.1% and the maximum porosity is 3.9%. Each frame is a dimensionless time of 4 (i.e the time it takes melt to flux through the reactive zone). Note that as the porosity in the channels grows, the porosity in the surrounding area compacts leading to extreme localization such that over 90% of the melt flux is carried in less that 20% of the area
Panel B shows the same run but for height normalized porosity, i.e. at every height the porosity is linearly mapped between its minimum and maximum value at the height z.
|C||D|| Movies showing the time-dependent evolution of porosity and
concentration for a reactive flow problem for a 1-D
upwelling melting column of dimensions 1x5 compaction
lengths (these runs are higher resolution than those in
A and B) Here the solid is upwelling
at rate W and melting due to adiabatic
decompression. The melts produced, however, are still
reactive and channeling proceeds.
Panel C shows porosity with a color map such that the minimum porosity is 0% and the maximum porosity is 1%. This run happens to be highly time dependent.
Panel D the normalized log of the concentration of a trace element with bulk partition coefficient D=0.0001. Blue colors are enriched and warm colors are depleted (apologies for the strange colormaps). Thus the channel centers are highly enriched while their edges, and the regions between the channels are extremely depleted. Note that the flux and the concentrations do not always match one-to-one.
| Movies showing the time-dependent evolution of porosity and
solid concentration field for a reactive flow problem
for a 2-D mid-ocean ridge geometry. The box here is 10x10 compaction
lengths (321x321 grid points...the images are 1 pixel
per grid point). The solid flow field is
given by corner flow and background melting is by
adiabatic decompression. This system is highly reactive
leading to a large number of channels.
Panel E shows porosity with a color map such that the minimum porosity is 0% and the maximum porosity is 2.8%. Panel F concentration field showing the proportion of soluble phase (pyroxene). The solid at the bottom enters with approximately 40% soluble phase which is rapidly diminished by melting and reaction. The reacted channels are apparent with the minimum amount of soluble phase in this run = 2%.