Different regimes of compaction driven how have been studied within the
framework of a poro-viscoelastic medium. A single dimensionless
parameter, the Deborah number De, has been identified, which enables the
portrayal of the solution from the purely viscous matrix limit (De much
less than 1) to the pore-elastic (De much greater than 1) matrix limit.
In viscous limit the evolution of a porosity disturbance (porosity wave)
is governed by nonlinear convection-diffusion equation, while in the
pore-elastic limit it evolves according to a Burgers-like non-linear
advection equation. In both regimes porosity waves of higher amplitude
propagate faster. However in the viscous limit porosity waves go through
each other in soliton-like fashion, while in pore-elastic limit they
coalesce and thus enhance melt segregation. The introduction of other
variables, such as chemistry, would induce different responses in the
flow for low and high De, allowing for diverse feedback situations.