Although melting is inferred to start at depths of 120 km or more in t
he mantle, little is known about the style of melt transport fi om the
source region to the surface. Geochemical observations require the tr
ansport of melt from depth to be fast, and that melt is not in chemica
l equilibrium with the matrix through which it passes. We present a mo
del which allows fast transport by an open melt conduit in a viscous p
ermeable matrix and discuss the possibility of chemical isolation in s
uch a conduit. We show that disturbances on the conduit surface propag
ate slowly upwards as solitary waves and cause melt to flow between th
e conduit and the surrounding porous matrix.