We present the results of an analytical model of porous flow of viscous melt into a steadily dilating "channel" (defined as a cluster of smaller veins) in downwelling subarc mantle. The model predicts the pressure drop in the mantle wedge matrix surrounding the channel needed to drive melt flow as a function of position and time. Melt is sucked toward the dilatant region at a near-constant velocity (10-5 s-1) until veins comprising the channel stop opening (t = τ). Fluid elements that complete their journey within the time span t < τ arrive at a channel. Our results make it possible to calculate the region of influence sampled by melt that surrounds the channel. This region is large compared to the model size of the channelized region driving flow. For a baseline dilation time of 1 year and channel half width of 2 m, melt can be sampled over an 80-m radius and has the opportunity to sample matrix material with potentially contrasting chemistry on geologically short timescales. Our mechanical results are consistent with a downgoing arc mantle wedge source region where melting and melt extraction by porous flow to a channel network are sufficiently rapid to preserve source-derived 238U-230Th-226Ra, and potentially also 226 Ra_2 10P15, disequilibria, prior to magma ascent to the surface. Since this is the rate-determining step in the overall process, it allows the possibility that such short-lived disequilibria measured in arc rocks at the surface are derived from deep in the mantle wedge. Stresses due to partial melting do not appear capable of producing the desired sucking effect, while the order of magnitude rate of shear required to drive dilation of ∼10-7 s-1 is much larger than values resulting from steady state subduction. We conclude that local deformation rates in excess of background plate tectonic rates are needed to "switch on" the dilatant channel network and to initiate the sucking effect.