Solidification in Channel Flows: Effects of Channel Irregularities on Transitional (Time-Dependent) Flow Behavior

The surfaces of basaltic lava channels evolve in both space and time from crust-free to crust-dominated. The presence or absence of stable lava crusts, in turn, dictates the rate of heat loss from the lava core and controls the mechanisms of lava flow advance. For this reason, we extended experimental studies of the cooling and solidification of channel flows to investigate unsteady behavior observed near the transition from `open channel' flow to `tube' flow in both uniform and irregular channels. The experiments used polyethylene glycol wax flowing at moderate Reynolds numbers under cold water down a 3m-long, sloping, rectangular channel. For a straight uniform channel, flows at conditions of 0.4 < U₀t_s/W < 1 initially developed a strong crust that spanned the entire width of the channel but continued to move downstream. With time, the crust backed up from the downstream end of the channel, and was repeatedly over-run by newly crusted flow from upstream. Hence the flow became progressively deeper in the distal regions, and the effects of the downstream end of the channel (a free fall into a reservoir) propagated towards the source. The result was a complex flow that evolved toward fully developed `tube' flow under a stationary, insulating roof. Up-flow propagation of lava tubes is observed at Mt. Etna, Italy (Calvari and Pinkerton, 1998) and Kilauea, Hawaii (Peterson et al., 1994) when slopes flatten and flows widen, or at channel bends and constrictions. We explored several configurations of channel geometry to examine their effect on time-dependent flow behavior. When a flow encountered an 80% expansion in channel width (at 1.2m from the source), the flow speed decreased at the expansion. This promoted the formation of rigid crust and shifted the onset of tube flow to larger values of U₀t_s/W. When the flow encountered a decrease in channel width (at 0.6m from the source), acceleration of the flow caused disruption of the surface crust inside the constriction. However, rotating pieces of crust sometimes blocked the entrance to the narrow region and thus promoted tube formation upstream. Flow over small obstructions placed within the channel acted to disrupt the central crust and inhibit tube formation. Flow through a sloping zig-zag channel (with an amplitude to wavelength ratio of 1:5) showed no significant differences from flow in a straight channel, except that conditions for the formation and upstream propagation of stationary crust were again shifted to larger flow speeds and higher temperatures. Together these observations suggest that stable crust formation in channelized lava flows may be very sensitive to changes in flow surface velocity generated by either irregularities in channel morphology or variations in lava flux.