Effects of conduit geometry on magma ascent dynamics in dome-forming eruptions

We develop a steady-state, two-phase flow model of magma ascent through an axisymmetric conduit of variable radius R and length L in order to quantify relationships between conduit geometry and magma ascent dynamics. Holding boundary conditions and chamber magma properties constant, we vary conduit geometry systematically and independently, such that the upper conduit radius increases or decreases by a factor of R_t/R_b (radius ratio; 0.4 ≤ R_t/R_b ≤ 2.5), above a change initiation height H (0.1 ≤ H/L ≤ 0.7), and over length L_e (L_e/L = 0.2), where R_t and R_b are conduit radius above (t) and below (b) the radius change and H is the height above the top of the magma chamber. Conduit widening causes a drop in overpressure and corresponding increase in gas volume fraction and magma acceleration over the whole length of the conduit, with all changes increasing in magnitude with increasing radius ratio. Magma ascent rate increases roughly as R² and volumetric flow rate subsequently increases as R⁴ when R_t = R_b = R. Both increasing R_t for a fixed R_b (increasing radius ratio) and increasing R_b for a fixed R_t (decreasing radius ratio), increase volume flow and magma ascent rates. Compared to changes in geometry, small changes in chamber pressure (< 5%) have a weak effect on flow rate. Many model runs produce a magma plug at the top of the conduit, largely due to permeable gas loss through conduit walls. In general, large radii and low radius ratios (i.e., nearly cylindrical conduits) favor thin, low-density plugs, which may facilitate sudden destruction of a plug, and thus enhance the likelihood of explosive over extrusive eruptions. These findings suggest that changes in conduit geometry, such as those caused by conduit erosion during explosive eruptions or by accretion of magma along conduit walls, are strongly coupled to magma ascent dynamics and should not be ignored when interpreting changes in eruptive behavior.