  Three-phase suspensions, of liquid that suspends dispersed solid particles
and gas bubbles, are common in both natural and industrial settings. Their
rheology is poorly constrained, particularly for high total suspended fractions
($\gtrsim 0.5$). We use a dam-break consistometer to characterize the rheology
of suspensions of (Newtonian) corn syrup, plastic particles, and CO$_2$
bubbles. The study is motivated by a desire to understand the rheology of magma
and lava. Our experiments are scaled to the volcanic system: they are conducted
in the non-Brownian, non-inertial regime; bubble capillary number is varied
across unity; and bubble and particle fractions are $0\leq\phi_{gas}\leq0.82$
and $0\leq\phi_{solid}\leq0.37$ respectively. We measure flow-front velocity
and invert for a Herschel--Bulkley rheology model as a function of
$\phi_{gas}$, $\phi_{solid}$, and the capillary number. We find a stronger
increase in relative viscosity with increasing $\phi_{gas}$ in the low to
intermediate capillary number regime than predicted by existing theory, and
find both shear-thinning and shear-thickening effects, depending on the
capillary number. We apply our model to the existing community code for lava
flow emplacement, PyFLOWGO, and predict increased viscosity and decreased
velocity compared with current rheological models, suggesting existing models
may not adequately account for the role of bubbles in stiffening lavas.
