  The rheology of suspensions showing discontinuous shear thickening (DST) is
well documented in conventional rheometer with rotating tools, but their study
in capillary flow is still lacking. We present results obtained in a homemade
capillary rheometer working in an imposed pressure regime. We show that the
shape of the experimental curve giving the volume flow rate versus the wall
stress in a capillary can be qualitatively reproduced from the curve obtained
in rotational geometry at imposed stress but instead of a sharp decrease of the
volume flow rate observed at a critical stress, this transposition predicts a
progressive decrease in flow rate. The Wyart-Cates theory is used to reproduce
the stress-shear rate curve obtained in rotational geometry and then applied to
predict the volume flow rate at imposed pressure. The theoretical curve
predicts a total stop of the flow at high stress, whereas experimentally it
remains constant. We propose a modification of the theory which, by taking into
account the relaxation of the frictional contacts in the absence of shear rate,
well predicts the high stress behavior. We also hypothesized that the DST
transition propagates immediately inside the capillary, once the wall shear
stress has reached its critical value: $\tau_R=\tau_c$, even if the internal
shear stress $\tau(r<R)$ is below the critical one. In this way the whole
experimental curve can be well reproduced by the modified W-C model.
