  It is well known that the transient behavior during drainage or imbibition in
multiphase flow in porous media strongly depends on the history and initial
condition of the system. However, when the steady-state regime is reached and
both drainage and imbibition take place at the pore level, the influence of the
evolution history and initial preparation is an open question. Here, we present
an extensive experimental and numerical work investigating the history
dependence of simultaneous steady-state two-phase flow through porous media.
Our experimental system consists of a Hele-Shaw cell filled with glass beads
which we model numerically by a network of disordered pores transporting two
immiscible fluids. From the measurements of global pressure evolution,
histogram of saturation and cluster-size distributions, we find that when both
phases are flowing through the porous medium, the steady state does not depend
on the initial preparation of the system or on the way it has been reached.
