  Understanding fluid movement in multi-pored materials is vital for energy
security and physiology. For instance, shale (a geological material) and bone
(a biological material) exhibit multiple pore networks. Double
porosity/permeability models provide a mechanics-based approach to describe
hydrodynamics in aforesaid porous materials. However, current theoretical
results primarily address steady-state response, and their counterparts in the
transient regime are still wanting. The primary aim of this paper is to fill
this knowledge gap. We present three principal properties -- with rigorous
mathematical arguments -- that the solutions under the double
porosity/permeability model satisfy in the transient regime: backward-in-time
uniqueness, reciprocity, and a variational principle. We employ the ``energy
method'' -- by exploiting the physical total kinetic energy of the flowing
fluid -- to establish the first property and Cauchy-Riemann convolutions to
prove the next two. The results reported in this paper -- that qualitatively
describe the dynamics of fluid flow in double-pored media -- have (a)
theoretical significance, (b) practical applications, and (c) considerable
pedagogical value. In particular, these results will benefit practitioners and
computational scientists in checking the accuracy of numerical simulators. The
backward-in-time uniqueness lays a firm theoretical foundation for pursuing
inverse problems in which one predicts the prescribed initial conditions based
on data available about the solution at a later instance.
