  This article is dedicated to localization of the principal eigenvalue (PE) of
the Stokes operator acting on solenoidal vector fields that vanish outside a
large random domain modeling the pore space in a cubic block of porous material
with disordered micro-structure. Its main result is an asymptotically
deterministic lower bound for the PE of the sum of a low compressibility
approximation to the Stokes operator and a small scaled random potential term,
which is applied to produce a similar bound for the Stokes PE. The arguments
are based on the method proposed by F. Merkl and M. V. W\"{u}trich for
localization of the PE of the Schr\"{o}dinger operator in a similar setting.
Some additional work is needed to circumvent the complications arising from the
restriction to divergence-free vector fields of the class of test functions in
the variational characterization of the Stokes PE.
