  In viscous particulate liquids, such as suspensions and polymer solutions,
the large-distance steady-state flow due to a local disturbance is commonly
described in terms of hydrodynamic screening -- beyond a correlation length
$\xi$ the response drops from that of the pure solvent, characterized by its
viscosity $\eta_0$, to that of the macroscopic liquid with viscosity $\eta$.
For cases where $\eta>>\eta_0$ we show, based on general conservation
arguments, that this screening picture, while being asymptotically correct,
should be refined in an essential way. The crossover between the microscopic
and macroscopic behaviors occurs gradually over a wide range of distances,
$\xi<<r<<\xi\sqrt{eta/\eta_0}$. In liquid-laden solids, such as colloidal
glasses, gels and liquid-filled porous media, where $\eta-->\infty$, this
intermediate behavior takes over the entire large-distance response. The
intermediate flow field, arising from the effect of mass displacement rather
than momentum diffusion, has several unique characteristics: (i) It has a
dipolar shape with a $1/r^3$ spatial decay, negative transverse components, and
vanishing angular average. (ii) Its amplitude depends on the liquid properties
through $\eta_0$ and $\xi$ alone; thus, in cases where $\xi$ is fixed by
geometry (e.g., for particulate liquids tightly confined in solid matrices),
the large-distance response is independent of particle concentration. (iii) The
intermediate field builds up non-diffusively, with a distance-independent
relaxation rate, making it dominant at large distances before steady state has
been reached. We demonstrate these general properties in three model systems.
