  Understanding the particle-scale transition from elastic deformation to
plastic flow is central to making predictions about the bulk material
properties and response of disordered materials. To address this issue, we
perform experiments on flow-stabilized solids composed of micron-scale spheres
within a microfluidic channel, in a regime where particle inertia is
negligible. Each solid heap exists within a stress gradient imposed by the
flow, and we track the positions of particles in response to single impulses of
fluid-driven compression or decompression. We find that the resulting
deformation field is well-decomposed into an affine field, with a constant
strain profile throughout the solid, and a non-affine field. The magnitude of
this non-affine response decays with the distance from the free surface in the
long-time limit, suggesting that the distance from jamming plays a significant
role in controlling the length scale of plastic flow. Finally, we observe that
compressive pulses create more rearrangements than decompressive pulses, an
effect that we quantify using the $D^2_\mathrm{min}$ statistic for non-affine
motion. Unexpectedly, the time scale for the compression response is shorter
than for decompression at the same strain (but unequal pressure), providing
insight into the coupling between deformation and cage-breaking.
