  Thermal fluctuations, geometric exclusion, and external driving all govern
the mechanical response of dense particulate suspensions. Here, we measure the
stress-strain response of quasi-two-dimensional flow-stabilized microsphere
heaps in a regime in which all three effects are present using a microfluidic
device. We observe that the elastic modulus and the mean interparticle
separation of the heaps are tunable via the confining stress provided by the
fluid flow. Furthermore, the measured stress-strain curves exhibit a universal
nonlinear shape which can be predicted from a thermal van der Waals equation of
state with excluded volume. This analysis indicates that many-body interactions
contribute a significant fraction of the stress supported by the heap.
