  Concentration gradients play a critical role in embryogenesis, bacterial
locomotion, as well as the motility of active particles. Particles develop
concentration profiles around them by dissolution, adsorption, or the
reactivity of surface species. These gradients change the surface energy of the
particles, driving both their self-propulsion and governing their interactions.
Here we uncover a regime in which solute-gradients mediate interactions between
slowly dissolving droplets without causing autophoresis. This decoupling allows
us to directly measure the steady-state, repulsive force, which scales with
interparticle distance as $F\sim {1/r^{2}}$. Our results show that the process
is diffusion rather than reaction rate limited, and the theoretical model
captures the dependence of the interactions on droplet size and solute
concentration, using a single fit parameter, $l=16\pm 3$~nm, which corresponds
to the lengthscale of a swollen micelle. Our results shed light on the
out-of-equilibrium behavior of particles with surface reactivity.
