We investigate steady state solutions of a nonlocal geometric PDE that serves as a simple model of simultaneous contraction and growth of grains called ooids in geosciences. As a main result of the talk I demonstrate that the parameters associated with the physical environment determine a unique, time-invariant (equilibrium) solution of the equation among smooth, convex curves embedded in $\mathbb{R}^2$. The model produces nontrivial shapes that are consistent with recorded shapes of mature ooids found in nature.