Rheology of suspensions of flat elastic particles

We consider a suspension of non-interacting flat elastic particles in a Newtonian fluid. We model a flat shape as three beads, carried along by the flow according to Stokes’ law, and connected by nonlinear springs, chosen such that the energy is quadratic in the area. In analogy with common dumbbell models involving two beads connected by linear springs, we solve the stochastic equations of motion exactly to compute the constitutive law for the stress tensor of a flat elastic particle suspension. A lower convected time derivative naturally arises as part of the constitutive law, but surprisingly the rheological response in strong extensional and strong contracting flows is similar to that of the classical Oldroyd-B model associated with dumbbell suspensions.