Optimization of bistable viscoelastic systems

We consider the flow of a viscoelastic fluid in a symmetric cross geometry. For small driving pressures the flow is symmetric, but beyond a certain critical pressure the symmetric flow becomes unstable; two stable asymmetric solutions appear, and forcing of the unstable symmetric flow beyond the critical pressure gives rise to increased hydraulic resistance. We have combined a state-of-the-art implementation for viscoelastic flow modeling with topology optimization in a high level finite element package (COMSOL). We use this framework on the cross geometry with the aim to reduce the critical driving pressure corresponding to the point of bistability, such that the effect is enhanced. The point of bistability is, however, not explicitly contained in the solution, so we opt for a heuristic approach based on the dissipation ratio between the asymmetric and unstable symmetric flow solutions. We find a design that significantly reduces the driving pressure required for bistability, and furthermore is in agreement with the approach followed by experimental researchers. Furthermore, by comparing the two asymmetric solutions, we succesfully apply the same approach to a problem with two fluids meeting in the cross.