Active chaotic mixing of yield stress fluids in an open channel flow

A numerical investigation of active mixing of yield stress fluids using a mixer recently proposed in El Omari et al. (Phys Rev Fluids 6(024):502, 2021. https://doi.org/10.1103/PhysRevFluids.6.024502) and tested experimentally with Newtonian fluids (Younes et al. in Int J Heat Mass Transf 187(122):459, 2022) is presented. As the Bingham number (defined by the ratio of the yield stress to the viscous stress) is increased past a critical value \(\text {Bn}_{\textrm{bulk}}^\textrm{crit}\approx 5\), a dramatic decrease of both the efficiency of the mixing process and of the homogeneity of the final mixture is observed. Further physical insights into this observation are obtained by a systematic analysis of the space-time dynamics of the flow fields in both Eulerian and Lagrangian frames. The numerical results show that the cascade of the passive scalar fluctuations from the wave numbers associated to the integral scale at which the passive scalar is injected down to the diffusive scale is obstructed by the emergence of a supplemental space scale associated to the characteristic size of the un-yielded material elements. The study is complemented by the discussion of two plausible solutions for alleviating the dramatic loss of mixing efficiency induced by the viscoplastic fluid behavior.