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The mixing of stratified miscible fluids with widely different material properties is a common step in biopharmaceutical manufacturing processes. Differences between the fluid densities and viscosities, however, can lead to order-of-magnitude increase in blend times relative to the blending of single-fluid systems. Moreover, the mixing performance in two-fluid systems can be strongly dependent on the Richardson number defined as the ratio of fluid buoyancy to fluid inertia. In this work, we combine lattice Boltzmann transport algorithm