Striation Thickness Distribution in Split-and-Recombine Mixers in the Stokes Regime

Abstract Slipt-and-recombine (SR) mixers typically operate in the Stokes flow regimes. Numerical and experimental studies have shown that a non-homogeneous distribution of the mixing scales is observed due to the difficulty of ensuring plug flow with viscous liquids. The parabolic velocity profile generated in the duct promotes the formation of larger mixing scales next to the walls and smaller scales in the centre of the duct. The mixing efficiency controlled by diffusion at the molecular scale depends on the non-ideal striation thickness decay. In this work, a simple model to estimate the distribution of mixing length scales in a SR mixer is proposed and compared to Computational Fluid Dynamics simulations. It is shown that the striation thickness of the largest scales in the flow decays at half the rate of an idealised baker's transformation, and that an SR mixer must be 1.81 times longer than an ideal one to achieve complete mixedness. The intensity of segregation is calculated for the largest mixing scales and set as an industrial design criterion for SR mixers. The main novelty of this work is the introduction of a new model to describe the non-homogeneous distribution of mixing scales in SR mixers.