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    High-fidelity simulations of two miscible fluids in small-scale turbulent mixers using a variational multiscale finite element method

    Dongjie Jia1,*, Mohammad Majidi1, Kurt D. Ristroph2,3, and Arezoo Ardekani1,†

    • 1School of Mechanical Engineering, Purdue University, West Lafayette, Indiana, USA
    • 2Department of Agricultural and Biological Engineering, Purdue University, West Lafayette, Indiana, USA
    • 3Davidson School of Chemical Engineering, Purdue University, West Lafayette, Indiana, USA

    • *Contact author: jia191@purdue.edu
    • †Contact author: ardekani@purdue.edu

    Phys. Rev. Fluids 11, 014502 – Published 26 January, 2026

    DOI: https://doi.org/10.1103/zxrs-4vy9

    Abstract

    Turbulent mixers have been widely used in industrial settings for chemical production and increasingly for therapeutic nanoparticle formulation by antisolvent precipitation. The quality of the product is closely related to the fluid and mixing dynamics inside the mixers. Due to the rapid timescales and small sizes of many turbulent mixing geometries, computational fluid dynamics simulations have been the primary tool used to predict and understand fluid behavior within these mixers. In this study, we used the residual-based variational multiscale finite element method to perform high-fidelity turbulent simulations on two commonly used turbulent mixers: the multi-inlet vortex mixer (MIVM) and the confined impinging jets mixer (CIJM). We simulated two geometric variations, two inlets and four inlets, of the MIVM and two different inflow ratios of the CIJM. Through detailed turbulence results, we identify differences in turbulence onset, total energy, and mixing performance of the two MIVM configurations. With the CIJM results, we demonstrate the effect of the flow rate ratio on the impingement behavior, and as a result, on the mixing performance and turbulence. The cross-comparison between the two mixers shows key differences in turbulence and mixing behaviors, such as the turbulence onset, the energy decay, and the output mixing index. This study demonstrates the importance of a high-accuracy numerical scheme in simulating the turbulent mixers and understanding the similarities and differences among mixers. Furthermore, the results show a potential for optimizing the operating conditions to achieve the best mixing performance.

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