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A CFD Digital Twin to Understand Miscible Fluid Blending

Abstract

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 algorithms with graphics card-based computing hardware to build accelerated digital twins of a physical mixing tanks. The digital twins are designed to predict real-time fluid mechanics with a fidelity that rivals experimental characterization at orders-of-magnitude less cost than physical testing. After validating the twins against measured single- and multi-fluid mixing data, we use them to explore the physics governing fluid blending in stratified two-fluid systems. We use output from the twins to provide general guidance on stratified two-fluid mixing processes, as well as guidance for building such models for other types of physical systems.

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References

  1. 1.

    (2019) Retrieved August 6, 2020, from M-Star CFD: http://mstarcfd.com

  2. 2.

    (2020)Retrieved August 6, 2020, from Amazon EC2 P3 Instances: https://aws.amazon.com/ec2/instance-types/p3/

  3. 3.

    Benchabane A, Bekkour K. Rheological properties of carboxymethyl cellulose (CMC) solutions. Colloid Polym Sci. 2008;286(10):1173–80.

    CAS  Article  Google Scholar 

  4. 4.

    Derksen JJ. Blending of miscible liquids with different densities starting from a stratified state. Comput Fluids. 2011;50(1):35–45.

    Article  Google Scholar 

  5. 5.

    Doran, P. M. (2013). Mixing. In Bioprocess Engineering Principles (2nd ed., pp. 255-332). London: Academic Press.

  6. 6.

    Gerhardt A, M. N. Protein aggregation and particle formation in prefilled glass syringes 2014; 103(6), 1601-1612.

  7. 7.

    Gikanga B, Chen Y, Stauch OB, Maa YF. Mixing monoclonal antibody formulations using bottom-mounted mixers: impact of mechanism and design on drug product quality. PDA J Pharm Sci Technol. 2015;69(2):284–96.

    CAS  Article  Google Scholar 

  8. 8.

    Guo, Z., & Shu, C. (2013). Lattice Boltzmann method and its applications in engineering (Vol. 3). World Scientific.

  9. 9.

    HE Vd. Lattice Boltzmann simulations for multi-scale chemical engineering 2018; 21(67-75).

  10. 10.

    Jameel, F., Czyzewski, A. M., Zhu, T., Sinha, K., & Nere, N. K. (2020). Development and scale-up of the mixing process for biopharmaceuticals. In Development of Biopharmaceutical Drug-Device Products (pp. 539-565). Springer.

  11. 11.

    Jun AH. Coefficient of variation. In Encyclopedia of Research Design 2010; (pp. 169-171).

  12. 12.

    Krüger T, Kusumaatmaja H, Kuzmin A, Shardt O, Silva G, Viggen EM. The lattice Boltzmann method. Springer International Publishing. 2017;10(978-3):4–15.

    Google Scholar 

  13. 13.

    Ma Z. Impeller power draw across the full Reynolds number spectrum. MS Thesis: University of Dayton; 2014.

    Google Scholar 

  14. 14.

    Mahler HC, M. R.. Induction and analysis of aggregates in a liquid IgG1-antibody formulation. 2005; 59((3)), 407-17.

  15. 15.

    Mohamad AA. Lattice Boltzmann method: fundamentals and engineering applications with computer codes. 2nd ed. London: Springer; 2019.

    Book  Google Scholar 

  16. 16.

    Nere NK, Patwardhan AW, Joshi JB. Liquid-phase mixing in stirred vessels: turbulent flow regime. Ind Eng Chem Res. 2003;42(12):2661–98.

  17. 17.

    Paul EL, Atiemo-Obeng VA, Kresta SM. Handbook of industrial mixing: science and practice: John Wiley & Sons; 2004.

  18. 18.

    Söderberg R, Wärmefjord K, Carlson JS, Lindkvist L. Toward a digital twin for real-time geometry assurance in individualized production. CIRP Ann. 2017;66(1):137–40.

    Article  Google Scholar 

  19. 19.

    Strand A. Investigation of blend time for turbulent Newtonian fluids in stirred tanks. Rochester Institute of Technology: MS Thesis; 2017.

    Google Scholar 

  20. 20.

    Succi S. The lattice Boltzmann equation: for fluid dynamics and beyond: Oxford University Press; 2001.

  21. 21.

    Sukop M, Thorne DT. Lattice Boltzmann modeling: Springer; 2006.

  22. 22.

    van Driest ER. On Turbulent Flow Near a Wall. 1956;23:1007–11.

    Google Scholar 

  23. 23.

    Van Leer B. Towards the ultimate conservative difference scheme III. Upstream-centered finite-difference schemes for ideal compressible flow. J Comput Phys. 1977;23(3):263–75.

    Article  Google Scholar 

  24. 24.

    Verzicco R, F. M. (2004). Flow in an impeller-stirred tank using an immersed-boundary method. 50(6). Retrieved from www.mstarcfd.com

  25. 25.

    Yang SS. GPU-accelerated large eddy simulation of stirred tanks. 2018; 181, 132-145.

  26. 26.

    Yu H, Girimaji SS, Luo L-S. Lattice Boltzmann simulations of decaying homogeneous isotropic turbulence. Phys Rev E. 2005;71(1):016708.

    Article  Google Scholar 

  27. 27.

    Yu Z, Finch BA, Hale DA. Mixing of stratified miscible liquids in an unbaffled tank with application in high concentration protein drug product manufacturing. Ind Eng Chem Res. 2018;57(9):3397–409.

    CAS  Article  Google Scholar 

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Correspondence to Nandkishor K. Nere.

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Thomas, J., Sinha, K., Shivkumar, G. et al. A CFD Digital Twin to Understand Miscible Fluid Blending. AAPS PharmSciTech 22, 91 (2021). https://doi.org/10.1208/s12249-021-01972-5

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KEY WORDS

  • miscible fluid mixing
  • computational fluid dynamics
  • lattice Boltzmann methods
  • digital twin
  • biopharmaceutical manufacturing