Continuum Scale Non Newtonian Particle Transport Model for Hæmorheology

Torsten Schenkel and Ian Halliday
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Torsten Schenkel: Department of Engineering and Mathematics, Sheffield Hallam University, Sheffield S1 1WB, UK
Ian Halliday: Department of Infection, Immunity and Cardiovascular Disease, University of Sheffield, Sheffield S10 2RX, UK

Mathematics, 2021, vol. 9, issue 17, 1-19

Abstract: We present a continuum scale particle transport model for red blood cells following collision arguments, in a diffusive flux formulation. The model is implemented in FOAM, in a framework suitable for haemodynamics simulations and adapted to multi-scaling. Specifically, the framework we present is able to ingest transport coefficient models to be derived, prospectively, from complimentary but independent meso-scale simulations. For present purposes, we consider modern semi-mechanistic rheology models, which we implement and test as proxies for such data. The model is verified against a known analytical solution and shows excellent agreement for high quality meshes and good agreement for typical meshes as used in vascular flow simulations. Simulation results for different size and time scales show that migration of red blood cells does occur on physiologically relevany timescales on small vessels below 1 mm and that the haematocrit concentration modulates the non-Newtonian viscosity. This model forms part of a multi-scale approach to haemorheology and model parameters will be derived from meso-scale simulations using multi-component Lattice Boltzmann methods. The code, haemoFoam, is made available for interested researchers.

Keywords: haemorheology; blood flow modelling; particle transport; numerical fluid mechanics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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