Numerical Simulation of the Motion and Deformation of Red Blood Cells and Vesicles in Microfluidic Flows

  • We study the mathematical modeling and numerical simulation of the motion and deformation of red blood cells (RBC) and vesicles subject to an external incompressible flow in a microchannel. RBC and vesicles are viscoelastic bodies consisting of a deformable elastic membrane enclosing an incompressible fluid. We provide an extension of the Finite Element Immersed Boundary Method based on a model for the membrane that additionally accounts for bending energy and also consider inflow/outflow conditions for the external fluid flow. The stability analysis requires both the approximation of the membrane by cubic splines (instead of linear splines without bending energy) and an upper bound on the inflow velocity. In the fully discrete case, the resulting CFL-type condition on the time step size is also more restrictive. We perform numerical simulations for various scenarios including the tank treading motion of vesicles in microchannels, the behavior of 'healthy' and 'sick' RBC which differWe study the mathematical modeling and numerical simulation of the motion and deformation of red blood cells (RBC) and vesicles subject to an external incompressible flow in a microchannel. RBC and vesicles are viscoelastic bodies consisting of a deformable elastic membrane enclosing an incompressible fluid. We provide an extension of the Finite Element Immersed Boundary Method based on a model for the membrane that additionally accounts for bending energy and also consider inflow/outflow conditions for the external fluid flow. The stability analysis requires both the approximation of the membrane by cubic splines (instead of linear splines without bending energy) and an upper bound on the inflow velocity. In the fully discrete case, the resulting CFL-type condition on the time step size is also more restrictive. We perform numerical simulations for various scenarios including the tank treading motion of vesicles in microchannels, the behavior of 'healthy' and 'sick' RBC which differ by their stiffness, and the motion of RBC through thin capillaries. The simulation results are in very good agreement with experimentally available data.show moreshow less

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Metadaten
Author:Thomas FrankeGND, Ronald H. W. HoppeGND, Christopher LinsenmannGND, Lothar Schmid, Carina Willbold, Achim WixforthORCiDGND
URN:urn:nbn:de:bvb:384-opus4-5359
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/677
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2010-09)
Type:Preprint
Language:English
Publishing Institution:Universität Augsburg
Contributing Corporation:University of Houston
Release Date:2010/06/17
Tag:finite element immersed boundary method; microfluidic flows; red blood cells; vesicles
GND-Keyword:Strömungsmechanik; Mathematische Modellierung; Numerische Strömungssimulation; Finite-Elemente-Methode; Retikulozyt; Mikrofluidik
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Physik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Numerische Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Physik / Lehrstuhl für Experimentalphysik I
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):Deutsches Urheberrecht mit Print on Demand