Numerical simulation of the motion of red blood cells and vesicles in microfluidic flows

• Published in: Computing and visualization in science Vol. 14; no. 4; pp. 167 - 180
• Main Authors: Franke, Thomas, Hoppe, Ronald H. W., Linsenmann, Christopher, Schmid, Lothar, Willbold, Carina, Wixforth, Achim
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.04.2011; Springer
• Subjects: Algorithms; Applied fluid mechanics; Biological and medical sciences; Calculus of Variations and Optimal Control; Optimization; Computational Mathematics and Numerical Analysis; Computer Applications in Chemistry; Exact sciences and technology; Fluid dynamics; Fluidics; Fundamental and applied biological sciences. Psychology; Fundamental areas of phenomenology (including applications); Hemodynamics. Rheology; Mathematics; Mathematics and Statistics; Multiphase and particle-laden flows; Nonhomogeneous flows; Numerical Analysis; Physics; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Vertebrates: cardiovascular system; Visualization; CFL-type condition; Vesicles; Stability analysis; Red blood cells; Finite element immersed boundary method; Microfluidic flows; Viscoelasticity; Pipe flow; Precision engineering; Inlet flow; Modeling; Spline approximation; Finite element method; Membrane; Stiffness; Microfluid; Outlet flow; External flow; Large pipe; Red blood cell; Capsule; Particle suspension; Immersed boundary method; Cubic spline; Incompressible flow; Upper bound; Internal fluid; Incompressible fluid; Microfluidics; Fluidics
• ISSN: 1432-9360; 1433-0369
• DOI: 10.1007/s00791-012-0172-1

We study the mathematical modeling and numerical simulation of the motion 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 by Boffi and Gastaldi (Comput Struct 81:491–501, 2003 ), Boffi et al. (Math Mod Meth Appl Sci 17:1479–1505, 2007 ), Boffi et al. (Comput Struct 85:775–783, 2007 ) 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.