9. Fluid Mechanics

This chapter provides an overview of fluid mechanics, emphasizing applications in models of blood flow. It begins with the physics of fluid motion, including the concepts of viscosity and idealized Newtonian fluids, before proceeding to the Navier Stokes equations for incompressible fluids. The concepts of laminar and non-laminar flow are also introduced, including Reynolds number and turbulent flow. Finally, the chapter describes techniques for modelling blood flow, including the use of Windkessel models (hydraulic circuit equivalents) that can be incorporated as boundary conditions in finite element models of blood flow, as well as non-Newtonian aspects of blood flow, which may be of relevance at low blood shear rates or small vessel diameters. Detailed examples of models solved in COMSOL include laminar flow in a circular tube, a multiphysics model of drug delivery in a coronary stent, aortic blood flow, as well as model of axial streaming of a blood cell using COMSOL’s moving mesh interface. The chapter ends with a small set of theoretical and computational COMSOL problems, with fully-worked answers provided in the solution section of the text.