Seminarium Instytutowego Seminarium Mechaniki im. W. Olszaka i A. Sawczuka

Towards a bottom-up approach of blood flow

Ch. Misbah

poniedziałek, 28 listopada 2011, godz. 10:00, sala Aula (II p.)

Blood is a complex fluid, and is predominantly composed by red blood cells (RBCs) that dictate its rheology. Unlike simple fluids, constitutive laws describing blood flow from a bottom-up approach (i.e. by taking explicitly into account the corpuscular nature of blood in order to extract macroscopic laws) remains to be done. Since the seminal work of Poiseuille (in the 19th century) until the end of the 20th century blood flow has been described by means of phenomenological continuum models that require many assumptions which are difficult both to justify and to validate. Most of the blood flow resistance occurs in the microvasculature (where oxygen is delivered by RBCs to bodily tissues) where it is clear that the corpuscular nature of blood cannot be disregarded, given the fact that the size of RBCs is of the order of that of blood vessels (but this does not exclude the relevance of the corpuscular nature in larger blood vessels, such as arteries and veins). After a general introduction, we present the current state of the art in modeling blood flow, with comparison, when possible, to experiments. Various methods are used to solve these problems, such as analytical perturbative methods, boundary integral formulation (based on the Greens functions techniques), phase-field and level-set approaches, Lattice Boltzmann methods. We shall briefly describe the virtues and drawbacks of each method. We shall present several achievements for a single entity under shear, Poiseuille, and Couette flows. We then describe results for a collection of entities, their interactions, their rheology, their clustering etc.