Numerical modelling and mathematical modelling of two-phase blood flow

Abstract

The study of two-phase blood flow through numerical and mathematical modeling has emerged as a crucial approach for understanding the complex behavior of blood, a non-Newtonian fluid comprising plasma and various cellular components, primarily red blood cells. This research aims to develop comprehensive models that capture the dynamics between these two distinct phases—fluid (plasma) and particulate (cells)—within the circulatory system. Mathematical modeling provides a framework for formulating the governing equations based on principles of fluid dynamics, mass conservation, and momentum transfer. These equations account for factors such as viscosity, density variations, interfacial interactions, and shear-thinning behavior. Numerical methods, including finite difference, finite element, and lattice Boltzmann techniques, are employed to simulate blood flow in various geometries representing arterial and microvascular networks. The models aid in predicting flow characteristics such as velocity profiles, pressure gradients, and hematocrit distribution under both physiological and pathological conditions. This dual-phase modeling enables the investigation of complex phenomena like cell aggregation, plasma skimming, and flow separation in stenosed or bifurcated vessels. The insights gained are instrumental in enhancing the understanding of cardiovascular health, optimizing biomedical device design, and improving clinical diagnostics. The study thus bridges theoretical fluid mechanics with practical applications in hemodynamics and medical research.