A New Approach to Model Confined Suspensions Flows in Complex Networks: Application to Blood Flow

The modeling of blood flows confined in micro-channels or micro-capillary beds depends on the interactions between the cell-phase, plasma and the complex geometry of the network. In the case of capillaries or channels having a high aspect ratio (their longitudinal size is much larger than their transverse one), this modeling is much simplified from the use of a continuous description of fluid viscosity as previously proposed in the literature. Phase separation or plasma skimming effect is a supplementary mechanism responsible for the relative distribution of the red blood cell's volume density in each branch of a given bifurcation. Different models have already been proposed to connect this effect to the various hydrodynamics and geometrical parameters at each bifurcation. We discuss the advantages and drawbacks of these models and compare them to an alternative approach for modeling phase distribution in complex channels networks. The main novelty of this new formulation is to show that albeit all the previous approaches seek for a local origin of the phase segregation phenomenon, it can arise from a global non-local and nonlinear structuration of the flow inside the network. This new approach describes how elementary conservation laws are sufficient principles (rather than the complex parametric models previously proposed) to provide non local phase separation. Spatial variations of the hematocrit field thus result from the topological complexity of the network as well as nonlinearities arising from solving a new free boundary problem associated with the flux and mass conservation. This network model approach could apply to model blood flow distribution either on artificial micro-models, micro-fluidic networks, or realistic reconstruction of biological micro-vascular networks.