Effects of coupling of mass transport and blood viscosity models for microchannel flows

Abstract

In this study, various aspects of a continuum transport model for blood, which is treated as a suspension of red blood cells, are thoroughly investigated. Earlier, treating blood as a suspension of rigid spherical particles in plasma was reasonably successful in mimicking flow dynamics in microchannels of size 40 μ m , comparable to 4 μ m , the dimension of a red blood cell (RBC). However, it is still not entirely clear whether such success owes to the coupling of mass and momentum transport, or to a sophisticated viscosity model for blood. To understand this in detail, we obtain semi-analytical solutions to the continuum model, in the presence and absence of the coupling of mass transport of RBCs, that connects the hematocrit concentration to the local viscosity, for fully developed blood flow in circular and rectangular microchannels. In this study, the transport of RBCs in flowing fluid is modeled by the diffusive flux model (DFM). Thus, overall, we have a hierarchy of continuum models using various viscosity models for blood, with progressive inclusion of physical complexities. Our results clearly highlight the importance of such a coupled approach, without which the results are quantitatively, and sometimes even qualitatively, different. In addition, our study serves as a thorough comparison of different viscosity models for blood, especially the steady state and transient models, recently proposed by Apostolidis and Beris (2014) and Apostolidis et al. (2015), respectively. We observe that, though the transient model reduces exactly to the description by the steady model over a range of low to moderate shear rates, the transient model shows some differences, especially for the RBC concentration in the low shear rate region. In the semi-analytical framework, the Darcy friction factor and cell free layer thickness have also been computed for circular cross-sections and a range of aspect ratios of a rectangular microchannel. Our results also indicate that the cell free layer attains a constant thickness when the aspect ratio of a rectangular microchannel reaches a critical maximum value for a specified average hematocrit. • Rectangular microchannel flow is investigated by coupling with the transport of RBC. • Even a finely tuned viscosity model without RBC transport is shown to be inadequate. • Frictional characteristics are derived in the form of a semi-analytical solution. • The model is found to predict the cell free layer thickness quite well. • The steady viscosity model overpredicts WSS when compared to the transient model.