A constitutive hemorheological model addressing the deformability of red blood cells in Ringer solutions

Abstract

Red blood cells (RBCs) can deform substantially, a feature that allows them to pass through capillaries that are narrower than the diameter of an undeformed RBC. Clearly, to understand how...

Elucidating the rheological implications of adding particles in blood

“…Throughout this work, we consider an isothermal and incompressible flow, meaning that both the total mass density, ρ , and the entropy density (or temperature) are excluded from the vector of state variables. At first, to describe the rheology and microstructure of nanoblood, we follow previous works (Stephanou 2020 , 2021 ; Stephanou and Tsimouri 2020 ) and consider RBCs as emulsions with a droplet morphology by using a constrained contravariant second-rank tensor, , such that det is equal to the squared volume of a RBC. We also define the dimensionless tensor so that .…”

“…At equilibrium, the tensor is equal to where and are the principal semi-axes of the RBC (see Fig. 1 of Stephanou and Tsimouri ( 2020 )), whose determinant is ; thus, (Stephanou 2020 ; Stephanou and Tsimouri 2020 ). If we then consider the typical values = 7.5 μm and 90 μm 3 , we must consider 3.06 μm (Stephanou and Tsimouri 2020 ).…”

“…1 of Stephanou and Tsimouri ( 2020 )), whose determinant is ; thus, (Stephanou 2020 ; Stephanou and Tsimouri 2020 ). If we then consider the typical values = 7.5 μm and 90 μm 3 , we must consider 3.06 μm (Stephanou and Tsimouri 2020 ). The mere use of the conformation tensor allows us to consider the deformability of RBCs but not their aggregation in normal blood, which leads to the exhibition of a yield stress at sufficiently low shear rates as a result of the network formed.…”

“…where is the velocity gradient tensor ( is the transpose of ), + is the rate-of-strain tensor, is the slip/non-affine parameter, is the ith invariant of tensor , for which , such that (see Stephanou and Tsimouri ( 2020 )), with the particle’s aspect ratio, is a numerical constant, and , and are characteristic relaxation times. Here, we consider as the characteristic particle rotational time, where is the particle rotational time at infinite dilution and the particle volume fraction (Stephanou 2018 ), the characteristic relaxation time related to the deformability of RBCs (Stephanou 2020 ), and the characteristic relaxation time for regeneration once the flow field has ceased.…”

“…In this work, we will employ non-equilibrium thermodynamics (NET) to develop a sophisticated mathematical model addressing the rheological behavior of nanoblood. To accomplish this, we will develop the model using the generalized bracket formalism (Beris and Edwards 1994 ) of NET (Beris and Edwards 1994 ; Grmela and Öttinger 1997 ; Öttinger and Grmela 1997 ; Edwards et al 2003 ; Öttinger 2005 ), by means of which several microstructured systems have been addressed up to date, such as, but not limited to, immiscible complex fluids (Edwards and Dressler 2003 ; Dressler and Edwards 2004 ; Dressler et al 2008 ; Grmela et al 2014 ; Mwasame et al 2017 ), polymer melts and solutions (Beris and Edwards 1994 ; Grmela and Öttinger 1997 ; Öttinger and Grmela 1997 ; Öttinger 2005 ; Stephanou et al 2009 , 2016 , 2020b ), polymer nanocomposites (Rajabian et al 2005 ; Eslami et al 2010 ; Stephanou et al 2014 ; Stephanou 2015 ), micellar systems (Germann et al 2013 ; Stephanou et al 2020a ), blood (Tsimouri et al 2018 ; Stephanou 2020 ; Stephanou and Tsimouri 2020 ), drilling fluids (Stephanou 2018 ), and thixotropic fluids (Stephanou and Georgiou 2018 ). The use of a NET formalism has the compelling advantage, over other approaches, that the constitutive model as a whole is guaranteed consistency with the laws of thermodynamics (as extended for beyond equilibrium systems).…”