2017-06-28
10:15 at HCP F 43.4

A rheological model for blood from nonequilibrium thermodynamics

Ioanna Tsimouri

Department of Chemical Engineering, University of Patras, Greece

Many deaths are the result of cardiovascular diseases associated with unusual blood rheological properties in the circulatory system [1]. Thus, understanding the rheological behavior of blood is paramount in providing insights on the causes of various diseases and the tailor-design of the transport of drug directly to the infected area [1]. Blood is mainly a suspension of elastic particulate cells, among which red blood cells (RBCs) dominate, in plasma, usually considered as a Newtonian fluid. The RBCs are deformable since they consist of an elastic membrane enclosing a hemoglobin solution (also considered a Newtonian fluid) [1,2]. It has been observed than under quiescent conditions, when the shear rate is not high enough (~ 1-5 s^-1) RBCs aggregate, forming column-like structures called rouleaux [1,2,3]. As the shear rate increases, rouleaux break and, after a critical shear rate, eventually only individual RBCs can be observed [1,3]. A constitutive model capable of predicting this dynamical behaviour is the one suggested by Owens and coworkers [4,5] in which each rouleaux is modeled by an elastic dumbbell and their time evolution is described using the Smoluchowski equation which does takes into account the forming and destruction of rouleaux [4]. In the present work, we derive Owens model within the framework of non-equilibrium thermodynamics, particularly using the generalized bracket formalism [6]. We appropriately consider the momentum density, m⁽ⁱ⁾ the number density, n_i, and the conformation tensor C⁽ⁱ⁾ for each rouleaux (including single RBCs) in the vector of state variables. We also suggest proper expressions for both the Poisson and Dissipation brackets and for the system Hamiltonian. Using the generalized bracket formalism, we are then able to reproduce Owens model and confirm its thermodynamic admissibility. Possible drawbacks of Owens model will be highlighted and propositions as to how they may be obviated will be presented.

References

[1] Yilmaz F., Gundogdu M. Y. (2008). Korea- Australia Rheology Journal, Vol. 20, No. 4, 197-211
[2] Pries A. R., Secomb T.W., Gaehtgens P. (1996). Cardiovascular Research, 32, 654-667
[3] Fedosov D. A. (2011). PNAS, Vol. 108, No. 29, 11772–11777
[4] Owens R. G. (2006). J. Non-Newtonian Fluid Mech. 140, 57–70
[5] Moyers-Gonzales M., Owens R. G., Fang J. (2008). J. Fluid Mech., 617, 327–354
[6] Beris A. N., Edwards B. J. ( 1994). Thermodynamics of Flowing Systems with Internal Microstructure, Oxford University Press: New York