Abstract
Shear stress on blood cells and platelets transported in a turbulent flow dictates the fate and biological activity of these cells. We present a theoretical link between energy dissipation in turbulent flows to the shear stress that cells experience and show that for the case of physiological turbulent blood flow: (a) the Newtonian assumption is valid, (b) turbulent eddies are universal for the most complex of blood flow problems, and (c) shear stress distribution on turbulent blood flows is possibly universal. Further we resolve a long standing inconsistency in hemolysis between laminar and turbulent flow using the theoretical framework. This work demonstrates that energy dissipation as opposed to bulk shear stress in laminar or turbulent blood flow dictates local mechanical environment of blood cells and platelets universally.
Highlights
Turbulence is ubiquitous, and is prominent in engineered cardiovascular devices as well as pathophysiological blood flow
Do the universality properties of turbulence hold in the most complex of blood flows considering Newtonian and nonNewtonian properties of blood? If so, will the distribution of shear stress acting on blood cells and platelets be universal? Here the term ‘‘universal’’ is used not to imply homogeneous isotropic turbulence (HIT), but rather loosely to emphasize the significant agreement between the distributions of instantaneous dissipative scales in complex in-homogeneous shear flows with the distributions observed in HIT as well as the robust presence of inertial range scaling[18,19,20,21]
The reconciliation that we offer through equation 4 is that it is not the Reynolds stress itself, but the product of the Reynolds stress and the local strain rate that determines the energy passed on to the cascade and the total energy dissipation rate, which as we have shown should set the viscous shear stress acting on blood cell membranes
Summary
Turbulence is ubiquitous, and is prominent in engineered cardiovascular devices as well as pathophysiological blood flow. The complex spatio-temporal fluctuations of shear stress leads to hemolysis and platelet activation [11,12]. A strong requirement of a physical theory is that it should make a link, in a manner independent of laminar and turbulent regimes of flow because the pertinent parameter is flow at the length scale of individual cells, where it is considered laminar. Another aspect that is important to consider is the notion of universality of turbulent structures despite the intermittency issue [6]. Do the universality properties of turbulence hold in the most complex of blood flows considering Newtonian and nonNewtonian properties of blood? If so, will the distribution of shear stress acting on blood cells and platelets be universal? Here the term ‘‘universal’’ is used not to imply homogeneous isotropic turbulence (HIT), but rather loosely to emphasize the significant agreement between the distributions of instantaneous dissipative scales in complex in-homogeneous shear flows with the distributions observed in HIT as well as the robust presence of inertial range scaling[18,19,20,21]
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