ON THE PULSATING FLOW BEHAVIOR OF A BIOLOGICAL FLUID: HUMAN BLOOD
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Introduction
The pulsatile pressure gradient driven flow of a non-newtonian fluid in a pipe is found in several industrial and biological situations. For example, blood flow in veins, enhanced oil recovery operations, polymer science (extrusion with oscillating dies). In this type of flow scheme, the liquid experiments a pulsating pressure gradient and there is no axial or transversal perturbation. One of the most interesting effects of this scheme is the flow enhancement caused by the pulsatile pressure gradient extra volumetric flow that results when comparing with the case of constant pressure driven flow. This difference can be estimated as a percentage of the difference between the two volumetric flows: the constant pressure volumetric flow and the time averaged pulsatile pressure volumetric flow :
(1)
Several studies have demonstrated that deviation from Newtonian fluid behavior is the main mechanism behind flow enhancement and this enhancement is proportional to the square of the relative amplitude of the oscillating pressure gradient and its magnitude depends on the shape of the viscosity function.
In particular, one of the most important biological fluids is human blood which is forced by a periodic pressure gradient through the human body.1From a rheological point of view, whole blood (plasma and cells) is a complex non-Newtonian fluid, and the main explanation for its complex behavior (viscoelasticity, shear-thinning, thixotropy) is to be found in the capability of aggregation, disaggregation, deformation, orientation and migration of the erythrocytes.2
Results and Discussions
Figure 1 shows the results of the model predictions in terms of the dimensionless fluidity versus the dimensional wall stress for different values of the dimensionless B number, which relates the zero shear rate viscosity to the infinity viscosity. Curves a, b correspond to the case of a shear thinning fluid with the infinite shear viscosity having a lower value than the zero shear rate viscosity and thus B>1.
Figure 1.Pulsatile dimensionless fluidity as a function of the dimensionless wall stress for different shear thinning conditions.
The case of curve c corresponds to the Newtonian case with constant viscosity over the whole shear rate interval (B=1), and curves d,e correspond to the shear thickening fluid case (B<1). The effect of the pulse can be observed in the intermediate shear region with curves a,b attaining a maximum fluidity value, and curves b,e attaining a minimum fluidity value. The Newtonian case is unaffected by the pulse as well as the Newtonian part of the curves of the shear thickening and shear thinning fluids. In the case of the shear thinning fluids (a,b) the effect of the pulse is to increase the fluidity of the system over the fluidity that the system would have with no pulse.
Conclusions
In this work a perturbation solution to a pulsating pressure gradient flow of a biological fluid using the BMP constitutive equation is analyzed for a general class of pressure gradient noises. The liquid was characterized by the BMP model. A necessary condition to obtain a fluidity enhancement in a structured fluid is that the fluid experiments transitions from a high structured state to a less structure one induced by flow
References
1. Moreno L, Calderas F, Sanchez-Olivares G, Medina-Torres L, Sanchez-Solis A, Manero O. Korea-Aust Rheol J 2015, 27, 1-10..
2. Moyers-Gonzalez M.A., R.G. Owens, and J. Fang, J. Fluid Mech 2008 617, 327-354.