Abstract
This short communication will establish a reasonably robust procedure to evaluate each of the parameters required in non-Newtonian constitutive relationships for human blood, viz. Cross, Carrau-Yasuda and modifications to Oswald-de Waele and Sisko fluids. For each of the rheological models presented herein the free parameter set to is optimally fitted to a compilation of digitized experimental data evident in the literature. It is shown that for three of the models to conserve structural identification the so-called low shear viscosity term should be set. The method presented herein is shown to minimize the square of the errors between the four suggested constitute relationships and empirical data. It is shown that, for the data set investigated here, parameters which had previously been assumed to be fluid properties exhibit different values depending on the selection of the constitutive relationship.
Highlights
Blood is a suspension of various solid cells in a liquid plasma, formed from a solution of proteins and minerals
In most of the cases investigated, the optimization routine reported that either an optimum solution was found or that a solution was obtained to acceptable accuracy
Good agreement is demonstrated with respect to values obtained from the Cross and Carreau-Yasuda constitutive relationships and those reported in the literature
Summary
Blood is a suspension of various solid cells in a liquid plasma, formed from a solution of proteins and minerals. The rheological properties of blood are influenced by individual characteristics of these components as well as factors such as haematocrit, amongst others [1,2]. Whilst plasma itself is a Newtonian fluid, addition of the blood cellular components alters its rheological behaviour towards a shear-thinning non-Newtonian fluid [1,2]. No single rheological model can capture all aspects of this complex fluid, and as such particular aspects can be modelled individually [2,3]. To this end, differing rheological models are applied when predicting flow characteristics depending on area of the circulatory system of interest. Blood is often approximated to a Newtonian fluid in arterial flows, though has been commonly modelled using the Cross [4,5,6,7] and Carreau-Yasuda [5,6,7,8,9,10,11] models; their constitutive relationships being defined respectively by: Φ (γ )
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