Viscoelastic capillary flow: the case of whole blood

The dynamics of spontaneous capillary flow of Newtonian fluids is well-known and can be predicted by the Lucas-Washburn-Rideal (LWR) law. However a wide variety of viscoelastic fluids such as alginate, xanthan and blood, does not exhibit the same Newtonian behavior.
In this work we consider the Herschel-Bulkley (HB) rheological model and Navier-Stokes equation to derive a generic expression that predicts the capillary flow of non-Newtonian fluids. The Herschel-Bulkley rheological model encompasses a wide variety of fluids, including the Power-law fluids (also called Ostwald fluids), the Bingham fluids and the Newtonian fluids. It will be shown that the proposed equation reduces to the Lucas-Washburn-Rideal law for Newtonian fluids and to the Weissenberg-Rabinowitsch-Mooney (WRM) law for power-law fluids. Although HB model cannot reduce to Casson’s law, which is often used to model whole blood rheology, HB model can fit the whole blood rheology with the same accuracy.
Our generalized expression for the capillary flow of non-Newtonian fluid was used to accurately fit capillary flow of whole blood. The capillary filling of a cylindrical microchannel by whole blood was monitored. The blood first exhibited a Newtonian behavior, then after 7 cm low shear stress and rouleaux formation made LWR fails to fit the data: the blood could not be considered as Newtonian anymore. This non-Newtonian behavior was successfully fit by the proposed equation.