The current work investigates the effect of blood viscoelasticity on the stress, velocity and haematocrit fields as well as the formation of the cell-depletion-layer for haemodynamics in microvessels lined with a glycocalyx layer. To this end, we advance the inhomogeneous constitutive model proposed by Moyers Gonzalez-Owens-Fang (2015), treating properly the shear induced RBC migration mechanism and incorporating the effect of plasma viscoelasticity. The enhanced model (en-model) can accurately reproduce the experimental data by Damiano-Long-Smith (2004) and provide reasonable predictions for the RBC distribution and the shear-stress along the luminal surface.
It is shown that blood viscoelasticity expressed in terms of the Deborah number is quite small (O(0.3)), but plays a crucial role in the formation of the cell-depletion-layer. In particular, there is a critical value of Deborah number above which the formation of the cell-depletion-layer occurs.