AXISYMMETRICAL PRESSURE-DRIVEN FLOW OF RIGID PELLETS THROUGH A CYLINDRICAL TUBE LINED WITH A DEFORMABLE POROUS WALL LAYER

A closed-form analytic solution for the motion of axisymmetric rigid p ellets suspended in a Newtonian fluid and driven under a pressure grad ient through a rigid impermeable cylindrical tube lined with a porous deformable biphasic wall layer is derived using mixture and lubricatio n theories. The analysis details the velocity distributions in the lub rication and wall layers as well as the solid-phase displacement field in the wall layer. Expressions for the shear stress and pressure grad ient are obtained throughout the lubrication and wall layers. Results are presented in terms of resistance, volume flow, and driving pressur e relative to smooth-walled tubes for cases both with and without rigi d spheres flowing in the free lumen. The analysis is motivated by its possible relevance to the rheology of blood in the microcirculation wh erein the endothelial-cell glycocalyx - a carbohydrate-rich coat of ma cromolecules consisting of proteoglycans and glycoproteins expressed o n the luminal surface of the capillary wall - might exhibit similar be haviour to the wall layer modelled here. Estimates of the permeability of the glycocalyx are taken from experimental data for fibrinogen gel s formed in vitro. In a tube without pellets lined with a porous wall layer having a thickness which is 15% of the tube radius and having a permeability in the range of fibrinogen gels, approximately a 70% grea ter pressure drop is required to achieve the same volume flow as would occur in an equivalent smooth-walled tube without a wall layer. If, i n the presence of this same wall layer, a rigid spherical pellet is in troduced which is 99.5% of the free-lumen radius, the apparent viscosi ty increases by as much as a factor of four with a concomitant reducti on in tube hematocrit of about 10% relative to the corresponding value s in an equivalent smooth-walled tube having the same sphere-to-tube d iameter ratio without a wall layer.