ALBERT

Description: An approach is presented that uses velocimetry data to estimate accurately the spatial distribution of viscosity in steady laminar parallel flows of incompressible linearly viscous fluids. The approach is generally applicable to Newtonian fluids with spatially varying viscosity or to particle-suspension flows where a non-uniform distribution of the particles contributes to spatial variations in the local effective viscosity of the suspension. Emphasis is placed on the application of these methods to steady axisymmetric blood flow in cylindrical glass capillary tubes and microvessels. In this context, the spatial variations in viscosity over the vessel cross-section are predicted where it is assumed that the rheological properties associated with a heterogeneous red blood cell suspension can be well approximated by a continuous generalized linearly viscous fluid having a spatially non-uniform viscosity. For such a fluid, an expression for the viscosity profile over the vessel cross-section is derived that satisfies the conservation principles of mass and momentum and depends upon the a priori determined velocity distribution, which is extracted from fluorescent micro-particle image velocimetry data obtained from microvessels in vivo. These profiles provide useful information about dynamic, kinematic and rheological properties of the flow that include expressions for the axial pressure-gradient component, the local shear stress distribution, and the relative apparent viscosity. In microvessels, the effect of the glycocalyx surface layer on the vessel wall is also accounted for in the analysis by modelling the layer as a uniformly thick porous medium. Velocimetry data are presented from in vivo measurements made in venules after the application of a light-dye treatment to degrade the glycocalyx. Results reveal that these methods are sufficiently sensitive to detect a reduction in glycocalyx thickness of ∼0.3 μm, which represents a fractional decrease in thickness of ∼60-70% when compared with results from a separately published data set obtained from venules having an intact glycocalyx. © 2004 Cambridge University Press.

Description: A three-dimensional analysis is presented of the Stokes flow, adjacent to a Brinkman half-space, that is induced or altered by the presence of a sphere in the flow field that (a) translates uniformly without rotating, (b) rotates uniformly without translating, or (c) is fixed in a shear flow that is uniform in the far field. The linear superposition of these three flow regimes is also considered for the special case of the free motion of a neutrally buoyant sphere. Exact solutions to the momentum equations are obtained in terms of infinite series expansions in the Stokes-flow region and in terms of integral transforms in the Brinkman medium. Attention is focused on the approach to the asymptotic limit as the ratio of Newtonian- to Darcy-drag forces vanishes. From the leading-order asymptotic approximations, implicit recursion relations are derived to determine the coefficients in the series solutions such that those solutions exactly satisfy the boundary and interfacial conditions as well as the continuity equations in both the Stokes-flow and Brinkman regions. For each of the three flow regimes considered, results are presented in terms of the drag force on the sphere and torque about the sphere centre as a function of the dimensionless separation distance between the sphere and the interfacial plane for several small values of the dimensionless hydraulic permeability of the Brinkman medium. Finally, the free motion of a neutrally buoyant sphere is found by requiring that the net hydrodynamic drag force and torque acting on the sphere vanish. Results for this case are presented in terms of the dimensionless translational and rotational speeds of the sphere as a function of the dimensionless separation distance for several small values of the dimensionless hydraulic permeability. The work is motivated by its potential application as an analytical tool in the study of near-wall microfluidics in the vicinity of the glycocalyx surface layer on vascular endothelium and in microelectromechanical systems devices where charged macromolecules may become adsorbed to microchannel walls. © 2004 Cambridge University Press.