The mechanics of blood flow in microvessels and microvessel permeability are reviewed. In the first part, characteristics of blood flow in vivo and in vitro are described from a fluid-mechanical point of view, and mathematical models for blood flow in microvessels are presented. Possible causes of the increased flow resistance obtained in vivo compared to in vitro are examined, including the effects of irregularities of vessel lumen, the presence of endothelial surface glycocalyx and white blood cells. In the second part, the ultrastructural pathways and mechanisms whereby endothelial cells and the clefts between the cells modulate microvessel permeability to water and solutes are introduced. Previous and current models for microvessel permeability to water and solutes are reviewed. These models examine the role of structural components of interendothelial cleft, such as junction strands and surface glycocalyx, in the determination of water and solute transport across the microvessel walls. Transport models in the tissue space surrounding the microvessel are also described.

The inertial migration of neutrally buoyant spherical particles in square channel flows was investigated experimentally in the range of Reynolds numbers (Re) from 100 to 1200. The observation of particle positions at several cross-sections downstream from the channel entrance revealed unique patterns of particle distribution which reflects the presence of eight equilibrium positions in the cross-section, located at the centres of the channel faces and at the corners, except for low Re. At Re smaller than approximately 250, equilibrium positions at the corners are absent. The corner equilibrium positions were found to arise initially in the band formed along the channel face, followed by a progressive shift almost parallel to the side wall up to the diagonal line with increasing Re. Further increase in Re moves the corner equilibrium positions slightly toward the channel corner, whereas the equilibrium positions at the channel face centres are shifted toward the channel centre. As the observation sites become downstream, the particles were found to be more focused near the equilibrium positions keeping their positions almost unchanged. These lateral migration behaviours and focusing properties of particles in square channels are different to that observed in microchannels at lower Re and to what would be expected from extrapolating from the results for circular pipes at comparable Re.

The lateral migration properties of a rigid spherical particle suspended in a pressure-driven flow through channels with square cross-sections were investigated numerically, in the range of Reynolds numbers (Re) from 20 to 1000. The flow field around the particle was computed by the immersed boundary method to calculate the lateral forces exerted on the particle and its trajectories, starting from various initial positions. The numerical simulation showed that eight equilibrium positions of the particle are present at the centres of the channel faces and near the corners of the channel cross-section. The equilibrium positions at the centres of the channel faces are always stable, whereas the equilibrium positions at the corners are unstable until Re exceeds a certain critical value, Re c . At Re ≈ Re c , additional equilibrium positions appear on a heteroclinic orbit that joins the channel face and corner equilibrium positions, and the lateral forces along the heteroclinic orbit are very small. As Re increases, the channel face equilibrium positions are shifted towards the channel wall at first, and then shifted away from the channel wall. The channel corner equilibrium positions exhibit a monotonic shift towards the channel corner with increasing Re. Migration behaviours of the particle in the cross-section are also predicted for various values of Re. These numerical results account for the experimental observations of particle distributions in the cross-section of micro and millimetre scale channels, including the characteristic alignment and focusing of the particles, the absence of the corner equilibrium positions at low Re and the progressive shift of the equilibrium positions with Re.

The motion of a rigid ellipsoidal particle freely suspended in a Poiseuille flow of an incompressible Newtonian fluid through a narrow tube is studied numerically in the zero-Reynolds-number limit. It is assumed that the effect of inertia forces on the motion of the particle and the fluid can be neglected and that no forces or torques act on the particle. The Stokes equation is solved by a finite element method for various positions and orientations of the particle to yield the instantaneous velocity of the particle as well as the flow field around it, and the particle trajectories are determined for different initial configurations. A prolate spheroid is found to either tumble or oscillate in rotation, depending on the particle–tube size ratio, the axis ratio of the particle, and the initial conditions. A large oblate spheroid may approach asymptotically a steady, stable configuration, at which it is located close to the tube centreline, with its major axis slightly tilted from the undisturbed flow direction. The motion of non-axisymmetric ellipsoids is also illustrated and discussed with emphasis on the effect of the particle shape and size.

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