Flow of axisymmetric red blood cells in narrow capillaries

Abstract

Flow of red blood cells along narrow cylindrical vessels, with inside diameters up to 8 μm, is modelled theoretically. Axisymmetric cell shapes are assumed, and lubrication theory is used to describe the flow of the suspending fluid in the gaps between the cells and the vessel wall. The models take into account the elastic properties of the red blood cell membrane, including its responses to shear and bending. At moderate or high cell velocities, about 1 mm/s or more, the membrane stress may be approximated by an isotropic tension which is maximal at the nose of the cell and falls to zero at the rear. Cell shape and apparent viscosity are then independent of flow rate. At lower flow velocities, membrane shear and bending stresses become increasingly important, and models are developed to take these into account. Apparent viscosity is shown to increase with decreasing flow rate, in agreement with previous experimental and theoretical studies.

Microviscometry reveals reduced blood viscosity and altered shear rate and shear stress profiles in microvessels after hemodilution

“…Nevertheless, no method has been developed for either quantitatively predicting or measuring the salient dynamic, kinematic, and rheological properties of microvascular blood flow in vivo other than in the single-file flow regime within capillaries of 5-8 m in diameter (4)(5)(6)(7). All attempts at analyzing microvascular blood-flow properties in microvessels above the capillary range have depended on knowledge of quantities, such as the axial pressure gradient within the vessel and the red-cell concentration of blood discharged by the vessel, which are essentially unknown in these vessels (2,3,8,9).…”

Large deformation of red blood cell ghosts in a simple shear flow

“…The simulations become unstable when local radii of curvature become small and the membrane appears to begin to buckle or fold. Secomb et al 13 have obtained steady-state axisymmetric shapes with cusps having neglected the bending stiffness of the RBC membrane. Although the bending stiffness of the RBC is small, k c =10 −12 erg, 34 it is necessary to smooth out the deformations and prevent buckling.…”

“…Zarda et al 12 used a membrane model with a finite dilation modulus and resistance to bending stresses, and simulated axisymmetric flow through capillaries using the finite element method. A membrane model that treats the membrane as locally area conserving but neglects bending resistance was used by Secomb et al 13 Simulations with this model can result in shapes with cusps at the trailing edge of the RBC due to the lack of bending resistance. Nonaxisymmetric geometry of nondeformable RBCs in capillaries has also been considered.…”

Fluid–body interactions: clashing, skimming, bouncing

“…The industrial applications are manifold including in particular ship slamming, sloshing and granular flows on chutes [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. There is also a huge number of biomedical applications [21][22][23][24][25][26][27][28][29][30][31], while sports applications are such as in skeleton bobsleigh. The work is on fluid-body interaction [32].…”