MODELING THE LOWER AND THE UPPER REGIME OF THE BLOOD UNIDIRECTIONAL FLOW IN MICRO-VESSELS

Autores

  • Gesse Arantes de Roure Neto UnB
  • Francisco Ricardo da Cunha UnB

DOI:

https://doi.org/10.26512/ripe.v2i12.21350

Palavras-chave:

Blood. Hydrodynamic diffusion. Non-Newtonian. Rheology. Cell-depleted layer.

Resumo

There is a formation of a cell-depleted layer adjacent to micro-vessel walls during blood flow in regime of creeping flow. This biological layer is of vital importance in the transport of oxygen-saturated red cells to the unsaturated tissues. In this work, we first discuss the physical mechanisms in this creeping flow which lead to the formation of a cell-depleted layer. The main non-dimensional physical parameter governing the layer formation are presented from a simple model of predicting the layer thickness in steady state. In particular, we study the blood flow in two different scales (i.e. lower and upper bound limit) of the in vitromicrocirculation. For this end we examine the capillary core flow solution in which the inner ï¬‚uid is considered a non-Newtonian one facing a small annular gap of a Newtonian plasma. This model is a good approximation for the blood flow occurring in the length scales of venules and arterioles diameters. In addition, we also propose a model for smaller vessels, like capillaries with diameter of few micrometers. In this lower bound limit we consider a periodic configuration of lined up paraboloidal cells moving in a flow under regime of lubrication approximation. So, the boundary condition in this lower flow limit considers the cell velocity and a numerical integration is used to solve the volumetric flux as a function of the pressure drop inside the capillary. The effect of the cell volume fraction in terms of the depleted layer thickness and cell aggregations is also investigated with this model. The influence of the wall irregularities on the flow is studied by using a simple sinusoidal model for the wall. Finally, an intrinsic viscosity of the blood is predicted theoretically for both the lower and upper bound regimes as a function of the non-dimensional vessel diameter, in good agreement with previous experimental works. We compare our theoretical predictions with experimental data and obtain a qualitative good for the classic Fahraeus-Lindqvist effect. A possible application of this work could be in illness diagnosis by evaluating of changes in the intrinsic viscosity due to blood abnormalities.

Downloads

Não há dados estatísticos.

Referências

Acrivos, A., Batchelor, G. K., Hinch, E. J., Koch, D. L. and Mauri, R. (1992). Longitudinal shear-induced diffusion of spheres in a dilute suspension, Journal of fluid mechanics 240: 651”“657.

Bird, R. B., Armstrong, R. C., Hassager, O. and Curtiss, C. F. (1977). Dynamics of polymeric liquids, Vol. 1, Wiley New York.

Chaffey, C., Brenner, H. and Mason, S. (1965). Particle motions in sheared suspensions, Rheologica Acta 4(1): 64”“72.

Chan, P.-H. and Leal, L. G. (1979). The motion of a deformable drop in a second-order fluid, Journal of Fluid Mechanics 92(01): 131”“170.

Cunha, F. R. and Hinch, E. J. (1996). Shear-induced dispersion in a dilute suspension of rough spheres, Journal of Fluid Mechanics 309: 211”“223.

Davis, R. H. (1996). Hydrodynamic diffusion of suspended particles: a symposium, Journal of Fluid Mechanics 310: 325”“335.

Einstein, A. (1956). Investigations on the Theory of the Brownian Movement, Courier Corporation.

F°ahræus, R. and Lindqvist, T. (1931). The viscosity of the blood in narrow capillary tubes, American Journal of Physiology”“Legacy Content 96(3): 562”“568.

Kennedy, M. R., Pozrikidis, C. and Skalak, R. (1994). Motion and deformation of liquid drops, and the rheology of dilute emulsions in simple shear flow, Computers & fluids 23(2): 251”“ 278.

Kim, S. and Karrila, S. J. (2013). Microhydrodynamics: principles and selected applications, Courier Corporation.

Klingel, R., Fassbender, C., Fassbender, T., Erdtracht, B. and Berrouschot, J. (2000). Rheopheresis: rheologic, functional, and structural aspects, Therapeutic Apheresis 4(5): 348”“357.

Oliveira, T. F. and Cunha, F. R. (2011). A theoretical description of a dilute emulsion of very viscous drops undergoing unsteady simple shear, Journal of Fluids Engineering 133(10): 101208.

Popel, A. S. and Johnson, P. C. (2005). Microcirculation and hemorheology, Annual review of fluid mechanics 37: 43.

Pries, A., Secomb, T. W., Gessner, T., Sperandio, M. B., Gross, J. F. and Gaehtgens, P. (1994). Resistance to blood flow in microvessels in vivo., Circulation research 75(5): 904”“915.

Schowalter,W., Chaffey, C. and Brenner, H. (1968). Rheological behavior of a dilute emulsion, Journal of colloid and interface science 26(2): 152”“160.

Skalak, R., Ozkaya, N. and Skalak, T. C. (1989). Biofluid mechanics, Annual review of fluid mechanics 21(1): 167”“200.

Smart, J. R. and Leighton Jr, D. T. (1991). Measurement of the drift of a droplet due to the presence of a plane, Physics of Fluids A: Fluid Dynamics (1989-1993) 3(1): 21”“28.

Sung, K., Schmid-Sch¨onbein, G., Skalak, R., Schuessler, G., Usami, S. and Chien, S. (1982).

Influence of physicochemical factors on rheology of human neutrophils., Biophysical journal 39(1): 101.

Downloads

Publicado

2017-01-10

Como Citar

Roure Neto, G. A. de, & Cunha, F. R. da. (2017). MODELING THE LOWER AND THE UPPER REGIME OF THE BLOOD UNIDIRECTIONAL FLOW IN MICRO-VESSELS. Revista Interdisciplinar De Pesquisa Em Engenharia, 2(12), 181–207. https://doi.org/10.26512/ripe.v2i12.21350