A continuum mechanics model for the Fåhræus-Lindqvist effect

The decrease in apparent relative viscosity that occurs when blood is made to flow through a tube whose diameter is less than about 0.3 mm is a well-known and documented phenomenon in physiology, known as the Fåhræus-Lindqvist effect. However, since the historical work of Fåhræus and Lindqvist (Amer. J. Physiol. 96(3): pp. 562–568, 1931), the underlying physical mechanism has remained enigmatic. A widely accepted qualitative explanation was provided by Haynes (Amer. J. Physiol. 198, pp. 1193–1200, 1960) according to which blood flows in microvessels with a core-annulus structure, where the erythrocytes concentrate within a central core surrounded by a plasma layer. Although sustained by observations, this conjecture lacks a rigorous deduction from the basic principles of continuum dynamics. Moreover, relations aimed to reproduce the blood apparent relative viscosity, extensively used in micro-circulation, are all empirical and not derived from the analysis of the fluid mechanical phenomena involved. In this paper, we apply the recent results illustrated in Guadagni and Farina (Int. J. Nonlinear Mech. 126, p. 103587, 2020), with the purpose of showing that Haynes’ conjecture, slightly corrected to make it more realistic, can be proved and can be used to reach a sound explanation of the Fåhræus-Lindqvist effect based on continuum mechanics. We propose a theoretical model for the blood apparent relative viscosity which is validated by matching not only the original experimental data reported by Fåhræus and Lindqvist (Amer. J. Physiol. 96(3), pp. 562–568, 1931), but also those provided by several subsequent authors.

NATURAL FILTRATION EQUATIONS. FIASCO “OF DARCY'S LAW”

The theory of natural filtration equations is given. The naturalness of the new filtration equations is that they are the exact consequences of the fundamental laws of physics, directly take into account the density and porosity of the soil, the viscosity and density of the filtration fluid, drainage, the influence of gravity, etc.the falsity of the traditional continuity equation in the filtration theory is Established. New filtration equations are derived from the equation of continuum dynamics in stresses, including the density and viscosity of the liquid and the porosity of the soil.Inadequacy of the modeling filter equations with the friction law of Newton. The efficiency of simulation of filtration by Jakupova equations based on the power laws of friction with odd exponents is numerically confirmed, with the use of which the calculations of filtration in the well, drainage under the influence of gravity, displacement of oil by water from the underground area through two symmetrically located pits are carried out.

Unified Space–Time Finite Element Methods for Dissipative Continua Dynamics

Based upon the extended framework of Hamilton’s principle, unified space–time finite element methods for viscoelastic and viscoplastic continuum dynamics are presented, respectively. For numerical efficiency, mixed time-step algorithm in time- and displacement-based algorithm in space are adopted. Through analytical investigation, we demonstrate that the Newmark’s constant average acceleration method and the present method are the same for viscoelasticity. With spatial eight-node brick elements, some numerical simulations are undertaken to validate and investigate the performance of the present non-iterative space–time finite element method for viscoplasticity.