It is well known that blood has non-Newtonian properties, but it is generally accepted that blood behaves as a Newtonian fluid at shear rates above 100 s-1. However, in transient conditions, there are times and locations where the shear rate is well below 100 s-1, and it is reasonable to infer that non-Newtonian effects could become important. In this study, purely viscous non-Newtonian (generalized Newtonian) properties of blood are incorporated into the simulation-based framework for cardiovascular surgery planning developed by Taylor et al. (1999, "Predictive Medicine: Computational Techniques in Therapeutic Decision Making," Comput. Aided Surg., 4, pp. 231-247; 1998, "Finite Element Modeling of Blood Flow in Arteries," Comput. Methods Appl. Mech. Eng., 158, pp. 155-196). Equations describing blood flow are solved in a patient-based abdominal aortic aneurysm model under steady and physiological flow conditions. Direct numerical simulation (DNS) is used, and the complex flow is found to be constantly transitioning between laminar and turbulent in both the spatial and temporal sense. It is found for the case simulated that using the non-Newtonian viscosity modifies the solution in subtle ways that yield a mesh-independent solution with fewer degrees of freedom than the Newtonian counterpart. It appears that in regions of separated flow, the lower shear rate produces higher viscosity with the non-Newtonian model, which reduces the associated resolution needs. When considering the real case of pulsatile flow, high shear layers lead to greater unsteadiness in the Newtonian case relative to the non-Newtonian case. This, in turn, results in a tendency for the non-Newtonian model to need fewer computational resources even though it has to perform additional calculations for the viscosity. It is also shown that both viscosity models predict comparable wall shear stress distribution. This work suggests that the use of a non-Newtonian viscosity models may be attractive to solve cardiovascular flows since it can provide simulation results that are presumably physically more realistic with at least comparable computational effort for a given level of accuracy.

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. Modeling of Magnetorheological Fluids by the Discrete Element MethodMagnetorheological (MR) fluids are fluids whose properties vary in response to an applied magnetic field. Such fluids are typically composed of microscopic iron particles ($ 1 À 20 lm diameter, 20 À 40% by volume) suspended in a carrier fluid such as mineral oil or water. MR fluids are increasingly proposed for use in various mechanical system applications, many of which fall in the domain of tribology, such as smart dampers and clutches, prosthetic articulations, and controllable polishing fluids. The goal of this study is to present an overview of the topic to the tribology audience, and to develop an MR fluid model from the microscopic point of view using the discrete element method (DEM), with a long range objective to better optimize and understand MR fluid behavior in such tribological applications. As in most DEM studies, inter-particle forces are determined by a force-displacement law and trajectories are calculated using Newton's second law. In this study, particle magnetization and magnetic interactions between particles have been added to the discrete element code. The global behavior of the MR fluid can be analyzed by examining the time evolution of the ensemble of particles. Microscopically, the known behavior is observed: particles align themselves with the external magnetic field. Macroscopically, averaging over a number of particles and a significant time interval, effective viscosity increases significantly when an external magnetic field is applied. These preliminary results would appear to establish that the DEM is a promising method to study MR fluids at the microscopic and macroscopic scales as an aid to tribological design.

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Classical hydrodynamic lubrication theory has been one of the most successful and widely used theories in all of engineering and applied science. This theory predicts that the force resisting the squeezing of a fluid between two parallel plates is inversely proportional to the cube of the fluid thickness. However, recent reports on liquid squeeze film damping in microsystems appear to indicate that experimentally measured damping force is proportional to the inverse of the fluid thickness to the first power—a large fundamental discrepancy from classical theory. This paper investigates potential limitations of lubrication theory in microsystems by theoretical and computational methods. The governing equations for a Newtonian incompressible fluid are solved subject to two-dimensional, parallel surface squeezing by an open-source computational fluid dynamics program called parallel hierarchic adaptive stabilized transient analysis (PHASTA), and by a classical similarity solution technique. At low convective Reynolds numbers, the damping force is determined as a function of the ratio of a reference film thickness H to a reference direction B along the film. Good agreement with classical lubrication theory is found for aspect ratios H/B as high as 1 despite the fact that lubrication theory requires that this ratio be “small.” A similarity analysis shows that when instantaneous convective Reynolds number is of order 10–100 (a range present in experiment), calculated damping deviates significantly from lubrication theory. This suggests that nonlinearity associated with high Reynolds numbers could explain the experimentally observed discrepancy in damping force. Dynamic analysis of beams undergoing small vibrations in the presence of a liquid medium further supports this finding.

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