A detailed model of red blood cell (RBC) transport in a capillary network is an indispensable element of a comprehensive model for the supply of the human organism with oxygen and nutrients. In this paper, we introduce a two-phase model for the perfusion of a capillary network. This model accounts for the special role of RBCs, which have a strong influence on network dynamics. Analytical results and numerical simulations with a discrete model and a generic network topology indicate that there exists a local self-regulation mechanism for the flow rates and a global de-mixing process that leads to an inhomogeneous haematocrit distribution. Based on the results from the discrete model, we formulate an efficient algorithm suitable for computing the pressure and flow field as well as a continuous haematocrit distribution in large capillary networks at steady state.

A simple extension of the classic Görtler–Hämmerlin (1955) (GH) model, essential for three-dimensional linear instability analysis, is presented. The extended Görtler–Hämmerlin model classifies all three-dimensional disturbances in this flow by means of symmetric and antisymmetric polynomials of the chordwise coordinate. It results in one-dimensional linear eigenvalue problems, a temporal or spatial solution of which, presented herein, is demonstrated to recover results otherwise only accessible to the temporal or spatial partial-derivative eigenvalue problem (the former also solved here) or to spatial direct numerical simulation (DNS). From a numerical point of view, the significance of the extended GH model is that it delivers the three-dimensional linear instability characteristics of this flow, discovered by solution of the partial-derivative eigenvalue problem by Lin & Malik (1996a), at a negligible fraction of the computing effort required by either of the aforementioned alternative numerical methodologies. More significant, however, is the physical insight which the model offers into the stability of this technologically interesting flow. On the one hand, the dependence of three-dimensional linear disturbances on the chordwise spatial direction is unravelled analytically. On the other hand, numerical results obtained demonstrate that all linear three-dimensional instability modes possess the same (scaled) dependence on the wall-normal coordinate, that of the well-known GH mode. The latter result may explain why the three-dimensional linear modes have not been detected in past experiments; criteria for experimental identification of three-dimensional disturbances are discussed. Asymptotic analysis based on a multiple-scales method confirms the results of the extended GH model and provides an alternative algorithm for the recovery of three-dimensional linear instability characteristics, also based on solution of one-dimensional eigenvalue problems. Finally, the polynomial structure of individual three-dimensional extended GH eigenmodes is demonstrated using three-dimensional DNS, performed here under linear conditions.

We present a model to predict the size of droplets dripping into an immiscible flowing fluid in glass capillary microfluidic devices. Despite the complex flow behavior in the confined geometry of microfluidic devices, we find that the size of dripping droplets can be accurately predicted by a simple analytic expression based on the ratio of shear and interfacial forces acting on the droplet surface, also known as the Capillary number. We show that data obtained for a wide range of fluid properties and flow conditions including single and multiple dripping events and other experimental data previously reported in the literature can be quantitatively described using one single universal value for the critical Capillary number leading to droplet rupture.

Every year, a quarter million patients receive prosthetic heart valves in aortic valve replacement therapy. Prosthetic heart valves are known to lead to turbulent blood flow. This turbulent flow field may have adverse effects on blood itself, on the aortic wall and on the valve performance. A detailed characterization of the turbulent flow downstream of a valve could yield better understanding of its effect on shear-induced thrombocyte activation, unphysiological wall shear stresses and hemodynamic valve performance. Therefore, computational simulations of the flow past a bioprosthetic heart valve were performed. The computational results were validated against experimental measurements of the turbulent flow field with tomographic particle image velocimetry. The turbulent flow was analyzed for disturbance amplitudes, dissipation rates and shear stress distributions. It was found that approximately 26% of the hydrodynamic resistance of the valve was due to turbulent dissipation and that this dissipation mainly took place in a region about one valve diameter downstream of the valve orifice. Farther downstream, the turbulent fluctuations became weaker which was also reflected in the turbulent velocity spectra of the flow field. Viscous shear stresses were found to be in the range of the critical level for blood platelet activation. The turbulent flow led to elevated shear stress levels along the wall of the ascending aorta with strongly fluctuating and chaotic wall shear stress patterns. Further, we identified leaflet fluttering at 40 Hz which was connected to repeated shedding of vortex rings that appeared to feed the turbulent flow downstream of the valve.

Although heart transplantation is a gold standard for severe heart failure, there is a need for alternative effective therapies. A dielectric‐elastomer aorta is used to augment the physiological role of the aorta in the human circulatory system. To this end, the authors developed a tubular dielectric elastomer actuator (DEA) able to assist the heart by easing the deformation of the aorta in the systole and by increasing its recoil force in the diastole. In vitro experiments using a pulsatile flow‐loop, replicating human physiological flow and pressure conditions, show a reduction of 5.5% (47 mJ per cycle) of the heart energy with this device. Here, the controlled stiffness of the DEA graft, which is usually difficult to exploit for actuators, is perfectly matching the assistance principle. At the same time, the physiological aortic pressure is exploited to offer a prestretch to the DEA which otherwise would require an additional bulky pre‐stretching system to reach high performances.