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Register a new userA non-linear fluid suspension model for blood flow
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Motivated by the complex rheological behaviors observed in small/micro scale blood vessels, such as the Fahraeus effect, plasma-skimming, shear-thinning, etc., we develop a non-linear suspension model for blood. The viscosity is assumed to depend on the volume fraction (hematocrit) and the shear rate. The migration of the red blood cells (RBCs) is studied using a concentration flux equation. A parametric study with two representative problems, namely simple shear flow and a pressure driven flow demonstrate the ability of this reduced-order model to reproduce several key features of the two-fluid model (mixture theory approach), with much lower computational cost.
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The biotransport of the intravascular nanoparticle (NP) is influenced by both the complex cellular flow environment and the NP characteristics. Being able to computationally simulate such intricate transport phenomenon with high efficiency is of far-reaching significance to the development of nanotherapeutics, yet challenging due to large length-scale discrepancies between NP and red blood cell (RBC) as well as the complexity of NP dynamics. Recently, a lattice-Boltzmann (LB) based multiscale simulation method has been developed to capture both NP scale and cellular level transport phenomenon at high computational efficiency. The basic components of this method include the LB treatment for the fluid phase, a spectrin-link method for RBCs, and a Langevin dynamics (LD) approach to capturing the motion of the suspended NPs. Comprehensive two-way coupling schemes are established to capture accurate interactions between each component. The accuracy and robustness of the LB-LD coupling method are demonstrated through the relaxation of a single NP with initial momentum and self-diffusion of NPs. This approach is then applied to study the migration of NPs in a capillary vessel under physiological conditions. It is shown that Brownian motion is most significant for the NP distribution in capillary vessels. For 1~100 nm particles, the Brownian diffusion is the dominant radial diffusive mechanism compared to the RBC-enhanced diffusion. For ~500 nm particles, the Brownian diffusion and RBC-enhanced diffusion are comparable drivers for the particle radial diffusion process.
We study fluid-structure interactions (FSIs) in a long and shallow microchannel, conveying a non-Newtonian fluid, at steady state. The microchannel has a linearly elastic and compliant top wall, while its three other walls are rigid. The fluid flowing inside the microchannel has a shear-dependent viscosity described by the power-law rheological model. We employ lubrication theory to solve for the flow problem inside the long and shallow microchannel. For the structural problem, we employ two plate theories, namely Kirchhoff-Love theory of thin plates and Reissner-Mindlin first-order shear deformation theory. The hydrodynamic pressure couples the flow and deformation problem by acting as a distributed load onto the soft top wall. Within our perturbative (lubrication theory) approach, we determine the relationship between flow rate and the pressure gradient, which is a nonlinear first-order ordinary differential equation for the pressure. From the solution of this differential equation, all other quantities of interest in non-Newtonian microchannel FSIs follow. Through illustrative examples, we show the effect of FSI coupling strength and the plate thickness on the pressure drop across the microchannel. Through direct numerical simulation of non-Newtonian microchannel FSIs using commercial computational engineering tools, we benchmark the prediction from our mathematical prediction for the flow rate-pressure drop relation and the structural deformation profile of the top wall. In doing so, we also establish the limits of applicability of our perturbative theory.
Driven or active suspensions can display fascinating collective behavior, where coherent motions or structures arise on a scale much larger than that of the constituent particles. Here, we report experiments and numerical simulations revealing that red blood cells (RBCs) assemble into regular patterns in a confined shear flow. The order is of pure hydrodynamic and inertialess origin, and emerges from a subtle interplay between (i) hydrodynamic repulsion by the bounding walls which drives deformable cells towards the channel mid-plane and (ii) intercellular hydrodynamic interactions which can be attractive or repulsive depending on cell-cell separation. Various crystal-like structures arise depending on RBC concentration and confinement. Hardened RBCs in experiments and rigid particles in simulations remain disordered under the same conditions where deformable RBCs form regular patterns, highlighting the intimate link between particle deformability and the emergence of order. The difference in structuring ability of healthy (deformable) and diseased (stiff) RBCs creates a flow signature potentially exploitable for diagnosis of blood pathologies.
Cardiovascular diseases, specifically cerebral aneurysms, represent a major cause of morbidity and mortality, having a significant impact on the cost and overall status of health care. In the present work, we employ a haemorheological blood model originally proposed by Owens to investigate the haemodynamics of blood flow through an aneurytic channel. This constitutive equation for whole human blood is derived using ideas drawn from temporary polymer network theory to model the aggregation and disaggregation of erythrocytes in normal human blood at different shear rates. To better understand the effect of rheological models on the haemodynamics of blood flow in cerebral aneurysms we compare our numerical results with those obtained with other rheological models such as the Carreau-Yasuda (C-Y) model. The results show that the velocity profiles for the Newtonian and the Owens models are approximately similar but differ from those of the C-Y model. In order to stabilize our numerical simulations, we propose two new stabilization techniques, the so-called N-Owens and I-Owens methods. Employing the N-Owens stabilization method enables us to capture the effect of erythrocyte aggregation in blood flow through a cerebral aneurysm at higher Weissenberg (We) and Reynolds (Re) numbers than would otherwise be possible.
A concentrated, vertical monolayer of identical spherical squirmers, which may be bottom-heavy, and which are subjected to a linear shear flow, is modelled computationally by two different methods: Stokesian dynamics, and a lubrication-theory-based method. Inertia is negligible. The aim is to compute the effective shear viscosity and, where possible, the normal stress differences as functions of the areal fraction of spheres $phi$, the squirming parameter $beta$ (proportional to the ratio of a squirmers active stresslet to its swimming speed), the ratio $Sq$ of swimming speed to a typical speed of the shear flow, the bottom-heaviness parameter $G_{bh}$, the angle $alpha$ that the shear flow makes with the horizontal, and two parameters that define the repulsive force that is required computationally to prevent the squirmers from overlapping when their distance apart is less than a critical value $epsilon a$, where $epsilon$ is very small and $a$ is the sphere radius. The Stokesian dynamics method allows the rheological quantities to be computed for values of $phi$ up to $0.75$; the lubrication-theory method can be used for $phi> 0.5$. A major finding of this work is that, despite very different assumptions, the two methods of computation give overlapping results for viscosity as a function of $phi$ in the range $0.5 < phi < 0.75$. This suggests that lubrication theory, based on near-field interactions alone, contains most of the relevant physics, and that taking account of interactions with more distant particles than the nearest is not essential to describe the dominant physics.
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