Radial migration of suspended particles and its effect on multispecies flow inside a conduit

实验表明，当多组分悬浮物流经管道时，较大的组分向管道轴线迁移，而较小的组分向外围漂移。这种被称为血浆筛选的现象对于减少血流损失尤其关键，在这种情况下，较大的细胞围绕中轴形成核心，将较小的颗粒留在血管壁附近。尽管过去有几项研究，但仍然不清楚等离子体筛选是由于多粒子流体动力学相互作用还是由于惯性动力学或细胞的变形性。同样，对于上述因素如何影响管道内的粘性耗散，目前还没有准确的认识。在我们提出的研究中，我们将量化每个贡献因素对柱面束缚多物种溶液中每个悬浮物种数密度的空间变化的单独影响。因此，我们将首先考虑压力驱动流中具有不同大小和偏心率的多物种刚性椭球系统，以考虑流体动力相互作用。然后，将惯性和粒子变形性逐一包括在内，以确定由于这些修改而导致的数密度的相对变化。对于每种情况，将计算通道内的压降，以描述不同流动条件下的粘性损失和流变性。拟议的分析的复杂性是许多倍的。首先，对于狭窄管道中的稠密悬浮物，颗粒间和颗粒壁面的粘性相互作用导致流动应力显著增加，并造成流体动摩阻力的巨大空间变化。因此，必须妥善解决数百个颗粒之间的相互作用以及颗粒与封闭圆柱体之间的相互作用。其次，如果考虑流体和溶质颗粒的惯性，控制方程就变得特别复杂。第三，如果悬浮体被认为是可变形的，则必须在未预先定义的表面上满足边界条件。幸运的是，我们最近发展的快速方法可以有效地求解这种情况下的流动方程。因此，我们将应用这项技术来克服预期的困难。智能优点：我们的关键数学创新是一种快速方案，该方案解决了存在代表管道和不同颗粒种类的不连续不同表面时的流场。传统的分子动力学、有限元和边界积分等方法在考虑数百个悬浮体时遇到了困难。相比之下，Stokesian动力学算法可用于此目的。然而，尽管斯托克动力学很有用，但它实际上仅限于无约束区域中的球形粒子。几次推广尝试都产生了不准确或特定情况的模拟。因此，本文的方法不能应用于圆柱约束下的椭球粒子。此外，顾名思义，它只适用于不含任何惯性项的Stokes方程。我们的推广方法解决了这些不足，以便我们可以解释惯性方程以及对应于管道约束的可变形多物种系统的不同几何形状。更广泛的影响：这项研究将解释抛物线流经管道时可变形粒子径向迁移的不同原因的相对重要性。这些结果将有助于理解血管中血浆筛选的原因以及由此对粘性消散的影响。由于筛查过程取决于血液成分的基本性质，这一现象中的任何差异都表明血液系统异常。因此，从长远来看，我们的分析将导致对血栓、血栓和异常出血等健康危害的定量预测。因此，通过注重及时预防而不是昂贵的治疗，可以降低医疗费用。除了胶体体系中的流动分析，我们的数学理论还有更广泛的科学意义。它也适用于其他方程或边界条件，如弹性力学或电动力学问题。如此广泛的应用范围将促进数学和生物流体学两门激动人心的课程，从而为研究生和本科生带来以研究为基础的教育。

When multispecies suspensions flow through conduits, experiments show that the larger species migrates towards the conduit axis whereas the smaller species drifts towards the periphery. The phenomenon known as plasma screening is especially crucial for loss reduction in blood flow where larger cells form a core around the axis leaving the smaller particles near the vessel walls. Despite several past studies, it is still not clear whether the plasma screening happens due to multiparticle hydrodynamic interactions or inertial dynamics or cell deformability. Similarly, there is still no accurate understanding on how the aforementioned factors affect the viscous dissipation inside the conduits. In our proposed study, we will quantify the individual effect of each contributing factor on the spatial variation of number density of each suspended species in a cylinder bound multispecies solution. Accordingly, we will first consider a multispecies system of rigid ellipsoids with different sizes and eccentricities in pressure driven flow to account for hydrodynamic interactions. Then, inertia and particle deformability will be included one by one to determine the relative changes in number density due to these modifications. For each case, the pressure drop inside the channel will be computed to describe the viscous loss and the rheological properties for different flow conditions. The complexity in the proposed analysis is manyfold. Firstly, for dense suspensions in narrow conduits, interparticle and particle wall viscous interactions cause major increase in flow stresses, and create huge spatial variation in hydrodynamic friction. Hence, the mutual interactions among hundreds of particles as well as between the particles and the confining cylinder have to be resolved properly. Secondly, if inertia of the fluid and the solute particles are taken into account, the governing equation becomes especially complicated. Thirdly, if the suspended bodies are considered deformable, the boundary conditions have to be satisfied on a surface which is not predefined. Fortunately, our recently developed fast methodology can efficiently solve flow equations in such situation. Thus, we will apply this technique to overcome the anticipated difficulties.Intellectual Merit: Our key mathematical innovation is a fast scheme which solves the flow field in presence of disconnected dissimilar surfaces representing the conduit and different species of particles. Conventional methods like molecular dynamics, finite element and boundary integrals encounter difficulties to take into account hundreds of suspended bodies. In contrast, Stokesian dynamics algorithm can be used for this purpose. However, despite its usefulness, Stokesian dynamics is actually restricted to spherical particles in unconfined domain several attempts for generalization yielded inaccurate or case specific simulations. So the method in the present form cannot be applied to ellipsoidal particles in cylindrical confinement. Moreover, as the name suggests, it is only valid for Stokes equation which does not involve any inertial term. Our generalized approach addresses these inadequacies so that we can account for inertial equations as well as different geometries corresponding to conduit bound deformable multispecies system.Broader Impact: This study will explain the relative importance of different causes contributing in radial migration of deformable particles in parabolic flow through a conduit. The resultant findings will be useful to understand the reason behind plasma screening in blood vessels and consequent effect on viscous dissipation. As the screening process depends on basic properties of blood components, any discrepancy in this phenomenon is indicative of hematological abnormality. Thus, in the long run, our analysis will lead to quantitative prediction of health hazards like thrombosis, embolism and abnormal hemorrhage. As a result, medical expenses can be reduced by focusing on timely prevention rather than expensive cure. Our mathematical theory has a wider scientific implication besides flow analysis in colloidal systems. It is applicable to other equations or boundary conditions as in elasticity or electrodynamics problems. Such broad scope of application will promote two stimulating courses on mathematics and biofluidics leading to research-based education of graduate and undergraduate students.