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

当多物种悬浮液流经导管时，实验表明，较大的物种向导管轴迁移，而较小的物种向周边漂移。 被称为血浆筛选的现象对于减少血流中的损失尤其重要，其中较大的细胞在轴周围形成核心，将较小的颗粒留在血管壁附近。 尽管过去的几项研究，它仍然不清楚是否等离子体屏蔽发生由于多粒子流体动力学相互作用或惯性动力学或细胞变形。 同样，对于上述因素如何影响管道内的粘性耗散，仍然没有准确的理解。在我们提出的研究中，我们将量化每个贡献因素的空间变化的每一个悬浮物种的数量密度在一个圆柱约束多物种的解决方案。因此，我们将首先考虑一个多物种系统的刚性椭球体具有不同的大小和偏心率的压力驱动流占流体动力学的相互作用。然后，惯性和颗粒变形性将被包括一个接一个，以确定由于这些修改数密度的相对变化。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特性。 所提出的分析的复杂性是多方面的。首先，对于狭窄管道中的稠密悬浮液，颗粒间和颗粒壁的粘性相互作用导致流动应力的显著增加，并产生巨大的流体动力学摩擦的空间变化。因此，必须正确地解决数百个粒子之间以及粒子与约束圆柱之间的相互作用。其次，如果考虑流体和溶质粒子的惯性，控制方程变得特别复杂。第三，如果悬浮体被认为是可变形的，则边界条件必须在未预定义的表面上满足。 幸运的是，我们最近开发的快速方法可以有效地解决这种情况下的流动方程。因此，我们将应用这种技术来克服预期的困难。智力优点：我们的关键数学创新是一个快速的计划，解决了流场中存在的断开不同的表面代表导管和不同种类的颗粒。传统的方法，如分子动力学，有限元和边界积分遇到困难，以考虑数百个悬浮体。相比之下，斯托克斯动力学算法可以用于此目的。然而，尽管它的有用性，斯托克斯动力学实际上是局限于球形粒子在无约束域几次尝试推广产生不准确或情况下特定的模拟。因此，本方法不能应用于圆柱形约束的椭球粒子。而且，顾名思义，它只适用于不包含任何惯性项的Stokes方程。我们的广义方法解决了这些不足之处，使我们可以考虑惯性方程以及不同的几何形状对应的管道约束变形multispecies system.Broader的影响：这项研究将解释不同的原因，有助于在径向迁移的变形颗粒通过管道的抛物线流的相对重要性。研究结果将有助于了解血管中血浆屏蔽的原因以及对粘性耗散的影响。由于筛查过程取决于血液成分的基本性质，因此这种现象中的任何差异都表明血液学异常。因此，从长远来看，我们的分析将导致对血栓形成，栓塞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，可以减少医疗费用。 我们的数学理论除了胶体系统中的流动分析外，还有更广泛的科学含义。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。这种广泛的应用范围将促进数学和生物流体学两个刺激课程，导致研究生和本科生的研究为基础的教育。

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.