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

悬浮颗粒的径向迁移及其对管道内多物质流的影响

• 批准号: 1034461
• 负责人: Sukalyan Bhattacharya
• 金额: $ 27.28万
• 依托单位: Texas Tech University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-07-15 至 2015-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1034461&HistoricalAwards=false
• 关键词: Radial; migration; suspended; particles; its

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.

当多物种悬浮液流过管道时，实验表明较大的物种向管道轴线迁移，而较小的物种向外围漂移。 这种被称为血浆筛选的现象对于减少血流损失尤其重要，其中较大的细胞围绕轴形成核心，而较小的颗粒靠近血管壁。 尽管过去进行了多项研究，但仍不清楚血浆筛选是否由于多粒子流体动力学相互作用、惯性动力学或细胞变形性而发生。 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，我们将量化每个影响因素对圆柱体多物种溶液中每个悬浮物种数密度空间变化的影响。因此，我们将首先考虑压力驱动流中具有不同尺寸和偏心率的刚性椭球体的多物种系统，以解释流体动力相互作用。然后，将惯性和粒子变形能力一一包括在内，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大幅增加，并在流体动力摩擦中产生巨大的空间变化。因此，必须妥善解决数百个粒子之间以及粒子与约束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，则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，则必须在未预定义的表面上满足边界条件。 幸运的是，我们最近开发的快速方法可以在这种情况下有效地求解流动方程。因此，我们将应用这项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种快速方案，该方案可以解决代表管道和不同种类颗粒的不相似表面的存在下的流场问题。分子动力学、有限元和边界积分等传统方法在考虑数百个悬浮体时遇到困难。相反，斯托克斯动力学算法可以用于此目的。然而，尽管斯托克斯动力学很有用，但它实际上仅限于无约束域中的球形粒子，几次泛化尝试都产生了不准确或特定情况的模拟。因此，目前形式的方法不能应用于圆柱约束中的椭圆体粒子。而且，顾名思义，它只对不涉及任何惯性项的斯托克斯方程有效。我们的通用方法解决了这些不足之处，以便我们可以解释惯性方程以及与管道束缚可变形多物种系统相对应的不同几何形状。更广泛的影响：这项研究将解释导致可变形粒子在通过管道的抛物线流中径向迁移的不同原因的相对重要性。由此产生的结果将有助于理解血管血浆筛查的原因以及随之而来的对粘性耗散的影响。由于筛查过程取决于血液成分的基本特性，因此这种现象的任何差异都表明血液学异常。因此，从长远来看，我们的分析将有助于对血栓形成、栓塞和异常出血等健康危害进行定量预测。因此，通过关注及时预防而不是昂贵的治疗可以减少医疗费用。 除了胶体系统的流动分析之外，我们的数学理论还具有更广泛的科学意义。它适用于弹性或电动力学问题中的其他方程或边界条件。如此广泛的应用范围将促进数学和生物流体学两门令人兴奋的课程，从而为研究生和本科生提供基于研究的教育。