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.
