Order and chaos in the flow of red blood cells

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PI: Freund, Jonathan Proposal Number: 1336972 It is well-known that in small tubes and capillary vessels, red blood cells flow in a strikingly regular lined-up column, with viscous stresses deforming them into bullet-like shapes. This regularity fails in larger vessels or tubes, where the cells take on varied and intricate shapes and flow with irregular and apparently chaotic interactions. This work will investigate this apparent bifurcation, leading to the onset of instability and chaotic motion. It is both an important fluid mechanical instability, with biophysical implications, and an important consideration in the design of microfluidic devices that process blood cells. Forming and maintaining uniform rows of cells in such a device will facilitate processing them on a cell-by-cell basis for diagnostic or filtering purposes.Intellectual Merit :Although hydrodynamic interactions at the low Reynolds numbers of flowing red blood cells are linear, the overall system is significantly nonlinear. Geometric nonlinearities associated with the cell positions and their deformable shapes present analytical challenges. A systematic approach is proposed to develop a description, with predictive capability, focusing in particular on the factors leading to the destabilitization of flowing red blood cell columns. A highly accurate simulation tool will be used for the collective motion of interacting and realistically flexible blood cells flowing within complex-geometry tubes or vessels. It is a spectral boundary integral solver, which has been used in several recent studies, including the fundamental analysis of blood flow in small tubes, the transport of magnetic nanoparticles for targeted drug delivery, and the biomedically important forces and transport effects of red blood cells on white blood cells as part of the inflammation response. Preliminary simulation results suggest the existence of a bifurcation between the lined-up flow and the apparently chaotic flow, which depends upon vessel diameter and cell volume fraction. Analytical work to describe the bifurcation will be pursued. The simulation will be used to calculate the linear interaction of all perturbation degrees of freedom and thereby will provide a complete linear dynamic model. This linear system will be analyzed with standard and, if necessary, transient algebraic growth methods to describe the behavior of small perturbations. A rigid-sphere analog is much more tractable and provides a starting-point for the proposed effort. An initial result for this is also presented. A goal is to advance understanding within a mathematical description to the point that a reduced dynamical description can then be used to predict phenomena of biological and microfluidic engineering importance.Broader Impacts :Studies such as this at the juncture of fluid mechanics, advanced simulation, applied mathematics, and biophysics are fundamentally interdisciplinary and therefore of high value from an educational perspective. In this particular case the analytical tools will translate into a reduced description that can both illuminate biophysical phenomena and provide guidance for the analysis and design of microfluidic devices. The PI will broaden the STEM impact of this work via the development and distribution of a user-friendly reduced model of cell interactions. This will be done in collaboration with undergraduate research assistants, and with the goal to enable simulation-based bio-microfluidic design projects for simplified blood-cell-handling devices.