The phenomenon of particle migration in microfluidic flows has long been studied and modelled. However, the application of such learning to practical devices has been limited. Of particular interest is the behaviour of red blood cells, or erythrocytes, in microfluidic devices due to their therapeutic device applications. Recent advances in micro-fabrication techniques has allowed for the application of such learning to a vast array of uses. The primary interest in our laboratory is that of a microfluidic membraneless kidney. Currently, over 400,000 US patients suffer from End Stage Renal Failure Disease, or total kidney failure. The dialysis treatment for these patients requires several hours per week of patient time at a treatment facility, induces a high-amplitude cyclic level of water and toxins in the patient's body, and generates discomfort during treatment due to the required pressure and rate of blood flow. Current treatment entails pumping blood through a membrane filter to remove water and returning the blood to the body over a 3-4 hour treatment 3 times per week. The filters tend to lose permeability over time, and the large surface interface provokes a large set of chemical reactions with blood components. The possibility of treating a patient's blood more steadily and outside of a clinic is truly an intriguing and desirable concept. However, current efforts to extend membrane technology to longer periods of dialysis, outside of the clinic, encounter two difficulties: (1) They require intermittent blood access which is painful, difficult, and potentially dangerous. (2) They do nothing to lessen either membrane fouling with concomitant losses in permeability or problems of biocompatibility occasioned by extensive exposure to artificial surfaces. We have proposed a wearable, indirect dialysis system that is permanently connected to the circulation. It employs direct (membraneless) diffusive contact between blood and a miscible “sheathing” fluid to extract water and toxins from the blood. The cell-free sheath fluid is then dialyzed and ultrafiltered to remove solutes and water and to force recirculation of desirable macromolecules. The dialyzed sheath is recirculated for further contact with the blood stream. The most important factor, by far, in such a system is preventing blood cells from entering the sheath fluid. Past research shows the tendency for such cells to migrate to the center of a flowing stream, and it is believed that blood cells can be retained with proper system design and operation. The nominal design of the current experimental device has a blood channel 100 microns thick flowing between two identical streams of sheath fluid also each 100 microns thick. Equilibrium of the contacted phases is dependent upon the diffusion coefficient of water and toxins in blood and the sheath fluid and is on the order of seconds for small molecules (water, ions, sugars etc.). The transient diffusion equation between static fluids, originally obtained by Loschmidt, yields a solution that closely follows a finite difference representation of the exchange. The sheath system is something that has intrinsic value for us in the application of studies here, but it is also a system that enables the general phenomenon of blood diffusion to be studied in a way that allows separation of the forced and ordinary diffusion components. Past research of other groups, computational fluid dynamic modelling, and experimental analysis in our own lab have shown that red blood cells should remain in the blood stream in high proportion. However a full understanding of the conditions to minimize cell migration from the center stream is unclear. To date, the study of erythrocyte migration has been performed in systems where the blood is bound by impermeable walls. It is well known that erythrocytes cross pathlines under laminar flow conditions due to either the inertia of the fluid, or, in the absence of inertial effects, shear induced migration relying on the deformability of red blood cells. Earlier studies have not considered the dynamics of the system if the blood is bounded not by walls, but by concentric fluids. One may say that this is tantamount to previous studies, but considering the blood as being diluted by the concentric fluids, this statement would be true only if blood enters the system equally distributed throughout the system. In the studies discussed here, blood enters the system via a central stream between two concentric flowing sheath streams, thus testing the theory of how the blood will treat the concentric fluid layers: as an extension of its original continuous phase or as a separate entity. Will the erythrocytes cross streamlines and migrate toward the center as in previous studies despite its seemingly far distance from the walls (thus negating the wall effects), or will the diffusion of blood away from the center stream (driven by the concentration gradient between the central blood-rich stream and peripheral blood-free stream and by particle-particle interactions) be too great to be compensated by the migrational tendencies of blood aforementioned? It is the purpose of this research to address such concepts. The results of such research have engineering applications in regards to artificial kidneys, plasmapheresis, and other biomedical therapies The purpose of this research is to quantify and model the major conditions that affect erythrocyte migration when blood flows in direct contact with 2 miscible blood-free streams. Also, obtaining basic knowledge of erythrocyte behaviour is vital to microfluidic devices designed around blood flows.

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