(368a) Migration of Deformable Blood Cells in Confined Shear Flows

Blood has been a subject of extensive interest for both medical and science applications alike. The analysis of circulating blood cells plays a pivotal role in the diagnosis of numerous physiological and pathological conditions. Although the principle rheological properties of blood have been explored for several decades [1], a more detailed understanding is needed for the optimization of miniature diagnostic devices which utilize the flow properties of blood in microfluidic geometries. As a direct consequence, the study of transport of deformable blood cells is crucial for the development of such microfluidic devices.

The primary objective of this investigation is to quantitatively understand the hydrodynamic lift of deformable blood cells in simple shear flow. The majority of approaches previously reported have been towards the measurement of physical parameters of individual cells. Due to the lack of quantitative drift data for cell populations, a clear understanding of the mechanics of blood flow in microcirculation still remains a huge challenge. In contrast to any computational and experimental studies done in the past, we have experimentally explored the migration phenomena under physiologically relevant viscosity ratios of O(1). The sedimentation velocities of the cells in the absence of shear and the equilibrium position as the shear rate increases were measured and this was directly related to the particle stresslet. This in turn was used to determine the rheologically measurable normal stress difference function N₁ - N₂. The current measurements are the first reported experimental values for normal stresses for a dilute suspension of blood cells. By comparison with the model of Schowalter et. al. [2], we may use the equilibrium positions and corresponding stresslet to deduce the effective surface tension of a drop equivalent to an RBC. Even though the red blood cell is not really a drop, its dynamics in a simple shear flow can be explained by fitting the experimental data to the drop model with an effective surface tension of 0.085 dynes/cm.

A parallel comparison could also be made with the theory of Vlahovska and Garcia [3] assuming the blood cell behaved like a viscous vesicle. The vesicle theory [3], being a perturbation theory valid at small excess areas, is questionable for a red blood cell which has an excess area of 4.6 and, in particular, does not explain the shear rate dependence of the normal stresses. In addition, the drift and the measured magnitudes of normal stresses are an order of magnitude less than what would be predicted for simple vesicles. For the more complex models of blood cells [4, 5, 6], the magnitudes of normal stress are consistent with the calculations of Spann et. al. [5] for the case of elastic vesicles in the biconcave tank treading regime and are an order of magnitude lower than those calculated for the prolate spheroid shape. Thus, the closest point of comparison for our measurements with the numerical calculations would be approximating the motion as that of a biconcave tank treading discoid. A comparison with the phase diagram of Yazdani and Bagchi [7] shows the transitions between the various intermediate shapes for a vesicle (eg. swinging, breathing etc.) as the capillary number is progressively increased. These transitions in shapes may give rise to the observed shear rate dependence of normal stresses.

References:

[1] Fåhræus R, Lindqvist T. The viscosity of the blood in narrow capillary tubes. American Journal of Physiology--Legacy Content. 1931;96:562-568.

[2] Schowalter W, Chaffey C, Brenner H. Rheological behavior of a dilute emulsion. J Colloid Interface Sci. 1968;26:152-160.

[3] Vlahovska PM, Gracia RS. Dynamics of a viscous vesicle in linear flows. Physical Review E. 2007;75:016313.

[4] Breyiannis G, Pozrikidis C. Simple shear flow of suspensions of elastic capsules. Theor Comput Fluid Dyn. 2000;13:327-347.

[5] Spann AP, Zhao H, Shaqfeh ES. Loop subdivision surface boundary integral method simulations of vesicles at low reduced volume ratio in shear and extensional flow. Physics of Fluids (1994-present). 2014;26:031902.

[6] Gross M, Krüger T, Varnik F. Rheology of dense suspensions of elastic capsules: normal stresses, yield stress, jamming and confinement effects. Soft matter. 2014;10:4360-4372.

[7] Yazdani AZ, Bagchi P. Phase diagram and breathing dynamics of a single red blood cell and a biconcave capsule in dilute shear flow. Physical Review E. 2011;84:026314.