The flow of sickle blood in glass capillaries: Fundamentals and potential applications

We have characterized the imbibed horizontal flow of sickle blood into 100-μm-diameter glass capillaries. We find that blood containing sickled cells typically traverses the capillaries between three and four times as slowly as oxygenated cells from the same patient for all genotypes tested, including SS, AS, SC and Sβ⁺ thalassemia blood. Blood from SS patients treated with hydroxyurea has a viscosity intermediate between the SS and AA values. Blood containing cells that are not rigidified, such as normal red cells or oxygenated sickle cells, follows a simple Lucas-Washburn flow throughout the length of the 3-cm capillary. By fitting the flexible-cell data to the Lucas-Washburn model, a viscosity can be derived that is in good agreement with previous measurements over a range of volume fractions and is obtained using an apparatus that is far more complex. Deoxygenation sickles and thus rigidifies the cells, and their flow begins as Lucas-Washburn, albeit with higher viscosity than flexible cells. However, the flow further slows as a dense mass of cells forms behind the meniscus and increases in length as flow progresses. By assuming that the dense mass of cells exerts a frictional force proportional to its length, we derive an equation that is formally equivalent to vertical imbibition, even though the flow is horizontal, and this equation reproduces the observed behavior well. We present a simple theory using activity coefficients that accounts for this viscosity and its variation without adjustable parameters. In the course of control experiments, we have found that deoxygenation increases the flexibility of normal human red cells, an observation only recently published for mouse cells and previously unreported for human erythrocytes. Together, these studies form the foundation for an inexpensive and rapid point-of-care device to diagnose sickle cell disease or to determine blood viscosity in resource-challenged settings.