The Surface-Tension-Driven Flow of Blood From a Droplet Into a Capillary Tube

Abstract

In tissue, medical, or dental engineering, when blood comes into contact with a new artificial material, the flow may be influenced by surface tension between the blood and the surface of the material. The effect of surface tension on the flow of blood is significant, especially in microscale. The leading edge of the flowing blood is the triple point where the blood, the material surface, and a stationary gas or fluid meet. The movement of the triple point, i.e., the advancing front of the flow, is driven by surface tension, resisted by viscous shear stress, and balanced by the inertial force (−mass×acceleration). In this article, the dynamics is illustrated in detail in the case of blood flowing into a capillary tube by contact. The capillary tube draws the blood into it. It is shown theoretically that initially the flow of blood in the capillary has a large acceleration, followed by a relatively large deceleration over the next short period of time, then the acceleration becomes small and oscillatory. The velocity history appears impulsive at first, then slows down. The history of the length of blood column appears smooth after integration. Existing solutions of the Navier–Stokes equation permit the analysis of simpler cases. Further fluid mechanics development is needed to meet the practical needs of bioengineering. The importance of experimental study of surface tension and contact angle over a biological surface or a man-made material as a future direction of research is pointed out.