Dye studies on flow through branching tubes

Abstract

This study was aimed at identifying the shape of the separating surface at the junction of two vessels and determining the shift in concentration profiles due to streamline bending at the junction. These data are useful in modeling phase separation during plasma skimming in serial microvascular bifurcations. It was hypothesized that the separating surface shape should be a function of the ratio of the branch diameters and the fractional flow split at the junction. Streamlines bend as blood flows through a junction thereby disturbing the concentration profile of several blood components downstream from the branch point. Model experiments have been conducted to test these ideas. Scaled-up dye studies have shown that the separating surface is indeed a function of the branch diameter ratio. When all branches have the same diameter the separating surface is virtually flat. When the side branch diameter is half that of the parent branch, the surface is curved, bulging away from the opening of the side branch. At Reynold's numbers greater than 20, when vortices form in the daughter branches, the shape of the separating surface is complicated and may even be discontinuous. Other dye experiments have been used to illustrate the magnitude of streamline bending. The data are then used to estimate the shift in concentration profiles due to flow through junctions. A technique for mapping upstream profiles to their corresponding downstream location has been developed. This mapping technique provides the necessary initial condition for the equation which describes the dispersion of red blood cells as they flow between the junctions.