Using centrifugation, bacteria can be separated from whole blood due to the differences in sedimentation velocity. These sedimentation velocities and differences in density cause the red blood cells (RBCs) to form a separate layer from the blood plasma, which still contains many platelets and bacteria. This creates a two-phase system, with differences in both viscosity and density between the layers. Upon deceleration different velocity profiles are produced for each phase, which can cause instabilities (or mixing) to occur in the system. Under high centrifugation forces, these two phases will remain stable and separated from each other. However, as the system slows down to stop, mixing has been observed under some conditions. The mixing in this system arises from Kelvin-Helmholtz instabilities. We have performed both a mathematical analysis of the instabilities in the two phase flow, as well as an experimental analysis to verify the theory. The mathematical analysis was performed through a nonlinear energy stability analysis because of the velocity dependence on time. This analysis provides the criteria for stability, not instability. Once the energy equations were obtained, numerical methods were used to determine the disk velocity when the system leaves the stable region. This does not guarantee that the system will mix but means that the system may mix if other forces are out of balance. The analysis predicts that the boundary of the stable deceleration regime has a parabolic shape when plotting the rate of deceleration against the current velocity. The experimental analysis of stability produced the criteria for instability. This analysis was performed by slowing the blood down at constant rates of deceleration. This allowed us to determine the disk speed at which the blood would mix for different rates of deceleration. Experiments were performed with deceleration rates from 100 RPM/s down to 1 RPM/s. Because this analysis gives criteria for instability and the mathematical analysis gave criteria for stability, there is a gap between the two. In this gap, the interface between the 2 phases may go unstable and is dependent on the viscosity, density, and velocity differences as well as the centrifugation forces. Also, because RBCs are cells and not a fluid, the experimental analysis seems to deviate even farther from mathematical analysis which assumed the RBCs to be a fluid. Due to these differences, the experimental analysis predicts more of a straight line than a parabolic shape when plotting the rate of deceleration against the current velocity. Our hypothesis is that the mathematical analysis overcompensates for stability in the system in the mid-range deceleration rates (10 RPM/s â 50 RPM/s).
Â For clinical applications, it may then be necessary to take the average between the mathematical and the experimental analyses so that the two-phase flow remains unmixed throughout the process and eliminate some of the overcompensation that the mathematical analysis predicts. This will lead to an optimized control of the system to allow for quick collection of bacteria from the blood.