Brian Storey, John Geddes and I just submitted a piece of work on spontaneous oscillations in a simple network containing two miscible fluids of differing viscosities. We catalogue spontaneous oscillations and numerically continue these behaviors through the high dimensional parameter space of the system. This technique allows us to construct interesting representations of the phase space that should be helpful in confirming our predictions. The preprint is located on arXiv.
The application that got us interested in the topic is microvascular blood flow. Here, the plasma is the less viscous constituent, and the red blood cells are the more viscous constituent. Experimentalists had since at least the early 1920s observed oscillations and direction reversal in blood flow in vivo. It seems like a natural assumption that these behaviors could be attributed to periodic forcing from the heart beat and/or regulation of the diameter of vessels to control flow. Our work has shown that even simple, geometrically static networks with no forcing can exhibit rich behaviors.
It's really interesting from an applied mathematical point of view that this same model applies to a lot of different physical systems, including lava flow and petroleum processing. In all these cases, there are two key components that lead to interesting behavior. First, the effective viscosity of the fluid is nonlinear with respect to the concentrations of the two fluids. Second, when a branch in the network splits into two daughter branches, the distribution of fluid phases in the daughter branches, known as skimming, can be a complicated function depending on the concentrations of the phases, the flow rate in the branch, and the geometry of the junction.
Recent work (by John, Brian and m has developed an empirical skimming model for a tabletop experimental setup. This should allow us to
It's really interesting from an applied mathematical point of view that this same model applies to a lot of different physical systems, including lava flow and petroleum processing. In all these cases, there are two key components that lead to interesting behavior. First, the effective viscosity of the fluid is nonlinear with respect to the concentrations of the two fluids. Second, when a branch in the network splits into two daughter branches, the distribution of fluid phases in the daughter branches, known as skimming, can be a complicated function depending on the concentrations of the phases, the flow rate in the branch, and the geometry of the junction.
Recent work (by John, Brian and m has developed an empirical skimming model for a tabletop experimental setup. This should allow us to
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