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Fluid networks
Fluidic networks can display complex behavior such as multiple stable equilibrium states and emergence of spontaneous oscillations under steady inlet conditions. Such behavior has been observed or predicted in a number of different networks, both man-made and natural, at a variety of scales. Some examples include the flow of blood through the microcirculation, the flow of picoliter droplets through microfluidic devices, the flow of magma through lava tubes, two-phase flow in refrigeration systems and water flow in solar steam generators. While the physics differ, the underlying phenomena are often similar. In all systems, the primary sources of heterogeneity in the network are a non-linear viscosity function and the partition rule for how the fluid distributes at a single network node.
The existence of non-linear dynamics in a network with many inter-connections containing fluids with complex rheology (such as blood in the microvasculature) may seem unsurprising. However, even the simplest networks with ordinary fluids can demonstrate extraordinarily complex behavior. We are working to develop and verify a new general theory for describing heterogeneity within and the dynamical behavior of fluid networks. We are taking a building block approach, fully describing the behavior of simple network elements and then adding complexity in a systematic manner. Our theoretical study is closely integrated with an experimental track to verify the key predictions of the theory. Further, the experiments will generate data on flow in single tubes and at single nodes, which are a critical input to the theory. Without the experimental data, it would be impossible to map the mathematical theory to specific physical manifestations.
Funding:
NSF DMS 1211640 Non-linear dynamics in fluid networks.
Student researchers: John Arakaki, Jacqui Baca, Greg Edelston, David Gardner, Geeta Gubba, Deborah Hellen, Casey Karst, Kyle McConnaughay, Erika Weiler
Collaborators: John Geddes, Olin College. Nathan Karst, Babson College.
Publications:
- Geddes, J.B., Storey, B.D., Gardner, D., & Carr, R.T. 2010 Bistability in a simple fluid network due to viscosity contrast. Physical Review E, 81, 046316. ( Full Text, ArXiv)
- Karst, C.M., Storey, B.D. and Geddes, J.B., 2013 Laminar flow of two miscible fluids in a simple network, Physics of Fluids 25, 033601. (Full Text, arXiv)
- Karst, N.J., Storey, B.D. and Geddes, J.B., 2014 Spontaneous oscillations in simple fluid networks. SIAM Journal on Applied Dynamical Systems, 13, 157-180. (Full Text, arXiv)
- Storey, B.D., Hellen, D.V., Karst, N.J., and Geddes, J.B., 2015 Observation of spontaneous oscillations in simple two-fluid networks. Physical Review E 91, 023004. (Full Text, arXiv)
- Karst, N.J., Storey, B.D. and Geddes, J.B. Oscillations and multiple equilibria in microvascular networks. Submitted.
- Storey, B.D., Geddes, J.B., Gardner, D., and Carr, R.T. 2009 Bistability in a simple fluid network due to viscosity contrast. APS Division of Fluids Dynamics Meeting, Minneapolis. (abstract) (Presentation)
- Karst, C., Storey, B.D., and Geddes, J.B. 2011 Distribution of two miscible fluids at a T-junction APS Division of Fluid Dynamics Meeting, Baltimore, MD. (abstract) (Presentation)
- Hellen, D., Weiler, E., Karst, N., Geddes, J., Storey, B. 2013 Spontaneous oscillations in simple fluid networks. APS Division of Fluid Dynamics, Pittsburgh, PA. ( Abstract)