Fluid flow between active elastic plates

Abstract

We propose a model of a channel flow between actively moving elastic plates as a framework for blood flow in active human arteries. The main difference from extant models is that our model is autonomous. It is a nonlinear partial differential equation governing the deformation of the plates involving sixth order spatial derivative. The equation has a similar structure to the model we proposed earlier to simulate another active system-spinning combustion front. References

• A. J. Roberts. A One-dimensional Introduction to Continuum Mechanics. World Scientific. Singapore, 1994.
• Strunin, D. V., Autosoliton model of the spinning fronts of reaction, IMA J. Appl. Math., 63, 1999, 163--177. doi:10.1093/imamat/63.2.163
• Huang, R. and Suo, Z., Wrinkling of a compressed elastic film on a viscous layer, J. Appl. Phys., 91, 2002, 1135--1142. doi:10.1063/1.1427407
• King, J. R., The isolation oxidation of silicon: the reaction-controlled case, SIAM J. Appl. Math., 49, 1989, 1064--1080. doi:10.1137/0149064
• L. D. Landau and E. M. Lifshitz. Theory of Elasticity. Pergamon. London, 1959, 57--60.
• S. Timoshenko and S. Woinowsky-Krieger. Theory of Plates and Shells. McGraw--Hill. New York, 1987.
• Sherwin, S. J., Formaggia, L., Peiro, J. and Franke, V., Computational modelling of 1D blood flow with variable mechanical properties and its application to the simulation of wave propagation in the human arterial system, Int. J. Numer. Meth. Fluids, 43, 2003, 673--700. doi:10.1002/fld.543
• C. Kleinstreuer. Biofluid Dynamics. Taylor and Francis. Boca Raton, 2006.
• Olufsen, M. S., Peskin, C. S., Kim W. Y., Pedersen, E. M., Nadim, A. and Larsen, J., Numerical simulation and experimental validation of blood flow in arteries with structured-tree outflow conditions, Annals of Biomedical Engineering, 28, 2000, 1281--1299. doi:10.1114/1.1326031
• Matthys, K. S., Alastruey, J., Peiro, J., Khir, A. W., Segers, P., Verdonck, P. R., Parker, K. H. and Sherwin, S. J., Pulse wave propagation in a model human arterial network: Assessment of 1-D numerical simulations against in vitro measurements, J. Biomech., 40, 2007, 3476--3486. doi:10.1016/j.biomech.2007.05.027