Multidimensional open system for valveless pumping
Bull. Korean Math. Soc. 2015 Vol. 52, No. 6, 1973-2000
https://doi.org/10.4134/BKMS.2015.52.6.1973
Published online November 30, 2015
Eunok Jung, Do Wan Kim, Jonggul Lee, and Wanho Lee
Konkuk University, Inha University, Konkuk University, National Institute for Mathematical Sciences
Abstract : In this study, we present a multidimensional open system for valveless pumping (VP). This system consists of an elastic tube connected to two open tanks filled with a fluid under gravity. The two-dimensional elastic tube model is constructed based on the immersed boundary method, and the tank model is governed by a system of ordinary differential equations based on the work-energy principle. The flows into and out of the elastic tube are modeled in terms of the source/sink patches inside the tube. The fluid dynamics of this system is generated by the periodic compress-and-release action applied to an asymmetric region of the elastic tube. We have developed an algorithm to couple these partial differential equations and ordinary differential equations using the pressure-flow relationship and the linearity of the discretized Navier-Stokes equations. We have observed the most important feature of VP, namely, the existence of a unidirectional net flow in the system. Our computations are focused on the factors that strongly influence the occurrence of unidirectional flows, for example, the frequency, compression duration, and location of pumping. Based on these investigations, some case studies are performed to observe the details of the flow features.
Keywords : valveless pumping, pump system, immersed boundary method, multidimensional model, unidirectional flow
MSC numbers : 76D05, 76M20, 76M25, 92-08
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