an:05490840
Zbl 1163.76011
Lee, Sunmi; Jung, Eunok
A two-chamber model of valveless pumping using the immersed boundary method
EN
Appl. Math. Comput. 206, No. 2, 876-884 (2008).
00243606
2008
j
76D05 76Z05 76M25 76M20 74F10 92C10
Liebau two-tank model; unidirectional mean flow; resonances
Summary: We present a new mathematical model of valveless pumping for a tube with two elastic chambers, which is motivated by the Liebau two-tank model [\textit{G. Liebau}, Naturwissenschaften 41, 327--328 (1954)]. The tube is partially soft and partially (almost) rigid, and the periodic pumping is applied at the asymmetric location of the soft tube. The immersed boundary method is used to investigate the important characteristics of valveless pumping as the previous experiments and mathematical models have been discovered. We observe the existence of a unidirectional mean flow and the dependence of mean flows on the frequency and on the compression duration of periodic pumping. We are able to explain the occurrence of local maximum or minimum mean flows due to the resonances of the system.