A two-chamber model of valveless pumping using the immersed boundary method

We present a new mathematical model of valveless pumping for a tube with two elastic chambers, which is motivated by the Liebau's two-tank model. The tube consists of partially soft and partially (almost) rigid and the periodic pumping is applied at an 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 have observed the existence of a unidirectional mean flow and the dependence of mean flows on the frequency and the compression duration of the periodic pumping. We are able to explain the occurrence of local maximum or minimum mean flows due to the resonances of the system.