Dynamical responses of a valveless fluid loop excited by the impact of a compression

Valveless pumping assists in fluid transport in various organisms and engineering systems. In a previous work, to study the actuator impact effects on valveless pumping, we constructed a piecewise-linear lumped-parameter model for a closed-loop system, which consists of two distensible fluid reservoirs connected by two rigid tubes. The preliminary asymptotic and numerical results of that work indicated that the system dynamics is rather rich and complex, and strongly depends upon the driving frequency of the actuator (which periodically compresses one of the distensible reservoirs) and other system parameters. Here, a more comprehensive numerical study on the aforementioned model is carried out, so as to clarify how many different types of system responses can be excited, and to locate the parameter boundaries within which each type exists. Moreover, by examining the driving-frequency dependences of a number of characteristic phases (such as the phase of the compression cycle at which the actuator collides with or separates from the distensible reservoir it acts upon), the interrelations between different types of system responses are identified.