Abstract
Valveless pumping, also known as Liebau effect, can be described as the unidirectional flow of liquid in a system without valves that is caused by the asymmetry of placing of the periodically working pump. Recently, the research in this field has been reevoked, partially due to its possible application in nanotechnologies. In this paper, a configuration of one pipe and one tank is considered from the mathematical point of view. Qualitative properties of a class of nonlinear differential equations that model the assumed system configuration are investigated. New sufficient conditions for the existence of positive T-periodic solutions are given. Correspondingly, exponential stability of periodic solution is treated. Presented results are new. They extend and complement earlier ones in the literature.
Highlights
Valveless pumping represents a mechanism of fluid propagation in one direction in a system where valves are not presented
Working with patients suffering from severe aortic insufficiency led him to the idea that unidirectional blood propagation could be achieved without valves
He demonstrated a valveless pumping in a system consisting of two tanks connected by a rubber tube
Summary
Valveless pumping represents a mechanism of fluid propagation in one direction in a system where valves are not presented. Working with patients suffering from severe aortic insufficiency led him to the idea that unidirectional blood propagation could be achieved without valves To check his assumptions, he demonstrated a valveless pumping in a system consisting of two tanks connected by a rubber tube. We focus on the existence and exponential stability of a positive T-periodic solution of nonlinear differential equation (2) where a ≥ 0, α, β ∈ (0, ∞), and q, r ∈ C([t0, ∞), R). The obtained results are, applied on the problem of valveless pumping in one pipe–one tank configuration (Section 4). The results for the existence of positive T-periodic solution and its exponential stability, presented in this paper, are new, extending and complementing some earlier ones in the literature
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
