Mathematical modelling and experimental investigation of multi-stage valve-less impedance pumping system - Kara kuni, Sharsad (2018)
Impedance pumping is a simple valve-less pumping mechanism which offers a low energy, low noise alternative for conventional pumping at micro and macro scales. When a fluid-filled elastic tube is connected to rigid tanks, a net flow in either direction can be induced by periodically compressing the elastic section asymmetrically from the ends. The flow generated is due to the mismatch in acoustic impedance between the elastic and rigid regions. Prior works show a complex non-linear behaviour of the flow in response to the compression frequency, including distinct resonance peaks and reversals in flow direction. The research study explores the physics behind the fluid flow through a tube caused by impedance difference and derives a simple yet useful mathematical model for Two-tank system based on Energy conserving compartment model (ECCM). Parameters investigated include pinch frequency, pinch location, and physical parameters of rigid tank and flexible tube. Material properties such as elastic tube radius and tube thickness have been shown to have role in net flow characteristics under external pumping. With larger tube radius and smaller tube thickness, substantial increase in net flow generated has been achieved at lower external pumping frequency. Phase synchronization between external pumping pressure and fluid flux at the junction between elastic tube and tanks is identified as a key factor in determining the direction of net power. The model derived is extended to Multi-tank system and the flow behaviours under similar conditions have been compared to Two-tank system. Introduction of middle tank has affected the flow characteristics of Open-tank impedance pumping. With respect to terminal tanks, symmetry in net flow characteristics with equal magnitude but opposite direction has been observed for pinching locations of same distance from both ends of the tube. For such case in Multi-stage system also exhibited net flow of same magnitude and same direction with respect to middle tank. .Multi-Stage model could generate higher net flow rate compared to Two-tank system in all equivalent cases due to the capacitance effect of middle tank making it a promising advancement in valve-less pumping. Experimental works were conducted to validate the developed mathematical model. Experiments using Two-tank model achieved highest net flow with tank level differences of 1.10cm and-1.15cm for pumping positions C=15 and C=4 respectively while equal level difference of 1.07cm achieved in both directions using numerical methods. Experiments involving Multi-tank model has shown a maximum net flow rate of 1.81cm and-2.06cm for positions C15|15 and C4|4 respectively while height difference of 2.19cm in both directions has been achieved using numerical simulation. Both methods of investigation demonstrate resonant excitation frequency to be around 7.2-7.3 Hz. It has been established using numerical and experimental data that the net flow direction caused by a particular excitation frequency for a given pinching position, the value of resonant frequency, and the flow behavior of impedance pumping has been well described using a simple, yet reliable numerical model developed. Due to its simplicity; it could be promising to extend to more complicated structures such as in coronary blood flow where branching and varying geometries are present or in designing a more complex controller for valve-less pumping model.