Acoustically switchable droplet ring resonators for droplet-based microfluidics
in: Temporal Proceedings (2013)
In our contribution we report on the development of a novel microfluidic operation unit for acoustically actuated resonance-based droplet sorting and stacking – a microfluidic ring resonator. Key element of the resonator is a circular microchannel element connected with an inlet and an outlet at opposite positions thus forming two branches of identical lengths. Branches are equipped with an integrated nozzle of different diameters for each branch. The first arriving droplet from inlet is automatically guided towards the branch with the larger nozzle diameter. At this stricture the droplet stops and the subsequent flow is bypassed through the opposite branch with the narrower nozzle. The second arriving droplet is guided through this branch and is stopped at the nozzle with the smaller diameter. Now the subsequent flow pushes the first droplet through the nozzle with the larger diameter due to the smaller Laplace pressure generated at the interface inside the nozzle with the larger diameter. All the other following droplets are pushed through this nozzle while the droplet catched at the narrower nozzle remains at its position. This droplet can be released on-demand by an acoustic event with the resonant frequency of the microfluidic resonator. A microfluidic ring resonator with resonance frequencies ranging from 0.1 to severalkHz can be implemented by an circular microchannel structure with an integrated nozzle. The system behaves as a damped resonator where the back driving force is generated by the pinned interface in dependency on it's volume elongation. The mass of the fluid inside the circular structure provides the inertial components whereas the viscous losses inside the fluid provide the damping. Thus, the system can be described by the standard second order differential equation of an oscillator with the pressure as potential and the volume flow as the transport unit. At laminar flow, expressed by low Reynolds numbers, the coefficients can be considered as constants. Mathematical models have been derived for the described system. Dependent on the geometric and hydrodynamic parameters of the applied fluids the resonator can be tuned towards a damped resonator, a critically damped, or an over damped resonator. Due to the non-linear correlation between the interface elongation volume and Laplace pressure, generated at the interface, an inharmonic oscillation is observed. The experimental data on resonator frequency and critical break-through parameters are in satisfying agreement with the mathematical models. Therefore, the geometric resonator properties can be determined prior preparation of the unit from the envisaged resonance frequency, operating conditions, and the fluid properties. This allows the model-based design of stacked arrangements of multiple resonators that perform sophisticated droplet sorting and stacking tasks.