Nonlinear wave interactions in pulsatile nanofluidics due to bending nanotube vibration: Net flow induced by the multiple resonances of complex pressure gradients and coupled fluid-tube forces

We study the dynamics of Newtonian fluids subject to complex pressure gradients within bent oscillating nanotubes. Pressure gradients with four different purely oscillatory time profiles are explored by theoretical means, in order to unveil the mechanism of interaction between the characteristic time of tube vibration and the multiple characteristic times involved in the complex pressure signal. We find out that all the characteristic times of the system are mixed as a consequence of the nonlinear fluid-tube coupling caused by Coriolis force, which is induced by the local nanotube rotation and is distinctive of micro- and nanometric confinements subject to vibration. Our computations predict a vast range of resonances, not only the ones expected when the magnitude of pressure frequency is close to the magnitude of tube frequency, but also resonances where the pressure frequency is considerably lower than the tube frequency. These resonances could be exploited to obtain controllable combined oscillatory and net flow rates, even when the actuator's frequencies cannot reach the tube vibration frequencies. Our findings provide a theoretical framework for future applications in generation of complex oscillatory and net flow rates with a single actuator, using relatively low instrumentation.