Liquid in a tube oscillating along its axis

• The oscillations under consideration have been analyzed numerically.
• Two different regimes of oscillations have been identified.
• The results are of interest in the context of the QCM-D sensors.

The Quartz Crystal Microbalance with Dissipation (QCM-D) sensing technique has become widely used to study various supported thin films and adsorption of biological macromolecules, nanoparticles, aggregates, and cells. Such sensing, based on tracking shear oscillations of a piezoelectric crystal, can be employed in situations which are far beyond conventional ones. For example, one can deposit tubes on the surface of a sensor, orient them along the direction of the sensor surface oscillations, and study liquid oscillations inside the oscillating tubes. Herein, we illustrate and classify theoretically the regimes of liquid oscillations in this case. In particular, we identify and scrutinize the transition from the regime with appreciable gradients along the radial coordinate, which are qualitatively similar to those near the oscillating flat interface, to the regime where the liquid oscillates nearly coherently in the whole tube. The results are not only of relevance for the specific case of nanotubes but also for studies of certain mesoporous samples.