Counter-intuitive phenomena that arise in fluids under the action of vibration have attracted considerable research interest since the 1950s. For example, in a vibrating volume of fluid, gas bubbles can sink and heavy particles can rise1–3. Moreover, a layer of fluid can be levitated above a layer of air by shaking the system vertically at a relatively high frequency (of the order of 100 hertz or more)4. Writing in Nature, Apffel et al.5 report another remarkable phenomenon associated with a vibrating, levitated layer of fluid: objects can float upside down on the lower interface of the fluid, as if gravity were inverted (Fig. 1). These phenomena have strong potential for practical use3, for example in systems that involve gas bubbles suspended in fluids (such as bubble column reactors used for gas–liquid reactions), and for the segregation and transport of material inclusions in fluids (as used in mineral processing and waste-water treatment).
The extraordinary behaviours of vibrating fluids are just a small fraction of the surprising phenomena that arise as a result of high-frequency vibrations more generally. Probably the most well-documented examples are the Stephenson–Kapitza pendulum6, in which a rigid pendulum balances upside down from a vibrating point of suspension, and the Chelomei pendulum2, in which a washer that can slide along a rod seems to ‘float’ when the rod is vibrated vertically.
Special branches of the fields of mechanics and rheology have long been established to study the physical effects of high-frequency vibrations7. Such studies have revealed that time-averaged forces, known as vibrational forces, occur in vibrating systems in addition to the forces that apply in analogous non-vibrating systems. It is these vibrational forces that lead to seemingly paradoxical phenomena, including the sinking of gas bubbles in vibrating liquids, and the levitation of fluid layers above air2,3. Vibrational forces have been used in practical applications, for example to enable the self-synchronization of the rotation of several bodies, and to separate and transport materials7.
Apffel and colleagues now add inverse floating to the list of what vibrational forces can do. In their experiments, the authors filled a container with a viscous liquid, and used a shaking device to vibrate the liquid vertically at high frequency. Air bubbles added to the liquid below a critical depth sank to the bottom of the container. The authors inflated sunken bubbles to produce a stable air layer with the liquid levitating on top. The maximum volume of levitating liquid studied was 0.5 litres, and the maximum width was 20 centimetres. Remarkably, Apffel et al. observed that small objects (up to 7 grams in mass and 2.5 cm in length or diameter) floated upside down on the lower side of the air–liquid interface (Fig. 1).
To explain their observations, the authors suggest that the effective gravity exerted on the fluid — the apparent gravitational force that acts on a vertically accelerating system — as well as that exerted on submerged and floating bodies, oscillates with time when the system is vibrated vertically. The immersed volume of the body floating on the lower interface of the fluid also oscillates with time. Apffel and co-workers propose that this causes a time-averaged force to be applied to the body. This force has an ‘antigravity’ effect that, for vertical vibrations of frequencies of 80 Hz or above, enables the body to float on the lower interface of the fluid. As is the case for the Stephenson–Kapitza pendulum6 and the Chelomei pendulum2, the stable states of Apffel and colleagues’ vibrating system correspond to potential-energy maxima, rather than minima.
The authors suggest a relatively simple mathematical description of the inverse-floating phenomenon. This description involves some simplifying assumptions, for example by supposing that the relationship between the pressure in the air layer and the height of the layer is linear. The simplifications somewhat limit the accuracy with which the authors’ theory describes the behaviour of the experimental system, leading to minor discrepancies with the observations.
It is also worth noting that the speed of sound in gas-saturated fluids is surprisingly low for a wide range of volumetric gas concentrations, and this has also been observed to produce antigravity effects3. For example, for air concentrations of 30–70%, the speed of sound is only 20 metres per second3; this compares with about 340 m s–1 in air, and about 1,450 m s–1 in water. When the speed of sound is this low, one or even several longitudinal (compression) standing waves can fit into a vibrating volume 1 m in height at frequencies of the order of 50 Hz. Heavy, rigid particles and gas bubbles are attracted to the points of minimum and maximum amplitude of these standing waves, leading to gravity-countering effects.
Apffel and colleagues’ work suggests that many remarkable phenomena arising in vibrating mechanical systems are yet to be revealed and explained, particularly at interfaces between gases and fluids, implying great potential for future research. More broadly, the analysis of the effects of high-frequency excitations on systems from other fields of science, such as chemistry, physics and biology, is another promising research topic8. In these systems, the excitation can be any periodic change in a property of the environment or medium in which a process is taking place. It will be exciting to discover what counter-intuitive phenomena can be induced by high-frequency excitations in non-mechanical systems — is there a chemical or biological counterpart of inverse gravity?
Nature 585, 31-32 (2020)