Acoustic levitation can be achieved with many different types of objects. A form that is often investigated is that of a small object levitating between a vibrating surface and a fixed reflector [1,2,3]. In our experiment, we will instead focus on objects being levitated solely by a vibrating surface. In this case, it is the levitated object itself which may act as the reflector. The objects levitated in this case tends to be larger and have a more planar surface. It is with this type that we observe not only FFAL but also NFAL as well as attractive forces. With little experimentation under different gravity conditions and a lot of promising applications, this variant can benefit greatly of an investigation in hypergravity.

The conditions of the system, which affect the approximations that can be used and which sets of equations may be utilised, differs per system. These can be parameters including but not limited to: the reflectivity of the object, the elastic deformation of the plate, the sizes of the plate & object and the frequency the plate is driven at. Other approximations can regard the air inbetween the vibrating surface and the object, the material propagating the pressure. Examples of these properties are its viscosity or its thermodynamic properties, such as it being adiabatic [5,6,7] or isothermal [8,9,10].

Far-Field Acoustic Levitation describes the state of acoustic levitation wherein the levitated object is much larger than the acoustic wavelength. This method of levitation relies on the formation of a standing wave between the object’s surface and one or more transducers. This creates what is called Standing Wave Acoustic Levitation, or SWAL. To accomplish this, typically objects need to be in a resonance state - meaning they have to be located at an integer number of half-wavelengths away from the transducers [17].

For an object experiencing far-field acoustic levitation, the time-averaged radiation pressure is given by $$ \lt p_{r} \gt = \frac{1}{2 \rho_{0} c_{0}^{2}} \lt p^{2} \gt - \frac{\rho_{0} \lt \boldsymbol{u} \cdot \boldsymbol{u} \gt}{2}, $$ where \( \rho_{0} \) is the fluid density and \( c_{0} \) is the sound velocity in the fluid [17].

From the radiation pressure, the total radiation force can be obtained using, $$ \boldsymbol{F_{rad}} = \int_{S_{0}} \lt p_{2} \gt \boldsymbol{n} dS, $$ where \( \boldsymbol{n} \) is the surface normal vector and \( S_{0} \) is the integration surface [17].

In this regime, the shape of the object is known to affect its levitated behaviour. For instance, more vertically curved objects are known to have a higher horizontal stability while too much curvature can result in a lower vertical radiation force [17]. Similarly, objects with large radii of curvature are also known to levitate at slightly lower heights [18].

In contrast to all the previously mentioned forms of acoustic levitation, attractive acoustic levitation is used with the levitated object below rather than above the vibrating surface - resulting in the object being attracted to the surface. While the theory behind this phenomenon is not yet fully understood, several observations have been made that can be used to predict certain behaviours.

For instance, [18,19] have observed that the levitation force seems to be attractive for transducers and objects with diameters much smaller than the acoustic wavelength and vice-versa, indicating the possible existence of a ‘transition diameter’. Similarly, a ‘transition distance’ must also exist since the object never physically touches the transducer. The location of this transition distance depends both on the vibration frequency [21] and on the vibration amplitude, as stated by [19] who were able to model the transition using an axisymmetric CFD simulation rather than an acoustic model.

As is the case for far-field acoustic levitation, a horizontal restoring force can also be observed for attractive acoustic levitation. This force can be attributed to acoustic streaming which causes the time-averaged air pressure between the object and transducer to be lower than its ambient counterpart - essentially causing a self-centering effect [20]. In addition, a self-orienting effect was also observed, which can be calculated using $$ \tau_{rad} = - \int_{S_{0}} p_{rad} \boldsymbol{r} \times \boldsymbol{n} dS, $$ where \( \tau_{rad} \) is the radiation induced torque, \( \boldsymbol{n} \) is the surface normal vector, \( S_{0} \) is the integration surface, and \( \boldsymbol{r} \) is the unit vector pointing from the centre of mass of the object to its surface [20].