# Vibrated Fluids in Microgravity

The fluids research program at E-USOC is funded by the Ministerio de Economía y Competitividad with the purpose of **investigating fluid phenomena induced by vibrations**, which play an important role in microgravity environments such as the International Space Station.

**Understanding the effects of vibrations** on confined fluid systems, whether gravity comes into play or not, **is critical to numerous scientific and engineering applications in physics, chemistry, and biology**. The response of the system naturally depends on the physical properties of the fluid(s) involved, on the properties of the domain (boundary conditions), and on the characteristics of the applied forcing (frequency, amplitude, orientation). Periodic forcing, for example, can induce free surface instabilities like Faraday waves, cross-waves, and frozen waves, while suppressing other phenomena like the Rayleigh-Taylor instability.

Pattern selection refers to the competition that typically occurs when the excited modes of the system occupy a lengthscale that is small compared to the extent of the domain, meaning that multiple states, with different spatial wavevectors and orientations, onset at (nearly) the same time. The fluid configuration that has attracted the most research in this area is the vertically forced Faraday system, where an open container of fluid of uniform depth with a stable flat interface is vibrated in a purely vertical fashion (i.e., perpendicular to the flat surface). These conditions, which imply that the initial state and the forcing are homogeneous and isotropic (in the extended limit), lead to theoretical simplifications, and conclusions, specific to that symmetry. More general forcing configurations, or more realistic treatment of the boundaries or meniscus waves, require these assumptions to be relaxed or dropped altogether. This is especially true in microgravity environments where the familiar preference for flat horizontal surfaces is absent.

###### Experiment

Experiments are performed using open containers of DC200 silicone oil or water. The container can be vibrated horizontally or vertically, or with any combination of the two. Measurements of the surface wave patterns are obtained using a free surface synthetic Schlieren technique (Moisy et al. Exp. Fluids 46, 1021-1036, 2009).

*Asymmetric surface wave pattern with combined horizontal and vertical forcing at 50Hz*

###### Results

A primary experimental observation is the preference for obliquely oriented (rotated) cross-wave patterns with horizontally forcing [1]. The angle of these patterns depends somewhat on boundary conditions and other experimental parameters, but seems to be a very general and robust characteristic of subharmonic waves in large-aspect-ratio systems driven by moderate to high frequencies like those used here (30-100 Hz). Another interesting result with horizontally forced systems is the appearance of modulated (quasiperiodic) solutions [3] related to the interaction of waves emanating from each endwall. These slowly modulated solutions alternate between one-sided and two-sided patterns and are very sensitive to the strength of the interaction (length of container, damping, detuning). With combined horizontal and vertical forcing, a variety of interesting new patterns and modulated solutions can be obtained and controlled with the forcing parameters.

###### Theory

An essential feature of any applicable theory in this regime is the distributed parametric forcing mechanism concentrated near each endwall. We have extended previous cross-wave theory, which considered this mechanism to be sufficiently localized to be treated simply as a boundary condition on the slow spatial scale characteristic of streamwise variation. The nonlinear Schrodinger equation with spatially distributed forcing obtained is in reasonably good agreement with experimentally measured thresholds [3]. Other interesting features arising from the presence of distributed forcing include families of "cross-wave" modes (modulated or not) with the same crosswise mode number but separated by the number of oscillations experienced within the (supercritical) forced region and, when interaction is strong, additional branches of modulated solutions with distinct frequencies [2]. Much of the phenomenology can be understood in the context of simplified models that include essential features (like distributed forcing) and in terms of symmetry-breaking. Numerical simulations are used extensively, particularly to understand how the surface wave instabilities investigated in the laboratory change in the absence of gravity. In microgravity environments, vibrations also cause a large scale reorientation of the fluid surface – configurations known as "vibroequilibria". Subsequent surface wave instabilities cannot be as easily separated into "Faraday wave" and "cross-wave" types and may also couple dynamically to the underlying vibroequilibria state.

###### Selected references

- J. Porter, I. Tinao, A. Laverón-Simavilla, and C. A. Lopez. Pattern selection in a horizontally vibrated container. Fluid Dyn. Res. 44, 065501 (2012).
- J. Porter, I. Tinao, A. Laverón-Simavilla, and J. Rodríguez. Onset patterns in a simple model of localized parametric forcing. Phys. Rev. E 88, 042913 (2013).
- I. Tinao, J. Porter, A. Laverón-Simavilla, and J. Fernández. Cross-waves excited by distributed forcing in the gravity-capillary regime. Phys. Fluids 26, 024111 (2014).