Faraday instability in a near-critical fluid under weightlessness

Finite-size effects on pattern selection in immiscible fluids subjected to horizontal vibrations in weightlessness

A detailed numerical investigation of frozen wave pattern selection in finite rectangular containers under microgravity conditions is presented. The column growth cycle controlling mode transitions is described and the instability diagram showing selected wave number as function of the vibrational velocity is obtained. In contrast to the continuous monotonic dependence of pattern wave number on forcing predicted by linear inviscid theory in the limit of infinitely long containers, the pattern selection process in finite domains is characterized by solution branches that persist over discrete forcing intervals. We describe how properties of the selected frozen wave pattern, including the finite critical forcing value, depend on container length. In long containers, a transition from nearly symmetric to asymmetric columnar development is found at sufficiently high forcing values, with the loss of (approximate) reflection symmetry evident in the mean flow associated with the transient growth of the pattern. The effect of container height is considered separately, in the limit of both shallow and deep layers. Shallow layers suppress the development of long-wave perturbations leading to higher wave-number patterns whose growth may be associated with an asymmetric series of collisions between developing columns and container boundaries. In thick layers, lower pattern wave numbers are observed and, although the column growth is on average more regular, the final state is often asymmetric. Finally, we compare our results with the dependence on container aspect ratio Γ=L/2H predicted by inviscid theory. For Γ≳2, finite-size effects are reasonably weak and the numerically obtained thresholds are similar to but slightly higher than the theoretical values, most likely due to viscous effects. For Γ≲2, finite-size effects come to the fore and onset is significantly delayed.

Band instability in near-critical fluids subjected to vibration under weightlessness

Periodical patterns (bands) developing at the interface of two immiscible fluids under vibration parallel to interface are observed under zero-gravity conditions. Fluids are slightly below their liquid-vapor critical point where they behave in a scaled, universal manner. In addition, liquid and vapor densities are close and surface tension is very low. Linear stability analyses and direct numerical simulation show that this instability, although comparable to the frozen wave instability observed in a gravity field, is nonetheless noticeably different when gravity becomes zero. In particular, the neutral curve minimum corresponds to the long-wave perturbations with k=0 and zero dimensionless vibrational parameter, corresponding to no instability threshold. The pattern wavelength thus corresponds to the wavelength of the perturbations with maximal growth rate. This wavelength differs substantially from the neutral perturbations wavelength at the same vibrational parameter value. The role of viscosity is highlighted in the pattern formation, with a critical wavelength dependence on vibration parameters that strongly depends on viscosity. These results compare well with experimental observations performed in the liquid-vapor phases near the critical point of CO_{2} (in weightlessness) and H_{2} (under magnetic levitation).