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• Influence of free surface heat transfer on the onset of oscillatory instability. • Thermo-capillary flow in curved liquid bridges under microgravity conditions. • Critical value for the onset of oscillatory flow instability. • 'Dynamic mode decomposition' technique to reveal the inherent flow dynamics. • Quantification of each characteristic mode. Three-dimensional and oscillatory thermo-capillary flow in a liquid bridge of 5 cSt silicone oil (Pr = 67) has been numerically investigated by performing dynamic mode decomposition (DMD) analysis applied to the time-resolved thermal data generated by the 'method of snapshots'. For various heat transfer conditions defined on the free surface of the curved liquid bridge, a series of dynamic modes has been extracted to unfold the underlying physical mechanism that governs the considered dynamical system. Unstable and neutral modes primarily accountable for the transition to the supercritical state established in the liquid bridge have been identified by decomposing the acquired temperature disturbances into spatial and temporal coherent structures. Under microgravity conditions, unsteady and three-dimensional computations are carried out in a liquid bridge of different volume ratios (VR = 0.9 and 1.1) using the finite volume method (FVM) to capture the dynamical evolution of temperature disturbances at the onset of oscillatory instability. The present numerical investigation is mainly aimed at providing broader insight into the complex fluid dynamic processes associated with the oscillatory thermal convection by determining the growth/decay rate and frequency of each characteristic mode with the help of DMD spectra. For each oscillation pattern, the dominant behavior of oscillatory thermo-capillary flow is revealed by its coherent structures. The characteristic modes having more energy content (dominant modes) are also analyzed by the norm of modes || ϕ || by demonstrating the frequency spectra of DMD analysis. [ABSTRACT FROM AUTHOR]

• Effect of free surface heat loss on the onset of supercritical state in liquid bridge is studied. • Critical value for the onset of oscillatory flow instability is numerically found out. • Critical mode of oscillatory instability is properly categorized based on azimuthal wave number. • 'Dynamic mode decomposition' analysis is employed to reveal the inherent flow dynamics. • Quantification of each dynamic mode is performed using frequency spectrum distribution. Present work describes a numerical investigation concerning the response of oscillatory thermo-capillary convection to free surface heat loss in a cylindrical half floating zone of high Prandtl number liquid (Pr =67) under microgravity conditions. Unsteady and three-dimensional computations have been carried out in the liquid domain using the finite volume method (FVM) to reveal the oscillatory thermo-fluid dynamic regimes at the onset of instability. The influence of different free surface heat loss conditions on the bifurcation from the basic steady axisymmetric state has been discussed in terms of critical azimuthal wavenumber, m. The dynamic evolution of the temperature disturbances at supercritical conditions are characterized by 'pulsating' and 'rotating' modes of spatio-temporal convection. The development of counter-propagating hydrothermal waves in azimuthal direction is found to be followed by an even mode of convection characterised by m = 2. The liquid bridge system exhibiting the well-known transition from periodic (m =2) to quasi-periodic behaviour (m =1) with an increase in Biot number, Bi has been analysed from both spatial and temporal points of view. The existence of both symmetric and asymmetric modes of the supercritical state for different Bi are presented. The dominant fluid dynamic information of 3D oscillatory state are extracted from a specific set of disturbance temperature data by employing a data-driven computational technique 'dynamic mode decomposition' (DMD). Various neutral, stable and unstable dynamic modes responsible for bifurcation to the 3D supercritical state are depicted with the help of DMD spectrum and the frequency spectrum. [ABSTRACT FROM AUTHOR]

Abstract: An experiment in microgravity conditions aboard the TEXUS-23 mission was performed to obtain the deformation up to breakage of a cylindrical liquid column in isorotation around an eccentric axis. In previous work, breakage rotation speed was predicted by a numerical method. This method was validated by comparison with analytical and experimental results. The non-symmetric breakage of the liquid column observed in the experiment, however, was not explained by the combined effect of rotation and eccentricity. In this work we use an extension of that method that includes an axial gravitational field. Thus the combined effect of rotation, eccentricity and axial gravity in the stability threshold and in the shape of the liquid bridge is analyzed. In particular, this analysis has allowed us to understand the non-symmetric breakage of the liquid column in the experiment. [Copyright &y& Elsevier]

Abstract: The experimental results obtained in experiment “STACO” made on board the Spacelab D-2 are re-visited, with image-analysis tools not then available. The configuration consisted of a liquid bridge between two solid supporting discs. An expected breakage occurred during the experiment. The recorded images are analysed and the measured behaviour compared with the results of a three dimensional model of the liquid dynamics, obtaining a much better fit than with linear models. [Copyright &y& Elsevier]

Abstract: A cylindrical liquid bridge supported between two circular-shaped disks in isorotation is considered. The effect of an offset between the rotation axis and the axis of the two supporting disks (eccentricity) on the stability of the static liquid bridge is investigated. A numerical method is used to find stable and unstable shapes and to determine the stability limit for different values of eccentricity. The calculated stability limits are compared with analytical results, recovering the same behavior. Numerical results have been also compared with the results of an experiment aboard TEXUS-23, recovering the stability limit and the equilibrium shapes. [Copyright &y& Elsevier]

Abstract: Linear stability analysis was performed to study the mechanism of transition of thermocapillary convection in liquid bridges with liquid volume ratios ranging from 0.4 to 1.2, aspect ratio of 0.75 and Prandtl number of 100. 2-D governing equations were solved to obtain the steady axi-symmetric basic flow and temperature distributions. 3-D perturbation equations were discretized at the collocation grid points using the Chebyshev-collocation method. Eigenvalues and eigenfunctions were obtained by using the Q–R method. The predicted critical Marangoni numbers and critical frequencies were compared with data from space experiments. The disturbance of the temperature distribution on the free surface causes the onset of oscillatory convection. It is shown that the origin of instability is related to the hydrothermal origin for convections in large-Prandtl-number liquid bridges. [Copyright &y& Elsevier]

Abstract: One of the most puzzling results of an experiment on the stability of long liquid columns under microgravity, performed aboard Spacelab-D2 in 1993 and named STACO, aiming at the analysis of deformations of nearly cylindrical liquid columns under several mechanical disturbances, is revisited here. It corresponds to the unexplained breakage of an 85mm long liquid bridge of low viscosity silicone oil, established between unequal discs of 30 and 28mm, intended to counterbalance the expected deformation by residual acceleration found in previous flights, and left idle because the vibrations and oscillations to be applied afterwards were not started, for fear of premature breakage. A detailed image analysis is performed to extract the maximum amount of data, to be able to check against available theories for axisymmetric and non-axisymmetric deformations of a liquid column. [Copyright &y& Elsevier]

Abstract: A liquid bridge of 15.0mm length L and 3.0mm radius r (aspect ratio A = L/r =5) from 2 cSt silicone oil (Pr =28) was established under microgravity during the flight of the sounding rocket MAXUS-4. Four different temperature differences ΔT =7, 9, 10, 12K have been applied between the ends for sufficient time to reach steady state thermocapillary flow conditions. The aim of the experiment – to observe the onset of hydrothermal waves and to measure their features, like the waves phase speed and the angle between the wave vector and the applied temperature gradient – was reached. Moreover, we can report about the occurrence of a further hydrodynamic structure or instability occurring at the same time in this experiment, namely convection cells of the type of the Bénard–Marangoni instability, drifting in the surface flow from the hot towards the cold side. The latter instability has not been observed in the liquid bridges with A =1 investigated normally, because of geometric restrictions. The Bénard–Marangoni instability is due to the cooling of the free liquid surface in our experiment. [Copyright &y& Elsevier]