Cylindrical Liquid Bridge Research Articles

A linear analysis of g-jitter effects on viscous cylindrical liquid bridges

This paper deals with the dynamics of isothermal, axisymmetric, cylindrical liquid columns held by capillary forces between two circular, concentric, solid disks; in particular, it deals with the dynamic response of the bridge to an excitation consisting of a small change in the value of the microgravity level. The problem has been solved by using a linearized one-dimensional Cosserat model, which includes viscosity effects, and with the axial velocity considered as constant in each section of the liquid bridge. The analysis has been performed by using the Laplace transform, and the time variation of both the axial velocity field and the liquid bridge interface have been obtained.

The periodic instability of thermocapillary convection in cylindrical liquid bridges

Thermocapillary convection (TC) in cylindrical liquid bridges (floating zones) of liquids with Prandtl numbers Pr=1, 7, and 49 is investigated experimentally. The zones have been heated from above or from below to study the influence of buoyant forces. Fourier analyses of temperature signals from zones covering systematically wide ranges of aspect ratios A and Marangoni numbers Ma have shown the existence of various forms of periodic and nonperiodic TC. This paper reports on periodic TC existing under certain conditions between the onset of time-dependent TC at the critical Marangoni number Mac and 7×Mac. From the measurements of the onset of periodic TC the dependence is reported for the threshold Mac and the period near the threshold τc on the aspect ratio. The development of periodic TC when further increasing Ma is shown by typical examples from measurements of the frequency and the amplitude of the oscillations. By correlation analyses from three temperature signals, different structures of periodic TC in the investigated A–Ma–Pr range were identified. Both the running waves with an azimuthal component (m≥1) and the axially running waves (m=0) were found and the findings of these and various other spatiotemporal structures of periodic TC were displayed in A–Ma/Mac state maps. These maps indicate as well the influence of the Prandtl number and of the buoyant forces on the preferred spatial structure of periodic TC, as discussed in the light of an already existing theory.

The effect of an axial electric field on the stability of a rotating dielectric cylindrical liquid bridge

The branching points of the shape families bifurcating from a cylindrical liquid bridge anchored on two plane-parallel electrodes, when subjected to rotation and an electric potential difference, are determined. It is shown that the cylindrical shape may be destabilized through either an axisymmetric mode or a C mode. The stable region in the parameter space is always enlarged as the electric field is increased.

Oscillatory response of a liquid column to counter-rotational excitation

A finite cylindrical liquid bridge consisting of incompressible and non-viscous liquid is subjected to a harmonic counter-rotational excitation of the top and bottom walls. The response of the free liquid surface and the velocity distribution has been determined and numerically evaluated. Since for a frictionless liquid the response exhibits singularities at the resonances, a semi-empirical damping was introduced in the resonance terms, of which the damping factor has to be determined by experiments.

Small amplitude thermocapillary flow and surface deformations in a liquid bridge

A cylindrical liquid bridge under asymmetric heating is investigated for small Reynolds, Prandtl, and capillary numbers. Flow field and surface deformation are calculated in terms of a Papkovich–Fadle series. The present analytical solution is in very good agreement with recent numerical results. A comparison with numerical simulations of the full Navier–Stokes equations without surface deformations is made.

Thermocapillary convection in liquid bridges: Solution structure and eddy motions

The steady thermocapillary convection in a cylindrical liquid bridge is considered in the absence of gravitational forces. The field equations are simplified by setting the Marangoni and Reynolds numbers equal to zero and the relative change in the surface tension is assumed to be very small, i.e., the appropriate capillary number is much less than unity. For suitable aspect ratios, there is a transition from a pattern of vortices determined by the applied surface temperature gradient to those of Moffatt type in the interior of the fluid. If the bridge is rotated, the equations can be modified by Coriolis terms but the parameter values are such that rotational effects tend to dominate the motion.

Non-linear oscillations of an inviscid liquid column under zero-gravity

For a frictionless cylindrical liquid bridge of finite length in zero-gravity the non-linear natural frequencies are determined for large free liquid surface amplitudes. The non-linear boundary conditions have been expanded up to terms of third order. It was found that the system exhibits a softening oscillation behavior, indicating that with increasing wave amplitudes the natural frequencies exhibit decreased magnitude as compared to linear theory. In addition higher modes and shorter liquid bridges show increased softening character.

Floating liquid zones

The aim of our experiment on the Spacelab Dl Mission was to study the stability of long liquid columns under microgravity. Nominal configuration was a cylindrical liquid bridge anchored at the edges of two equal solid discs, 35 mm in diameter. Mechanical stimuli were applied through the discs and the liquid outer shape recorded for analysis. Nominal experiment procedures [1] were similar to those proposed for Spacelab-1 (1983), where by wetting problems allowed only partial success [2]. The same Fluid Physics Module, but with corrected end discs and a manually operated syringe for liquid injection, was used.

The breaking of axisymmetric slender liquid bridges

Liquids held by surface tension forces can bridge the gap between two solid bodies placed not too far apart from each other. The equilibrium conditions and stability criteria for static, cylindrical liquid bridges are well known. However, the behaviour of an unstable liquid bridge, regarding both its transition toward breaking and the resulting configuration, is a matter for discussion. The dynamical problem of axisymmetric rupture of a long liquid bridge anchored at two equal coaxial disks is treated in this paper through the adoption of one-dimensional theories which are widely used in capillary jet problems.

Rotating finite liquid systems under zero-gravity

The coupled natural frequency equation for rotating cylindrical liquid bridges of finite length consisting of one liquid or two immiscible liquids are presented. Various important cases such as a single liquid around a center core, two immiscible liquids in a completely filled circular cylindrical container, two immiscible liquids exhibiting besides the interface also an outer free surface have been treated. Natural frequencies and surface- and interface elevations have been treated numerically.

Coupled oscillations of a solidly rotating liquid bridge

The coupled natural frequency equations for rotating and non-rotating cylindrical liquid bridges of finite and infinite length consisting of one liquid or two immiscible liquids are presented. Various important cases such as a single liquid with a free surface, two immiscible liquids in a completely filled circular cylindrical container, two immiscible liquids exhibiting besides the interface also an outer free surface and one liquid around a rigid cylindrical core are treated. Special cases such as infinite liquid columns or infinite media are presented for rotating and non-rotating systems. Some of the cases have been treated numerically, and for some of them the stability of the system has been determined.