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M. Lyell and G. B. McFadden ACMD*

A liquid column is the configuration of interest in a number of past and (proposed) future experimental investigations in the microgravity environment. A liquid column typically consists of a finite volume of fluid suspended by surface tension between two co-axial solid disks. Even in the absence of gravity, the maximum attainable length of a liquid column is limited by stability considerations; for example, Lord Rayleigh showed that a cylindrical liquid column is unstable if its length exceeds its circumference. The dynamics of the slender column breakage are of interest to fluid physicists. From a technological view-point, the idealization of the float zone (utilized in crystal growing) as a liquid bridge (column) motivates study of this configuration. Interest in the response of the column interface to forcing is due to the acceleration environment which has been experienced in the microgravity environment of the space shuttle ``laboratory''.

In the initial phase of this work, the forcing is taken to be steady-state, and is oriented perpendicular to the longitudinal axis of the column. The forcing results in a column whose interface is deformed from that of a circular cylinder. The stability of this deformed column with respect to perturbations is then investigated.

The governing equations are those of conservation of mass and momentum. The analysis is inviscid and linearized and irrotational motion is assumed. Boundary conditions are those of zero normal velocity at the end disks of the column, and the anchored triple contact line condition. The linearized normal force balance and the kinematic condition are imposed on the fluid column interface. An integral equation for the conservation of volume also occurs.

Suitable nondimensionalization of the governing equations results in the appearance of the Bond number and a slenderness parameter in the equations. The velocity potential satisfies Laplace's equation. The problem reduces to one of satisfaction of the interface conditions at the column interface subject to the anchored triple contact line and conservation of volume conditions. A Galerkin-type expansion of the interface in a Fourier series (plus polynomial term) involving the spatial variable in the longitudinal direction is utilized. Orthogonal properties are employed to remove the spatial dependencies. It is found that azimuthal modes are coupled. The stability problem reduces to an infinite eigenvalue problem with the vector of unknowns composed of the coefficients of the interface and velocity field. This system is truncated and eigenfrequencies are determined.

Results to date indicate that the interface perturbations separate into two families of shapes; those odd or even about the midplane of the column. For a range of slenderness parameters and Bond numbers, the deformed column has been found to be unstable to interface perturbations in the case of the odd family. The even family is currently under investigation. It is planned to extend this work to include a time-periodic forcing term. The extended problem will involve Floquet analysis.

This work is being performed as part of the intended effort of Dr. Margaret Lyell while on sabbatical from the Mechanical and Aerospace Engineering Department of West Virginia University. Dr. Geoffrey McFadden has been involved in this effort also.