The Sensitivity of a Non-Isothermal Liquid Bridge to Residual Acceleration

Liquid bridges appear in a variety of industrial processes, for example in the well-known floating-zone crystal growth technique. This crystal growth method has received much attention in recent years. In particular, there have been a variety of experiments on spacelab missions. These experiments are motivated by the fact that the microgravity environment affords the possibility of an increase in the stability of the melt meniscus and a reduction in buoyancy-driven convection. However, within the spacecraft there is a residual acceleration with variable magnitude and orientation. Under certain conditions, the response of the free surface of a liquid bridge to time-dependent residual accelerations will lead to zone breakage. In this paper the steady and unsteady behavior of isothermal and nonisothermal liquid bridge systems under normal and low gravity conditions is examined. The full nonlinear governing equations are recast in terms of a stream-function vorticity formulation together with a non-orthogonal coordinate transformation. The latter allows an irregular free boundary to coincide with a coordinate line (or surface) without the need to solve a coupled set of Laplace equations. The resulting equations are discretized using a centered finite difference scheme for space, and an Adams-Bashforth-Crank-Nicolson scheme is used for time. The equations are solved by the A.D.I. method and a Picard type iteration is used on the boundary condition for the balance of force normal to the free surface. For non-isothermal bridges, residual acceleration affects the system by causing internal buoyancy flows and fluctuations in the shape of the bridge which interact with the thermocapillary flow caused by surface tension gradients. For the cases examined, the shape of the bridge is found to be more sensitive to typical spacecraft accelerations than the buoyancy driven flow. The effect of thermocapillary flow on the surface shape is found to be small for the range of capillary and Reynolds numbers considered.