Armin De Lazzer

Influence of lateral acceleration on capillary interfaces between parallel plates

The paper considers limits for the refill of capillary liquid vanes of propellant management systems for low gravity applications under the influence of residual acceleration. The limit of existence of a connected capillary liquid interfaces in the vanes is analyzed. A mathematical approach to describe the characteristics of a liquid meniscus in the vane is derived under the assumptions of a quasi static interface and negligible viscous and inertia forces. Analytical considerations allow to determine the maximum width of the liquid column within the vane that can be stabilized by capillary forces. If the width of the capillary vanes exceeds this limit, the vane will be only partially filled. The consecutive equation is solved analytically with the approximation that the lateral acceleration does not distort the asymptotic shape of the free surface extended along the edges of the vanes from a circular cylindrical shap. The resulting relations can readily be analyzed and provide very clear insight into the di.erent limits for the meniscus to exist. The results of the approximate solution are compared with numerical solutions considering the actual shape of the distorted free surface. Although the global shape of the existence chart and the lower limits of existence are rather well predicted by the approximate solution, considerable deviations from the numerical solution can be observed for the upper limits with repect to Bond number and maximum width of the vanes. The numerical solution therefore should be preferred. Additionally, the numerical solution does not provide mere existence criteria but real static (geometric) stability criteria. Experimentally, the behaviour of liquid interfaces in vanes was studied under microgravity conditions in a drop tower, using a micro-g centrifuge to impose variable lateral accelerations on the liquid column between the vanes. The results of the experiment are shown to be in very good agreement with the analytical predictions. The analytical approach presented thus yields a powerful means to determine static stability limits of interface configurations subject to lateral forces for arbitrary geometries of the supporting capillary.