# Study of the behavior of liquid menisci formed during dipping-extraction of a solid rod in a free liquid surface

#### Abstract

Several studies involving the shapes and stability of liquid menisci formed during the dipping and extraction of a solid rod from a liquid basin have been reported in the literature. This problem is referred to as the 'rod in free surface' problem. However, all of the studies were conducted by assuming that the radius of the basin is very large (i.e., infinite, relative to the rod) and that, at the extremity of the basin, the slope and/or curvature of the liquid surface are both zero. Under the former assumption, the volume conservation condition is satisfied by assuming that the free liquid surface level remains the same as the original level; this simplifies the solution of the governing equations. Both of these assumptions, which are difficult to satisfy in most practical applications, impose severe restrictions on the results that have been reported. In this study, a variational finite element method is employed to study the shapes and stability of liquid menisci formed during the extraction of a vertical rod with circular cross section from a liquid contained in a circular basin with finite radius. Results showing the effects of the radius ratio (i.e., ratio of the radius of the basin to the radius of the solid rod), the Bond number, which involves the density and surface tension of the liquid and the radius of the solid rod, and the contact angle of the liquid at the outer extremity of the basin on the meniscus profile and stability, are presented. The results are compared to those found in the literature (for special cases) and those obtained experimentally in this study. These results indicate that the critical extraction height (i.e., the distance between the undersurface of the vertical solid rod and original free liquid surface), at which the liquid meniscus becomes unstable, increases with increasing radius ratio and reaches a limiting value equal to that for the unbounded case. Also, for the range of radius ratios and bond numbers investigated in this research, the critical extraction height is independent of the contact angle at the outer extremity of the basin.

#### Recommended Citation

Su, Jun, "Study of the behavior of liquid menisci formed during dipping-extraction of a solid rod in a free liquid surface" (2007). *Dissertations (1962 - 2010) Access via Proquest Digital Dissertations*. AAI3277081.

http://epublications.marquette.edu/dissertations/AAI3277081