Theoretical and experimental analysis of the equilibrium contours of liquid bridges of arbitrary shape

Abstract

The equilibrium shape of the liquid bridge interface is analyzed theoretically and experimentally. Both axisymmetric and nonaxisymmetric perturbations are considered. The axisymmetric deviations are those related to volume effects, the difference between the radii of the disks, and the axial forces acting on the liquid bridge. The nonaxisymmetric deviations are those due to the eccentricity of the disk and the action of lateral forces. The theoretical study is performed using three different techniques: (i) an analytical expansion around the cylindrical solution, (ii) a finite difference scheme, and (iii) an approximate numerical approach valid only for slight nonaxisymmetric deviations. The results of the three methods are compared systematically. There is a very good agreement between the analytical and the numerical approaches for contours which are close to cylindrical, and the agreement extends to configurations with only moderate deviations from cylindrical. Experiments are performed using the so-called neutral buoyancy or plateau technique. Theoretical and experimental contours are compared considering a wide range of values for the parameters characterizing the perturbations. In general, the finite difference method provides reasonably accurate predictions even for large deviations of the liquid bridge contour from cylindrical.

Minimum volume of long liquid bridges between noncoaxial, nonequal diameter circular disks under lateral acceleration

“…Such a volume reduction process is recorded by the CCD cameras, so that from the recorded images just before the breaking, the liquid bridge contours are determined by using standard interface detection techniques already used in liquid bridge problems, 6,7 and from these contours the liquid bridge volume, V ͑the minimum volume stability limit͒, as well as the volume of liquid between the smaller disk and the liquid bridge neck, V d , are calculated. To calculate such volumes it is assumed that liquid bridge cross sections are ellipses, which agrees with published analytical approximations for the shape of liquid bridge interfaces 3,8 ͑additional details can be obtained upon request from the authors͒. Cross-sectional area distributions, S͑z͒, of liquid bridges at stability limits corresponding to different values of the eccentricity are represented in Fig.…”

Sub-micrometer precision of optical imaging to locate the free surface of a micrometer fluid shape

“…The integration of the Young-Laplace equation was performed using the Runge-Kutta method, and the initial conditions and capillary pressure which lead to the boundary conditions and prescribed volume were found by the secant method. More details of the calculation can be found elsewhere [10].…”

“…Those solutions were obtained by considering the volume and fixed-contact-line boundary conditions measured from the images, and the literature values of the surface tension and liquid density. It can be easily verified that, due to the very small value of the Bond number, errors smaller than 10% in the surface tension and liquid density values do not affect significantly the solution to the Young-Laplace equation [10]. The integration of the Young-Laplace equation was performed using the Runge-Kutta method, and the initial conditions and capillary pressure which lead to the boundary conditions and prescribed volume were found by the secant method.…”

Gravity Effect on the Axisymmetric Drop Spreading

“…Myshkis et al (1987) investigated asymptotically some axisymmetric problems of capillary equilibrium. Some theoretical and experimental results for liquid bridges were obtained in (Montanero et al 2002).…”