The profiles of axially symmetric menisci

The shape and forces of axisymmetric menisci have been calculated for sessile drops, pendant drops and liquid bridge profiles. The tables of Bashforth & Adams have been extended into the liquid bridge region by generating profiles beyond the 180 degrees angle of their study, and into regions covered by a much wider range of shape factor. Numerical integration of the Laplace equation was performed by using a first-order method originally proposed by Lord Kelvin but adapted and modified for use with high-speed computers. Tables have also been generated, by the same techniques, of profiles of a wide range of asixymmetric menisci that do not cross the axis of symmetry. Such tables include the shape of a meniscus formed by a rod at a free liquid surface. This second group of tables greatly extended the region over which liquid bridge shapes could be obtained. Closed menisci of the type of Bashforth & Adam's tables are defined by one shape factor $\beta $, but open menisci require two parameters to identify their shape. The general properties of these shape factors are discussed. The volume of any part of the meniscus bounded by two horizontal planes has also been derived and its relationship to the forces acting between the planes is given. The tables (400 pages)$\dagger $ are not reproduced here but the main features of these profile shapes are summarized and discussed with the aid of graphs.