Shape and the Stability of Pendent Drops

This book develops a unified analytical framework for understanding the shape and stability of pendent drops governed by hydrostatic balance, pinned boundaries, and Rayleigh–Taylor instability. Through a systematic treatment of both volume-controlled and pressure-controlled configurations, it shows how gravitational and capillary forces interact to produce turning points, symmetry-breaking transitions, and instability thresholds. By using potential-energy methods, variational principles, and symmetry arguments, the authors demonstrate that the full nonlinear behavior of drop configurations can be characterized without explicitly solving the associated eigenvalue problems. The resulting framework, based on a tractable one-dimensional model and extendable to axisymmetric and more general geometries, provides a clear approach for analyzing equilibrium drop behavior across a wide range of physical settings.

Lewis E. Johns is Professor Emeritus of Chemical Engineering at the University of Florida, Gainesville. He received his B.S. (1957) and Ph.D. (1964) in Chemical Engineering from Carnegie Institute of Technology. He worked as a research scientist at Dow Chemical in Midland, Michigan (1961–1967), and then joined the University of Florida, where he served on the faculty from 1967 to 2019. Ranga Narayanan is Distinguished Professor of Chemical Engineering at the University of Florida, Gainesville. He received his B.Tech. (Honors) in Chemical Engineering from the University of Madras (1971), and his M.S. (1973) and Ph.D. (1978) from the Illinois Institute of Technology. He worked as a research engineer at the Amoco Research Center in Naperville, Illinois (1976–1981), and has been on the faculty at the University of Florida since 1981.