Maximal liquid bridges between horizontal cylinders.
We investigate two-dimensional liquid bridges trapped between pairs of identical horizontal cylinders. The cylinders support forces owing to surface tension and hydrostatic pressure that balance the weight of the liquid. The shape of the liquid bridge is determined by analytically solving the nonlinear Laplace-Young equation. Parameters that maximize the trapping capacity (defined as the cross-sectional area of the liquid bridge) are then determined. The results show that these parameters can be approximated with simple relationships when the radius of the cylinders is small compared with the capillary length. For such small cylinders, liquid bridges with the largest cross-sectional area occur when the centre-to-centre distance between the cylinders is approximately twice the capillary length. The maximum trapping capacity for a pair of cylinders at a given separation is linearly related to the separation when it is small compared with the capillary length. The meniscus slope angle of the largest liquid bridge produced in this regime is also a linear function of the separation. We additionally derive approximate solutions for the profile of a liquid bridge, using the linearized Laplace-Young equation. These solutions analytically verify the above-mentioned relationships obtained for the maximization of the trapping capacity.
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics , University of Cambridge, Centre for Mathematical Sciences , Wilberforce Road, Cambridge CB3 0WA, UK.
Himantha
0000-0001-5149-3712
H
Cooray
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK; Faculty of Science, University of Bristol, Bristol BS8 1UH, UK; School of Mathematics and Statistics, University of New South Wales, Sydney, New South Wales 2052, Australia.
Herbert E
HE
Huppert
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK; BP Institute, Bullard Laboratories, Bullard Laboratories, University of Cambridge, Madingley Road, Cambridge CB3 0EZ, UK; Department of Earth Sciences, Bullard Laboratories, University of Cambridge, Madingley Road, Cambridge CB3 0EZ, UK.
Jerome A
JA
Neufeld
Laplace–Young equation; fluid statics; liquid bridges; liquid interfaces