Q. Jl Mech. Appl. Math. (2005) 58 (2), 201–212 © Oxford University Press 2005; all rights reserved.
Computation of capillary surfaces for the Laplace–Young equation
( 1 Department of Civil & Building Engineering, Loughborough University, Loughborough LE11 3TU, 2 The Mathematical Institute, Oxford University, 24-29 St Giles', Oxford OX1 3LB )
A novel hybrid finite-element/finite-volume numerical method is developed to determine the capillary rise of a liquid with a free surface (under surface tension and gravitational forces). The few known exact analytical solutions are used to verify the numerical computations and establish their accuracy for a range of liquid contact angles. The numerical method is then used to ascertain the limitations of a number of theoretical approximations to solutions for the capillary rise in the linearized limit, for special geometries such as plane walls, concentric cylinders and in a wedge of arbitrary included angle. The existence of a critical wedge angle for a given contact angle is verified. However, the effect of slight practical rounding of wedge corners dramatically reduces the theoretical corner height.
Received 12 March 2004. Revise 2 August 2004.
