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Computation of capillary surfaces for the Laplace–Young equation

By C. F. Scott, G. C. Sander and John Norbury


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

Topics: Partial differential equations, Fluid mechanics
Year: 2005
DOI identifier: 10.1093/qjmamj/hbi005
OAI identifier:

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