The Mathematical Institute, University of Oxford, Eprints Archive

Computation of capillary surfaces for the Laplace–Young equation

Scott, C. F. and Sander, G. C. and Norbury, John (2005) Computation of capillary surfaces for the Laplace–Young equation. The Quarterly Journal of Mechanics and Applied Mathematics, 58 (2). pp. 201-212.


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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.

Item Type:Article
Subjects:O - Z > Partial differential equations
D - G > Fluid mechanics
Research Groups:Oxford Centre for Industrial and Applied Mathematics
ID Code:304
Deposited By: Gareth Wyn Jones
Deposited On:27 Oct 2006
Last Modified:29 May 2015 18:19

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