# Accurate numerical solutions to stationary free surface problems from capillarity

## Abstract

The paper considers two static problems from capillarity. The first one consists in the determination of the surface of a liquid in a capillary tube and the second in the computation of the shape of a sessile or pendent drop of liquid of a given volume, both configurations being considered in the gravitational field. From the mathematical point of view both problems are nonlinear two-point boundary value problems which include in their formulations additional geometrical unknowns, i.e., the so-called free boundary value problems. Computationally they are laborious problems since they involve non-normal Jacobian matrices. The resulting numerical difficulties are considerably reduced by treating these problems by a collocation method in conjunction with the continuation with respect to the parameters. The method is implemented by the MATLAB code bvp4c. The numerical evaluations of the free surfaces are in reasonable accordance with asymptotic estimations.

## Authors

Călin-Ioan Gheorghiu
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)

## Keywords

capillarity; free boundary value problem; liquid gas interface; sessile; pendent drop; collocation; matlab; bvp4c.

### References

See the expanding block below.

## Cite this paper as

C.I. Gheorghiu, Accurate numerical solutions to stationary free surface problems from capillarity, Phys. Part. Nuclei Lett., 5 (2008), 286-289.
doi: 10.1134/s154747710803031x

## PDF

##### Journal

Physics of Particles and Nuclei Letters

##### Publisher Name

SP MAIK Nauka/Interperiodica

1547-4771

1531-8567