A mathematical model for the accurate computation of the shape of a three-dimensional axisymmetric gas bubble compressed between two horizontal plates is presented. An explicit form of the interface is given by the equation of minimal surfaces, based on an approximation of slow displacements. Conservation of the volume is guaranteed by the introduction of a multiplier. Contact angles are taken into account. The shape of the bubble is numerically solved with a quasi-Newton method that presents fast convergence properties. Numerical results are presented for various compression rates and contact angles.
© de Gruyter 2008