Approximate analytical solution to non-linear Young-Laplace equation with an infinite boundary condition

In this article we deal with the Young-Laplace differential equation in finite domain with an infinite boundary condition, describing the capillary pressure difference within the interface of two static (heterogeneous) fluids. Introducing a new state function, we first transform the equation to derive finite boundary conditions, then apply successive approximation to determine explicit solution. Numerical analysis shows the efficacy of the procedure already in the second approximation.