How to solve the axisymmetric Young-Laplace equation

$$\frac{z'(r)}{r \sqrt{z'(r)^2+1}}+\frac{z''(r)}{\left(z'(r)^2+1\right)^{3/2}}=z(r)$$

with b.c.s

$$z'(1)=-2$$$$z'(\infty)=0$$

where $z=Z/l_c$ and $r=R/l_c$ are dimensionless height and radius, $Z$, $R$ are the corresponding real height and radius, $l_c=\sqrt{\frac{\gamma }{g \rho }}$ is capillary length, $\gamma$ is surface tension, $g$ is the acceleration of gravity and $\rho$ is the density difference between phases. The solution of the problem describes the shape of meniscus outside of a cylinder, how can I obtain it with NDSolve?