Figure below shows a micro gripper used for conveying very small objects (i.e. the spherical object in Figure) and putting them in desired place using capillary force principal in a liquid bridge.
To calculate the maximum weight that this capillary gripper can pull up, considering both "Laplace pressure term" applied to wet section in top of the sphere and "surface tension force" applied to the interface of liquid and air, one can write:
$F_T=\gamma . (contact\ line\ length)$
$(2\gamma/R) \pi R_a^2+2\pi R_a\gamma sin(\theta+\alpha)=4/3(\pi R^3\rho g)$
What condition should we apply to this equation in order to determine the maximum weight of sphere that gripper can pull up before the bridge breaks up.