In a [previous question](https://physics.stackexchange.com/questions/47021/how-to-find-out-the-maximum-radius-of-a-hole-that-can-keep-water-stay-in-a-conta), the following is answered in a general sense:

>Assume I have a inverse cone which holds 200ml water. I am going to cut the tip of the cone to create a small hole. How to calculate the maximum radius of the hole that the water will still stay in the container ?

However, what is not clear to me is whether the material of the vessel matters. The surface tension of water IN AIR is used in the answer ($\gamma \approx 7.3×10^{-2}~N/m$); however, I would think the surface tension and contact angle between the water and the cup have an effect. 

For example if I have a one cone cup that is hydrophobic and one cone cup that is hydrophilic will the hole size necessary to stop the water dripping out be the exact same?