*Before introducing my question I would like to outline the fact that I'm a coder, so I can be wrong when using some kind of terminology.*

What is a good model for computing the flow, the shape and all the geometric properties of the water? ( and other similar liquids in general, like mixtures based on water or some more oily and viscous substances )

I assume that this kind of simulation will be based on particles, which means entities that are part of the domain that defines the "drop" of water, but what I need is the math, the equations and the mathematical model/s; I have no idea what is the math behind a liquid that meets a surface and if there is any algorithm or model that can be translated into machine code to compute that.

To keep things simple I'm not considering the air and what kind of properties the air can possibly modify, or any other extra variable outside the domain of this drop of liquid, like adding a inclined plane where the drops, let's say that for now I'm considering a vector and an X quantity of liquid, this quantity is than sprayed or just dropped on the surface and I should be able to reproduce a realistic dispersion of the water on the surface, even better I should be able to compute different liquids with different properties at the same time, like water and oil.