As I said in the previous post, the Egyptian artists mixed pigment with egg or acacia sap which is also known a gum arabic. Both are binders for a water based paint. Another binder for water based paint is acrylic or egg yolk or even sometimes the whole egg. Often egg is used as a binder in oil painting also.
The equivalent to this in oil painting is linseed oil or whatever oil is used such as poppy seed or walnut. The binder holds the pigment particles together. Otherwise, if you just mixed the dry pigment with water and painted on your substrate, the pigment would not adhere to the surface and would fly away in the wind. It must have a glue like substance such as the acacia sap, egg, acrylic, alkyd, or oil to make it stick.
Acacia resin. Image courtesy Wikipedia