How does one compare the "stickiness" of different substances on a certain surface?
Does glue A stick better to steel than glue B?
Does water stick better to steel than oil?
Ah, such an innocent question. In a previous job I spent six months trying to understand what controlled the stickiness of polymer solutions, before admitting the task was beyond the funding I had available (such is industrial research, but to be fair when they bought my soul they paid me a lot for it :-).
Some things are obviously relevant. When a liquid touches a solid, whether it wets that solid depends on the balance of the solid-liquid, solid-air and liquid-air contact angles. If the liquid has a high contact angle it isn't going to stick to the surface. Predicting the contact angle is hard, though some basic principles are obvious. Water is bristling with polar O-H bonds so it tends to wet polar surfaces and not wet apolar ones like e.g. wax. Oil is the reverse: it easily wets waxy surfaces but not polar ones. Neither oil not water will wet PTFE surfaces.
Incidentally, you ask about steel. Water wets steel better than oil does, but commercial lubricating oils have surfacants in them that improve the wetting of the steel by the oil. But note that the experiments are done on extremely clean steel surfaces. In the real world steel rapidly acquires a film of oxide and grease that can affect the wtting properties in either direction.
Anyhow, wetting a surface is only part of the stickiness. Compare a sugar solution with a salt solution. As the sugar solution dries it gets extremely sticky (as the parent of any small child can tell you!) but a salt solution of the same concentration does not get sticky. Clearly the visco-elastic properties of the fluid are important as well as the wetting, but beyond the obvious conclusion that energy dissipation in the fluid is important I didn't come to any great insights concerning the details.
Kind of more of a chemistry question but…
If you're looking for widely accepted mathematical definition of adhesion I would recommend the IUPAC Goldbook definition of Work of Adhesion/Seperation
If you are just interested in making a quantitative measurement of "stickiness" without understanding the specific process that makes any particular substances stick to another, all you have to do is measure how readily a substance can be pulled off another via a constant force.
For example, to measure the stickiness of a fluid against steel, you could just poor some on a reference slab of steel, tilt the steel to a specific angle and measure how long it took how much of the fluid to drain off. Your "Stickiness" units would then be something like ((initial volume) - (final volume)) / time.
The best measurements are usually the simplest.
Adhesive manufactures like 3M just glue things together and measure how much force on various vectors it takes to break the bond. They test every conceivable conditions of environment but that's basically what it boils down to.