The adhesion between two solids is characterized by the adhesion energy. If you have two solids adhered at an interface and you want to pull them apart, I understand that you have to supply the energy described by the surface energy (J/m^2) times the area (m^2).

Intuitively, it seems like there should also be a minimum adhesive force. If I try to separate two materials at an interface using a tiny force, it is never going to act over a distance so it will never do any work. There is then, presumably, some minimum amount of force required to separate them. This force would of course be specific to the angle at which it was applied (pulling vs peeling, for example). Is this adhesive force a property used for analysis? Is it generally extensible, ie, if I double the surface area of an interface does the specific adhesive force (N/m^2) stay the same?

Secondarily, what is the relationship between the force and work required to de-adhere to materials at an interface? If the energy required is characterized by a adhesive energy, $E$, and I pull them apart with force $F$, what is the characteristic length over which the work is done? $\int dE/dF$? Is the adhesive energy you might look up in a table not actually appropriate for finding the required force?

• There are too many questions is one question. You should highlight the most important questions so that the probability increases that someone will answer your question. Apr 20 '17 at 14:27

Mechanical interlocking due to surface roughness plays a significant role in practical adhesion (e.g. the mean peeling force required to de-adhere an interface). This is in addition to the surface energy values of the materials as they appear in the literature, if they were measured using a surface force apparatus with atomically smooth material coupons.

The contact areas and lines of force for the purposes of mechanical analysis will vary depending on the size and shape of asperities, presence of contaminants, and wettability by the adhesive—possibly by orders of magnitude (cf. stress risers).

Two very rough surfaces with large surface areas, effectively wet by an adhesive, or having few interfacial voids through plastic deformation of each other's asperities, will have a higher adhesive energy as a result. Surfaces of the same materials, but smoother, will have lower adhesive energy.

See Pocius (2012), Adhesion and Adhesives Technology, 3e, § 6.5 for a concise discussion on the topic. Most textbooks on tribology have a section on adhesion.