The Young–Dupré equation (Thomas Young 1805, Lewis Dupré 1855) dictates that neither γ nor γ can be larger than the sum of the other two surface energies. The consequence of this restriction is the prediction of complete wetting when γ > γ + γ and zero wetting when γ > γ + γ. The lack of a solution to the Young–Dupré equation is an indicator that there is no equilibrium configuration with a contact angle between 0 and 180° for those situations.
A useful parameter for gauging wetting is the spreading parameter S,
When S > 0, the liquid wets the surface completely (complete wetting).
When S < 0, partial wetting occurs.
Combining the spreading parameter definition with the Young relation yields the Young–Dupré equation:
which only has physical solutions for θ when S < 0.