Many technological processes require control of liquid spreading over solid surfaces. When a drop is placed on a surface, it can completely wet, partially wet, or not wet the surface. By reducing the surface tension with surfactants, a nonwetting material can be made to become partially or completely wetting. The excess free energy (σ) of a drop on a solid surface is:
:* γ is the liquid–vapor interfacial tension
:* γ is the solid–liquid interfacial tension
:* γ is the solid–vapor interfacial tension
:* S is the area of liquid–vapor interface
:* P is the excess pressure inside liquid
:* R is the radius of droplet base
Based on this equation, the excess free energy is minimized when γ decreases, γ decreases, or γ increases. Surfactants are absorbed onto the liquid–vapor, solid–liquid, and solid–vapor interfaces, which modify the wetting behavior of hydrophobic materials to reduce the free energy. When surfactants are absorbed onto a hydrophobic surface, the polar head groups face into the solution with the tail pointing outward. In more hydrophobic surfaces, surfactants may form a bilayer on the solid, causing it to become more hydrophilic. The dynamic drop radius can be characterized as the drop begins to spread. Thus, the contact angle changes based on the following equation:
:* θ is initial contact angle
:* θ is final contact angle
:* τ is the surfactant transfer time scale
As the surfactants are absorbed, the solid–vapor surface tension increases and the edges of the drop become hydrophilic. As a result, the drop spreads.