Young's equation balances the three interfacial tensions that meet at the contact line where a liquid drop touches a solid: γ_SV = γ_SL + γ_LV·cosθ, where γ_SV is solid–vapor tension, γ_SL is solid–liquid tension, γ_LV is liquid–vapor (surface) tension and θ is the equilibrium contact angle.

What surfactant does

Surfactant molecules are amphiphilic — a polar head and a nonpolar tail — so they adsorb at the water–air interface, disrupting the hydrogen-bond network responsible for water's high γ_LV (≈72 mN/m) and dragging it down toward 25–35 mN/m. Many surfactants also adsorb at the solid–liquid interface, lowering γ_SL, especially on greasy or waxy (hydrophobic) solids where they can partially dissolve the soil layer.

Critical micelle concentration

Below the CMC, added surfactant keeps populating the liquid–vapor interface and γ_LV keeps falling. Past the CMC, the interface is saturated — extra molecules instead assemble into micelles dispersed in the bulk liquid, so γ_LV plateaus. This simulation reproduces that plateau explicitly.

Why low contact angle matters for cleaning

A cleaning solution has to physically touch the surface it is meant to clean. A high contact angle means the liquid beads up and only contacts a small footprint; a low contact angle means it spreads and sheets, penetrating fabric weave, fine crevices and grime particles far more completely — which is why detergents are surfactant solutions, not just water.

Droplet geometry

Each droplet is a genuine spherical cap: given a target contact angle θ, the sphere radius R is solved so the cap volume V = (πR³/3)(1−cosθ)²(2+cosθ) stays constant, then base radius a = R·sinθ and height h = R(1−cosθ) follow. That is why the droplet visibly flattens and widens — not just squashes — as θ falls.