Capillary Wave Theory — Interface Roughness

Parameters

Surface tension γ 1.0 Temperature T 1.0 Gravity g 0.0 System size L 200 qmax cutoff 30

Interface Statistics

Width w² (measured)—

Width w² (theory)—

Capillary length λ_c—

T/γ ratio—

About

Capillary wave theory (Buff, Lovett, Stillinger 1965): thermal fluctuations roughen fluid interfaces. Each Fourier mode h_q has amplitude ⟨|h_q|²⟩ = T/(γq² + ρΔg). In 2D without gravity, the interface width diverges logarithmically: w² ~ (T/2πγ) ln(L/a). This is detected in X-ray scattering from liquid surfaces.