Fig. 3.

Dispersion relation for a single bilayer membrane with interleaflet damping. The black and gray solid lines are the fast and slow viscous modes respectively. The dotted line represents the conventional bending mode: $\gamma =\kappa q_0^3/4\eta$ (adapted from Fig. 2 of [21], κ = 10⁻¹⁹ J, k = 0.07 J/m², d = 10⁻⁹ m, η = 10⁻³ J s/m³, μ = 10⁻⁹ J s/m², b_f = 3 × 10⁹ J s/m⁴ are used for the plot).