The equation is obtained by making a couple of simple approximations, the first is by equating the stress at the surface due to the concentration gradient of surfactant (which drives the Marangoni flow) with the viscous stresses (that oppose flow). The Marangoni stress ∼ ∼ ( ∂ ∂ γ γ / ∂ ∂ r ) , i.e., gradient in the surface tension due gradient in the surfactant concentration (from high in the centre of the expanding patch, to zero far from the patch). The viscous shear stress is simply the viscosity times the gradient in shear velocity ∼ ∼ μ μ ( u / l ) , for l the depth into the water of the flow due to the spreading patch. Roché and coworkers assume that the momentum (which is directed radially) diffuses down into the liquid, during spreading, and so when the patch has reached a radius r , l ∼ ∼ ( ν ν r / u ) 1 / 2 , for ν ν = μ μ / ρ ρ the kinematic viscosity, which is the diffusion constant for momentum in a fluid. Equating the two stresses