Maximum likelihood estimate â of the characteristic speed between solid particles. The particle size is τ_f = 0.003 and the solid concentration (Z = Σ_solid/ Σ_total) is 0.074 for all the simulations. The procedure is to select particle pairs with separation less than D and compute â from Eq. (27). Extrapolating to D → 0 gives a rough estimate of the characteristic collision speed â₀. The region in green corresponds to 0 ≤ â₀ ≤ 2σ_a and the 1σ confidence interval for the slope.