O-CMF vs stirred cell and spiral-wound module

Model: Geraldes V., Fan H., Yang M., Rodrigues M., Elimelech M. — "Predicting concentration polarization in Ortho-Centrifugal Membrane Filters for NF/RO membrane screening." Preprint under review, Journal of Membrane Science (2026). Thermo-physical properties at 20 °C from Table 1 of the same work (PEG 35 kDa: Table A.1, data of Pires et al.). Correlation k_c/U* = 0.261 𝒢^1/4 Sc^−1/4, with the finite-permeation closure Ξ(φ) of Geraldes & Afonso (2006), Γ = R_int φX / (1 + (1 − R_int) φX), X = (1 + 0.26 φ^1.4)^1.7, exact in R_int — used for every solute and device, since film theory (valid only for φ ≲ 1.5) is a special case of it. In the O-CMF, ν and D are evaluated at the film concentration ½(c_m + c₀). In the stirred cell and the spiral-wound module (forced convection) the correlations keep the bulk properties and k_c is multiplied by the weak viscosity correction (ν_m/ν₀)^−0.075 found in the reconstructed radial cross-flow cell (36 runs); evaluating a Re^0.875Sc^0.25 law at the film concentration would over-correct. Validated against DNS for Sc ∈ [700, 2200] and 𝒢 ∈ [7×10⁻⁹, 5×10⁻⁶] (mean relative deviation ~7%, maximum ~22%), and against twelve reconstructed PEG 35 kDa ultrafiltration experiments in the O-CMF (Pereira, MSc thesis, IST 2026; Sc ≈ 3×10⁴, Γ 2–66, φ 1.4–7, within ±20 % in Γ). Membrane classes are indicative permeabilities; B defaults to the value backed out of the PEG reconstructions (R_int ≈ 0.96–0.996) for that solute, and to Table 1 values for the others.