OSN property guide

1. Where the properties enter

The concentration-polarisation correlation of the simulator is k_c/U* = 0.261 𝒢^¼ Sc^−¼ with 𝒢 ∝ β·c₀·(J_v/U*). The properties therefore enter through three numbers per solute–solvent pair: the densification coefficient β (how much the density rises per unit solute mass concentration), the kinematic viscosity ν(c) and the diffusivity D_AB(c), with Sc = ν/D. The error in each propagates into k_c with weights ¼ (β) and ¼ (ν/D through Sc, together with the property evaluation at the film concentration).

2. Density and β from a partial specific volume

For c kg of solute per m³ of solution with partial specific volume v̄ (m³/kg), the solute occupies c·v̄ and the solvent the rest:

v̄ is taken at infinite dilution; for the concentrations of interest (≤ 5–10 wt %) this is a good approximation for non-associating solutes, but see §4.

Sensitivity — how much an error in v̄ matters

β is a difference (1 − ρ₀v̄), so an error in v̄ is amplified by ρ₀v̄/(1 − ρ₀v̄) on the way to β:

But β enters the mass-transfer coefficient only through 𝒢^¼, so the effect on k_c is small. Running the CP Calculator solver for PEG 35 kDa (6000 rpm, 20 °C, R_obs = 0.98) with β changed by −25 % / +25 %:

3. Partial specific volume of PEG

3.1 Oligomers, from experimental densities

Apparent specific volumes φ(w) = [1/ρ − (1−w)/ρ₀]/w were extrapolated to w → 0 using published density series of ethylene glycol oligomers at 298.15 K (NIST ThermoML Archive; articles in §9). The pure-water density used when an article does not report w = 0 is the median of the archive (997.0 kg/m³).

In the two organic solvents v̄ is about 1 % higher than in water for the same oligomer.

3.2 From oligomers to the polymer: group model

The molar volume is linear in the number of ethylene-oxide units: V^∞(n) = n·V_EO + V_ends, with M = 44.053 n + 18.015 g/mol.

• Our three oligomer points (n = 1–3) give V_EO ≈ 37.7 cm³/mol and V_ends ≈ 17 cm³/mol. Three short oligomers cannot fix the polymer limit on their own.
• For the polymer limit we use V_EO = 37.0 cm³/mol, which Mollica (1978) reports as independent of chain length and end groups stated in the abstract of the original (densities of ethylene glycol to tetraethylene glycol and of carbowaxes 600–15 000 g/mol at 25 °C, 5–100 g/L; full text not read), with V_ends = 18.0 cm³/mol (close to the molar volume of water; ends = one H and one OH).
• This reproduces the oligomers within 1 %: EG 0.886 (measured 0.878), DEG 0.867 (0.863), TEG 0.859 (0.864).

3.3 Consequence for PEG 35 kDa

4. Why β must not be computed from pure-component densities

Ideal volume additivity (ρ_id = 1/Σ w_i/ρ_i) predicts the density of binary mixtures within ≤ 1–2 % over the whole composition range (3.8 % at worst, water + oligo-ethers). But β depends on the density increment at low concentration, which is small, and there additivity fails. Ratio of measured to additive increment at w ≤ 0.10 (median, 298 K region, NIST data):

Hydrating solutes contract the mixture (increment 10–37 % larger); amphiphilic ethers are density-matched to water (increment ≈ 0). The simulator therefore uses a measured or literature v̄, never pure-liquid densities, for β.

5. Solvents: density and viscosity

Pure-solvent data come from the Choupo/ChemSep v8.3 correlations (liquid viscosity: Andrade or ChemSep Eq. 101; density from V_liq at 25 °C). They were compared with all pure-liquid points at ambient pressure in the NIST archive (about 14 000 points). Median relative error of μ(T) over the temperatures in the data, and density at 298 K:

Water is included as a reference solvent, so the same solute can be compared in water and in the organic solvents. Its Andrade fit overestimates μ by about 2 % at 25 °C; the Vogel form ln μ = A + B/(T − C) from the same database is used instead (0.89 mPa·s at 298 K).

The comparison is not fully independent (ChemSep and NIST share literature sources) and a few outlier points in the archive were not removed; medians and percentiles are used for that reason.

6. Diffusivity

6.1 Small and API-sized solutes: Wilke–Chang

φ = 1.9 for methanol, 1.5 for ethanol, 1.0 for non-associating solvents; V_A by Le Bas additive volumes (C 14.8, H 3.7, O 7.4, N 10.5/12.0 for primary/secondary amines, −15 per ring). Compared with published infinite-dilution values at 298–328 K:

6.2 PEG and macromolecules not yet validated

Wilke–Chang was fitted to small molecules and is not used for chains. For PEG the plan is Stokes–Einstein, D = k_BT/(6πμR_h), with R_h from a power law R_h ∝ M^0.57 in water. The simulator currently uses R_h = 0.0145·M^0.571 nm, a water power law that could not be confirmed in the original source; a supplement of a later study quotes a different exponent (≈ 0.54) for PEG. At 35 kDa and 20 °C the formula gives D ≈ 3.8×10⁻¹¹ m²/s, close to the estimate used for the measured PEG 35 kDa laws (4.0×10⁻¹¹ m²/s, itself an estimate: no measurement exists), so the check is not independent. For PEG 35 kDa the simulator keeps the measured D_A(c) of Pereira (2026), with D_A(0) an estimate (stated on the simulator page).

6.3 Concentration dependence of viscosity

For polymers: [η] = K M^a (Mark–Houwink, constants from the Polymer Handbook for each solvent) and η/η₀ = 1 + [η]c + k_H([η]c)². Near limiting flux the wall viscosity controls k_c (Peeva et al. 2026 find k ∝ η⁻² for PEG 35 kDa in acetonitrile), so these constants decide the result and each one is listed in the simulator with its source. For PEG the simulator uses [η] = 0.0125·M^0.78 mL/g (Mark–Houwink constants that could not be confirmed in the original; another study reports different constants, K = 0.0068 mL/g and a = 0.67 for 1–8000 kg/mol, which would give a six times lower [η] at 35 kDa and does not reproduce the measured viscosity below). The constants used give ν/ν₀ = 1.48 at 10 g/L for PEG 35 kDa in water, against 1.50 from the measured law (Pereira 2026), so in water they are consistent with measurement; in organic solvents they are assumed. partly verified

7. Hypotheses and limits

1. Dilute solutions: v̄ at infinite dilution; no excess volume at 5–10 wt % beyond what the oligomer data show.
2. Temperature around 298 K (v̄ and R_h have temperature dependences not modelled yet; tabulated solvent μ(T) is).
3. Pressure ≈ ambient; the compression of liquids at 10–60 bar changes ρ by < 0.5 % and is neglected.
4. No solvent-membrane interaction: swelling, adsorption and solvent-induced conformational change are outside the model (Peeva et al. discuss them as sources of deviation).
5. Acetonitrile v̄ for PEG and all macromolecular D and η values are estimates until direct measurements are added.
6. Proteins: no data from the archive (the NIST archive has none); properties will come from the original literature, one protein at a time.

7b. Consistency check against the measured PEG 35 kDa laws

The device-comparison page uses measured property laws for PEG 35 kDa in water at 20 °C (ν(c), D_A(c), π(c) from the CFD reconstructions of Pereira 2026, Table A.1; data of Pires et al.). The OSN simulator uses exactly those laws whenever the solvent is water, the solute is PEG with M = 35 000 ± 1 500 g/mol, T = 20 °C and no property is overridden. Otherwise it uses the generic estimates of this guide. To check how far the generic estimates are from the measured case, the same PEG 35 kDa/water problem was solved with both (generic run at 21 °C, UF permeance 32 LMH/bar, B = 0.5 LMH, O-CMF):

Two modelling choices behind the generic estimates are calibrated on this single measured case: the collective diffusivity D(c) = D₀(1 + 0.15 [η] c), and the semi-dilute osmotic pressure π = (RT/M) c [1 + 0.73 (c[η])^1.3]. Calibrating on one polymer and one solvent is a limitation; they are replaced as soon as measurements in other solvents are available. A first version of the page used D(c) = D₀/η_rel(c), which collapses the film diffusivity at high concentration and over-predicted Γ by about a factor of 10 for this case; that assumption was removed.

8. Check it yourself

Defaults reproduce the table values: PEG 35 kDa in water (β ≈ 1.63×10⁻⁴), and 1-amino-2-methylanthraquinone in methanol at 308.2 K (μ = 0.474 mPa·s from the Andrade fit): Wilke–Chang ≈ 1.4×10⁻⁹ m²/s against 1.44–1.60×10⁻⁹ m²/s measured (four points at that temperature).

9. Sources

Data. NIST/TRC ThermoML Archive, v. 2020-09-30, DOI 10.18434/mds2-2422 (the arrangement is NIST's; the measurements belong to the articles below). Pure-component correlations: ChemSep v8.3 (Kooijman & Taylor), accessed through the Choupo component database. Cite the primary articles, not the archive.

Primary articles used for v̄ of oligomers (DOI): 10.1016/j.fluid.2015.07.030, 10.1016/j.jct.2015.05.024, 10.1016/j.jct.2018.02.022 (water + triethylene/diethylene glycol); further series from the same archive for ethylene glycol in water, DMSO and DMF.
Diffusion (dilute solutes in alcohols): 10.1021/je700539w (phenol, benzaldehyde, acetophenone in methanol and ethanol, 298.15 K); 10.1016/j.fluid.2016.01.010 (amino- and bis(methylamino)anthraquinone, 308–328 K).

• Peeva L., Oxley A., Livingston A.G., Selectivity control in organic solvent nanofiltration – membranes or process? J. Membr. Sci. 737 (2026) 124613, doi:10.1016/j.memsci.2025.124613.
• Koutsou C.P., Karabelas A.J., J. Membr. Sci. 399–400 (2012) 60–72, doi:10.1016/j.memsci.2012.01.029.
• Mollica (1978), Volumetric properties of dilute aqueous solutions of poly(ethylene glycols): repeat-unit partial molar volume of CH₂CH₂O 37.0 mL/mol at 25 °C, independent of end groups and chain length (abstract read; journal reference to be completed).
• Cruz C.S., Martins F., Cardoso M.J., Barcia P.S., Volumetric study of aqueous solutions of polyethylene glycol as a function of the polymer molar mass, J. Solution Chem. 38 (2009) 957–981, doi:10.1007/s10953-009-9388-1 (PEG 3000–20 000, 283.15–313.15 K; abstract read, numerical values not checked).
• Costa et al., Density, refractive index, apparent specific volume, and electrical conductivity of aqueous solutions of poly(ethylene glycol) 1500 at different temperatures, J. Chem. Eng. Data 59 (2014) 339–345, doi:10.1021/je400802t (apparent specific volume 0.8336–0.8528 cm³/g, as quoted in the abstract).
• Ambrosone L., Sartorio R., Vescio G., Vitagliano V., Volumetric properties of aqueous solutions of ethylene glycol oligomers at 25 °C, J. Chem. Soc., Faraday Trans. 92 (1996) 1163–1166, doi:10.1039/FT9969201163 (limiting partial molar volumes linear in the number of ethoxy groups; abstract read).
• Geraldes V. et al., predictive concentration-polarisation correlation (preprint under review), doi:10.2139/ssrn.6528979; Pereira (MSc thesis, IST 2026) for PEG 35 kDa property fits.