1 · Batch
2 · Product & second species
3 · Solvent & temperature
4 · Spiral-wound module
5 · CentrivaLab run
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Six-tube run sheet
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| Pos. | Batch state | cP batch (g/L) | second | feed C0,P (g/L) | feed C0,I (g/L) | ΔP (bar) | mass (g) | Jv (LMH) | time (min) | exp. cp,P (g/L) |
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Feed concentrations are the cartridge feeds that reproduce the module's wall concentrations at each batch state — they are not the batch concentrations. Positions pair adjacent masses opposite each other (1↔4, 2↔5, 3↔6).
Batch trajectory
Product and second species vs time
C·J diafiltration optimisation parameter
| Stage | duration (h) | V (L) | cP (g/L) | second species | product lost (%) | cm,P max (g/L) |
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Enter measured results and re-integrate the batch
Per tube: permeate collected, collection time and permeate concentrations. The tool converts them to the membrane's flux and intrinsic rejection at each wall concentration, redraws the C·J curve with the measured points and re-integrates the batch with the measured response.
| Pos. | cP batch | Vp (mL) | time (min) | cp,P (g/L) | cp,I (g/L) | → J (LMH) | → cm (g/L) | → Lp (LMH/bar) | → Rint |
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Model & validity
Batch. Well-mixed tank recirculated through the module; the tank state is integrated in permeate-volume steps (1/400 of the batch volume). Concentration removes permeate; diafiltration adds fresh solvent at the permeate rate (constant volume). Product loss is the integral of the permeate concentration.
Module. 1-D plug flow along the feed channel as in the Test Planner: Schock & Miquel (1987) mass transfer per species, film model, van't Hoff osmotic pressure of both species (× the osmotic factor), channel friction. Feed viscosity rises linearly with product concentration by the entered coefficient; diffusivities follow Stokes–Einstein at that viscosity.
Second species. An impurity is a second solute with its own rejection and mass transfer. In a solvent exchange the old solvent permeates freely (its fraction decays as e−N), and the mixture density is linear, ln μ linear, in the volume fraction — a first approximation; the tubes measure what the mixture actually does.
Cartridge. Buoyancy-driven polarisation model of Geraldes et al. (2026); the product drives the buoyancy, the impurity is treated as a dilute tracer with its own diffusivity. Each tube's feed is solved so that the run-mean wall concentrations of product (and impurity) equal the module's at that batch state; one speed is shared, set from the mean ΔP and mean feed density, and the ΔP of each tube at its own density is reported.
Diafiltration optimum. The diafiltration time for N diavolumes is N·mP/(A·J(c)·c): it is shortest where J·c is largest (Ng, Lundblad & Mitra, Sep. Sci. Technol. 11 (1976) 499; the "DF optimisation parameter C·Jf" of the Millipore TFF brief). Under gel polarisation this is clim/e; here J(c) comes from the module model and, after the run, from the tubes. In a solvent exchange the curve is measured in both solvents. The analytical checks shown use constant observed rejection: product loss = 1 − e(R−1)(ln VCF + N), contaminant remaining = e(R−1)N.
Validity. Van't Hoff underestimates the osmotic pressure of concentrated solutions: use the osmotic factor from a measured value. The O-CMF correlation is dimensionless and applies whenever 𝒢, Sc and Jv/k are within the ranges over which it was established (𝒢 7×10−9–5×10−6, Sc 700–2200, Jv/k ≤ 1.5); at batch concentrations of g/L and above these are normally met in organic solvents, and each tube is checked. β and D are estimated from density and molar mass — replace them by measured values when available; the two-concentration signature test in the Test Planner guide confirms the model in your system. Solvents denser than the product (β ≤ 0) are outside the model.