Permea

instantaneous flux

run summaryderived

transport diagnosticsat cursor

wall c_w

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polarization c_w/c_b

–

Péclet J/k

–

limiting flux

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gel margin c_w/c_g

–

osmotic Δπ

–

spiegler–kedem sieving fitSuryawirawan 2024

observedintrinsicSK fitmeasured

ionic strength · M

fit on

σ reflection–

Pₘ permeability–fitted

k 7.3 µm/s · Suryawirawanr² –

data noise0%

fit intrinsic (de-polarized) sieving, never observed — or σ/Pₘ won't transfer across crossflow/TMP.

process time vs switch c*reduced-order · Ng/Foley

impurity clear.100×

feed conc10 g/L

optimal control α(c) · bang-bang

switch at c*–optimal

buffer · cvdf baseline–

buffer · optimized dvd–

– buffer saved vs naive cvdf

the economically optimal diafiltration is a constant-volume step at a specific concentration, not at the feed (Ng/Foley).

flux vs TMP–

flux–TMPlimiting fluxoperating point

flux @ TMP

–

limiting flux

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TMP headroom

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at c_b

–

osmotic Π @ c_b

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rel. viscosity

–

below the knee, flux is pressure-controlled (raise TMP). at the plateau it's mass-transfer-limited — more TMP only thickens the gel; only crossflow lifts it.

process flowsheetTFF · batch

batch TFF: the retentate recirculates through the cassette; permeate leaves through the membrane. concentrate removes permeate (volume ↓); diafilter adds buffer to hold volume while washing impurity out.

excipient exchangeconstant-volume DF

salt σ′1.0buffer σ′0.92stabilizer σ′0.3

diavolumes

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ionic remaining

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salt cleared

–

DV → 99% wash

–

diafiltration exchanges the solvent: a freely-permeable excipient washes out as e^(−σ′·DV); a retained one persists. conductivity ≈ ionic species remaining. the washout law is validated vs the Pall desalting table + Loewe 2022 (measles UF/DF); σ′ are representative excipient values.

sensitivity · Δ throughput±20%

top driver

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its swing

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baseline

–

2nd driver

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one-at-a-time: each input is perturbed ±20% with the rest held; bars show the swing in throughput (flux × area). the longest bar is the variable to control — or pin down — first.

credibility · model cardRO-Crate

mass balance–

grid convergence–

flux regime–

sieving fit–

parameters–

engine–

a model card travels with the run — what's checked (mass balance, grid convergence), the calibrated parameter preset, and provenance — the suite's rigor contract, exportable as RO-Crate / JSON-LD.

scale-up sizingengine-derived

batch volume100 L

process time4 h

membrane area

–

cassettes

–

product

–

buffer

–

membrane area = (batch volume × permeate fraction) / (run mean flux × process time) — sized from the run's actual flux, cassettes at 2.5 m² each.

permea recipe lab: design a ultrafiltration/diafiltration recipe and operating point, then scrub and play back the simulated run as the concentration figure and state strip animate; an optimize assist suggests the time-optimal switch concentration.