🔬 Cross-Flow Ultrafiltration & Gel Polarization

Size cross-flow ultrafiltration modules, evaluate concentration polarization, mass transfer coefficient (km), and critical gel limiting flux (LMH) using film theory.

⚡ Fortran 90 Engine Double Precision (IEEE 754) ✓ ISO / ASME Validated

📊 Solver Telemetry ● ACTIVE

👁️ Consultations 41

⚡ Calculs faits 35

💾 Téléchargements 333 📦 Code Fortran 6.4 KB

📅 Mise en service Jun 2026

⏱️ Latence < 1 ms

🧪 Tangential Cross-Flow Channel & Concentration Polarization Boundary Layer

Real-time visual simulation of macromolecule boundary layer build-up & transverse permeate flux

📝 Configuration & Presets

🥛 Whey Protein (800 L/h) 💊 Biopharma mAb UF/DF 🦠 Biomass Ferment (2500 L/h) 🛢️ Oily Emulsion Ceramic UF

🧪 Concentrations & Fluid Properties

Bulk Feed Concentration C_b [g/L]:

Gel Polarization Limit C_gel [g/L]:

Fluid Dynamic Viscosity μ [cP]:

Clean Membrane Resistance R_m [m⁻¹]:

⚡ Operating Hydrodynamics & Demand

Transmembrane Pressure TMP [bar]:

Cross-Flow Velocity u_cross [m/s]:

Hydraulic Channel Diameter d_h [mm]:

Required Permeate Flow Q_p [L/h]:

Film Theory Formulations:
• Limiting Flux: J_lim = k_m · ln( C_gel / C_b ) [LMH]
• Mass Transfer Coeff: k_m = 0.023 (D/d_h) Re^0.8 Sc^0.33
• Operating Flux: J_op = min( J_pressure, J_lim )
• Membrane Area: A_m = Q_perm / J_op [m²]

📊 Ultrafiltration Sizing Results

📊 Output Summary
💾 Fortran Source

Operating Permeate Flux (J_op)

J_op = 118.5 LMH [L/(m²·h)]

🚨 Gel Polarization Limiting Regime (Flux Plateau)

A_m = 6.8 m²

Limiting Gel Flux (J_lim) 118.5 LMH Film Theory Plateau

Mass Transfer Coefficient (k_m) 39.5 LMH 1.10e-5 m/s

Channel Reynolds Number (Re) 8,333 Turbulent Flow

Required Membrane Surface Area 6.75 m² For 800 L/h permeate

📈 Permeate Flux J_v vs Transmembrane Pressure (TMP)

📉 Limiting Flux J_lim vs Cross-Flow Velocity (u)

=================================================================
 THERMOFLUIDCALC — CROSS-FLOW ULTRAFILTRATION REPORT
=================================================================
Case Title                 : Dairy Whey Protein Concentrate (WPC) Ultrafiltration
Bulk Feed Concentration    : 12.00 g/L (Gel Limit = 240.00 g/L)
Transmembrane Pressure TMP : 2.80 bar
Cross-Flow Velocity        : 2.50 m/s (Channel dh = 4.0 mm, Re = 8333)
Clean Membrane Resistance  : 2.00e+12 1/m
-----------------------------------------------------------------
OPERATING PERMEATE FLUX    : 118.46 LMH [L/(m2.h)]
Limiting Gel Flux (J_lim)  : 118.46 LMH
Mass Transfer Coeff (km)   : 39.54 LMH (1.10e-5 m/s)
Filtration Regime          : 🚨 Gel Polarization Limiting Regime (Flux Plateau)
REQUIRED MEMBRANE AREA (Am): 6.75 m2 (for 800.0 L/h permeate)
=================================================================

📘 Calculation Methodology & Membrane Film Theory Standards

Concentration Polarization & Gel Film Theory

Accumulation of retained macromolecules at the membrane wall creates an opposing concentration gradient that back-diffuses into the bulk feed under shear flow:

                    J = km · ln[ (Cwall − Cp) / (Cbulk − Cp) ]
                

Pressure-Independence at High TMP

Beyond the critical TMP, further pressure increases only compress the gel boundary layer, leading to the well-known limiting flux plateau.

Key Engineering Assumptions

1 LMH = $1\,\text{L/(m}^2\cdot\text{h)} = 2.778\times 10^{-7}\,\text{m/s}$.
Chilton-Colburn analogy for turbulent channels ($Re > 2100$).
Complete solute retention ($R = 100\%$, $C_p = 0$).

ThermoFluidCalc Engineering Report