Skip to main content
CalcStack

Hollow-Fiber Ultrafiltration Permeate Flux Calculator

Hollow-fiber ultrafiltration and tangential flow filtration (TFF) are critical unit operations for harvesting antibodies, concentrating proteins, and cell clarification.

Average pressure driving force across membrane wall (TMP = 0.5*(Pin + Pout) - Pperm).

Clean membrane pure water permeability in L/(m2*h*bar).

Bulk protein or macromolecule concentration in feed stream.

Limiting gel polarization wall concentration (typically 100-300 g/L for proteins).

Laminar shear back-diffusion mass transfer coefficient from boundary layer.

Calculated Result
90.0 LMH

Actual Permeate Flux

Clean Membrane Flux (J₀)

90.0 LMH

Gel Limit Flux (J_gel)

146.2 LMH

Filtration Regime

Pressure-Dependent (Linear Regime)

Calculation Breakdown

  1. J₀ = Lp · TMP90.0 LMH
  2. J_gel = k · ln(C_g / C_b)146.2 LMH
  3. J = min(J₀, J_gel)90.0 LMH

What Is the Hollow-Fiber Ultrafiltration Permeate Flux Calculator?

Crossflow ultrafiltration forces feed broth tangentially across hollow fibers to sweep rejected solutes away and limit fouling cake buildup.

As rejected proteins accumulate at the membrane wall, concentration polarization creates an osmotic backpressure and viscous gel layer.

How Does the Hollow-Fiber Ultrafiltration Permeate Flux Calculator Work?

At low TMP, flux increases linearly with pressure in the clean membrane Darcy regime.

At higher TMP, solute convective arrival matches back-diffusion into the bulk, causing flux to plateau at a constant gel-layer limit independent of pressure.

Hollow-Fiber Ultrafiltration Permeate Flux Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

J_0 = L_p \cdot \text{TMP}, \quad J_{gel} = k \cdot \ln\left( \frac{C_g}{C_b} \right), \quad J = \min(J_0, J_{gel})

Calculates pressure-driven clean flux and film-theory mass-transfer gel polarization limiting flux.

How to Use the Hollow-Fiber Ultrafiltration Permeate Flux Calculator

  1. Enter transmembrane pressure (TMP) in bar and membrane permeability in LMH/bar.
  2. Input bulk feed concentration and known gel polarization concentration Cg.
  3. Specify boundary layer mass transfer coefficient k (determined from Graetz-Leveque correlations).

Step-by-Step Example Calculation

Ultrafiltration Flux Standard Case

Input Values:

transMembranePressureBar:1.5
hydraulicPermeabilityLmhBar:60
feedSoluteConcentrationGPerL:8
gelConcentrationGPerL:120
massTransferCoeffMPerS:0.000015
Worked Steps: Representative engineering benchmark scenario.

Understanding Your Result

Actual permeate flux indicates the sustainable operating processing rate in LMH (liters per m2 per hour).

Filtration regime indicates whether increasing TMP will yield higher throughput or merely compress foulant cakes.

Operating slightly below the gel-polarized threshold prevents severe membrane fouling.

Factors That Affect the Result

  • Crossflow shear rate: Higher lumen recirculation velocity elevates k, directly raising the gel-limiting flux.
  • Bulk concentration Cb: As filtration concentrates the retentate batch, ln(Cg/Cb) shrinks, reducing flux.
  • Temperature: Higher temperatures lower broth viscosity and increase Brownian solute diffusivity.

When Should You Use This Calculator?

  • Sizing membrane area for downstream biopharmaceutical ultrafiltration/diafiltration (UF/DF) systems.
  • Optimizing crossflow harvest of monoclonal antibodies, vaccines, and recombinant enzymes.

Assumptions & Limitations

  • Assumes 100% solute membrane rejection (reflection coefficient sigma = 1.0).
  • Does not model long-term pore adsorption or irreversible chemical scaling.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Film-theory concentration polarization formulation coupled with linear Darcy hydraulic permeability.

Related Calculators

Explore more tools and calculators in Biology Calculators

Bioreactor kLa & Oxygen Transfer Rate Calculator

Calculates the volumetric oxygen mass transfer coefficient (kLa) and maximum Oxygen Transfer Rate (OTR) in aerobic bioprocesses via dynamic gassing-out.

Monod Chemostat Microbial Growth Kinetics Calculator

Calculates steady-state substrate and biomass concentrations, volumetric productivity, and washout dilution rate in continuous stirred-tank bioreactors.

Acres Per Hour Calculator

Calculate how many acres per hour you can mow, harvest, or cultivate, and estimate the total time required for your property or field.

Allele Frequency Calculator

Calculate dominant and recessive allele frequencies (p and q), genotype proportions, and test for Hardy-Weinberg equilibrium from observed counts.

Animal Mortality Rate Calculator

Calculate cumulative mortality rate, flock or herd survival rate, and daily loss rates with veterinary production health benchmarks.

Annealing Temperature Calculator

Calculate PCR primer melting temperature (Tm) and optimal annealing temperature (Ta) with salt correction and GC clamp analysis.