9.3 Transport phenomena in membrane separations

Membrane separations rely on diffusion, convection, and sieving to move molecules across barriers. These mechanisms, driven by concentration gradients, pressure differences, and size exclusion, form the basis for various industrial separation processes.

Understanding mass transfer equations is crucial for modeling membrane behavior. Fick's law, the solution-diffusion model, and Darcy's law describe different transport phenomena. Factors like concentration polarization and fouling impact membrane efficiency, while strategies such as surface modification and hybrid processes enhance performance.

Transport Mechanisms in Membrane Separations

Transport mechanisms in membrane separations

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• Diffusion drives spontaneous movement of molecules from high to low concentration areas primarily in dense membranes
  • Concentration gradient propels molecular motion
  • Predominant in gas separation and reverse osmosis
• Convection moves molecules via bulk fluid flow in porous membranes
  • Pressure gradient or external forces induce movement
  • Prevalent in ultrafiltration and microfiltration processes
• Sieving separates based on size exclusion rejecting larger molecules
  • Pore size determines separation efficiency
  • Applied in protein fractionation and particle removal (blood cells)

Mass transfer equations for membranes

• Fick's law of diffusion quantifies diffusive flux relative to concentration gradient
  • $J = -D \frac{dC}{dx}$ where J represents diffusive flux, D diffusion coefficient, C concentration, x distance
  • Utilized in modeling gas permeation through polymeric membranes
• Solution-diffusion model applies to dense membranes involving sorption, diffusion, desorption
  • Flux equation: $J_i = -D_i K_i \frac{dp_i}{dx}$ with D_i as diffusion coefficient, K_i solubility coefficient, p_i partial pressure
  • Describes transport in reverse osmosis and pervaporation
• Darcy's law characterizes convective flow through porous media
  • $J = -\frac{k}{\mu} \frac{dP}{dx}$ where k denotes permeability, μ viscosity, P pressure
  • Applied in modeling ultrafiltration and microfiltration processes

Factors affecting membrane performance

• Concentration polarization accumulates rejected species near membrane surface
  • Creates additional mass transfer resistance
  • Reduces effective driving force in desalination processes
• Fouling deposits particles or solutes on membrane surface or within pores
  • Types include cake formation, pore blocking, adsorption
  • Decreases permeate flux and alters selectivity in wastewater treatment
• Membrane compaction densifies membrane structure under pressure
  • Reduces permeability particularly in polymeric membranes
  • Affects long-term performance in high-pressure applications (seawater desalination)
• Temperature influences diffusion rates and solution viscosity
  • Generally increases permeability but may decrease selectivity
  • Critical in gas separation and pervaporation processes
• pH and ionic strength impact membrane charge and solute-membrane interactions
  • Affect both permeability and selectivity
  • Important in protein separation and electrodialysis

Strategies for enhancing membrane efficiency

• Hydrodynamic improvements reduce concentration polarization
  • Increase cross-flow velocity
  • Implement turbulence promoters or spacers in spiral-wound modules
• Membrane surface modification enhances selectivity and reduces fouling
  • Alter surface chemistry (hydrophilicity, charge)
  • Introduce functional groups for specific interactions (affinity membranes)
• Pulsed or variable pressure operation periodically relieves concentration polarization and fouling
  • Applied in reverse osmosis and ultrafiltration systems
  • Enhances long-term membrane performance
• Feed pretreatment removes foulants and adjusts solution properties
  • Implement filtration, pH adjustment, or chemical addition
  • Crucial in wastewater treatment and desalination processes
• Membrane cleaning protocols maintain performance
  • Chemical cleaning removes foulants (acids, bases, enzymes)
  • Backwashing for porous membranes in water treatment
• Advanced module designs optimize flow patterns and reduce dead zones
  • Spiral-wound configuration for high packing density
  • Hollow fiber modules for large surface area-to-volume ratio
• Hybrid processes combine membrane separation with other techniques
  • Membrane bioreactors integrate biological treatment with membrane filtration
  • Forward osmosis-reverse osmosis systems for enhanced water recovery