4.3 Advanced Mass Transfer

Multicomponent mass transfer is a complex process involving the movement of multiple species across interfaces. This topic explores models like Fick's law and Maxwell-Stefan equations, which describe diffusion and interactions between components in various geometries.

Interfacial phenomena play a crucial role in mass transfer, affecting processes like extraction and adsorption. Understanding concepts like interfacial tension, Marangoni effects, and instabilities is key to optimizing mass transfer equipment and reactor design in chemical engineering applications.

Multicomponent Mass Transfer and Interfacial Phenomena

Models for multicomponent mass transfer

Top images from around the web for Models for multicomponent mass transfer

• 

  Thermo-osmotic pressure and resistance to mass transport in a vapor-gap membrane - Physical ... View original

  Is this image relevant?

• 

  ACP - Maxwell–Stefan diffusion: a framework for predicting condensed phase diffusion and phase ... View original

  Is this image relevant?

• 

  MS - Heat transfer and MHD flow of non-newtonian Maxwell fluid through a parallel plate channel ... View original

  Is this image relevant?

• 

  Thermo-osmotic pressure and resistance to mass transport in a vapor-gap membrane - Physical ... View original

  Is this image relevant?

• 

  ACP - Maxwell–Stefan diffusion: a framework for predicting condensed phase diffusion and phase ... View original

  Is this image relevant?

1 of 3

Top images from around the web for Models for multicomponent mass transfer

• 

  Thermo-osmotic pressure and resistance to mass transport in a vapor-gap membrane - Physical ... View original

  Is this image relevant?

• 

  ACP - Maxwell–Stefan diffusion: a framework for predicting condensed phase diffusion and phase ... View original

  Is this image relevant?

• 

  MS - Heat transfer and MHD flow of non-newtonian Maxwell fluid through a parallel plate channel ... View original

  Is this image relevant?

• 

  Thermo-osmotic pressure and resistance to mass transport in a vapor-gap membrane - Physical ... View original

  Is this image relevant?

• 

  ACP - Maxwell–Stefan diffusion: a framework for predicting condensed phase diffusion and phase ... View original

  Is this image relevant?

1 of 3

• Fick's law for multicomponent diffusion describes mass transport driven by concentration gradients
  • Generalized Fick's law accounts for interactions between diffusing species: $J_i = -\sum_{j=1}^{n-1} D_{ij} \nabla C_j$
  • Maxwell-Stefan equations consider the relative velocities and driving forces between components
• Mass transfer coefficients quantify the rate of mass transfer in multicomponent systems
  • Individual mass transfer coefficients $k_i$ describe the transfer rate of each component
  • Overall mass transfer coefficients $K_i$ account for the combined resistance of all components
• Modeling mass transfer in various geometries enables the analysis of different systems
  • Planar systems include membranes for separation and thin films for coating (liquid membranes, polymer films)
  • Cylindrical systems are common in separation processes and catalytic reactors (hollow fiber membranes, packed bed reactors)
  • Spherical systems are relevant in dispersed phase systems and particle-fluid interactions (emulsion droplets, catalyst pellets)

Interfacial phenomena in mass transfer

• Interfacial tension and surface energy play a crucial role in mass transfer across interfaces
  • Young-Laplace equation relates the pressure difference across a curved interface to its radius and surface tension: $\Delta P = \frac{2\gamma}{R}$
  • Gibbs adsorption isotherm describes the relationship between surface tension and the chemical potentials of adsorbed species: $d\gamma = -\sum_{i=1}^n \Gamma_i d\mu_i$
• Mass transfer across interfaces occurs in various systems and processes
  • Liquid-liquid interfaces are essential in extraction and emulsification (solvent extraction, liquid-liquid microfluidics)
  • Gas-liquid interfaces are involved in absorption and desorption processes (gas scrubbing, aeration)
  • Solid-fluid interfaces play a role in adsorption and dissolution phenomena (activated carbon adsorption, mineral leaching)
• Marangoni effects and interfacial instabilities can enhance or hinder mass transfer
  • Marangoni number quantifies the relative importance of surface tension gradients and viscous forces: $Ma = \frac{d\gamma/dx}{\mu D/L}$
  • Interfacial turbulence induced by Marangoni effects can significantly enhance mass transfer rates (Marangoni convection)

Mass Transfer Equipment Design and Optimization

Design of mass transfer equipment

• Distillation columns are widely used for separating liquid mixtures based on differences in volatility
  • Equilibrium stages and the McCabe-Thiele method are used for the design and analysis of distillation columns
  • HETP represents the efficiency of a distillation column in terms of the equivalent height of an ideal stage
  • Multicomponent distillation and azeotropes require advanced design considerations (extractive distillation, pressure-swing distillation)
• Absorption and stripping columns are employed for gas-liquid mass transfer operations
  • Packed columns use structured or random packing materials to provide a large interfacial area for mass transfer (Raschig rings, Pall rings)
  • Tray columns utilize perforated plates or valve trays to create a series of equilibrium stages (sieve trays, bubble-cap trays)
  • Mass transfer and hydraulic considerations, such as flooding and pressure drop, are critical in column design
• Liquid-liquid extraction equipment is used for separating components based on their solubility differences
  • Mixer-settlers and column extractors provide contact between immiscible liquid phases (perforated plate columns, Karr columns)
  • Centrifugal extractors and coalescing devices enhance phase separation and improve extraction efficiency (Podbielniak extractors, electrostatic coalescers)
• Membrane separation processes rely on selective permeation of components through a membrane
  • Pervaporation, gas separation, and reverse osmosis are common membrane-based separation processes
  • Membrane materials and module configurations are selected based on the specific application (polymeric membranes, ceramic membranes, spiral-wound modules, hollow fiber modules)

Mass transfer in reactions and reactors

• Mass transfer effects in heterogeneous reactions can limit the overall reaction rate
  • Gas-solid reactions can be described by the shrinking core model, which accounts for diffusion and reaction resistances (noncatalytic gas-solid reactions)
  • Gas-liquid reactions are often analyzed using film theory and penetration theory to describe mass transfer and reaction at the interface (gas absorption with chemical reaction)
  • Liquid-solid reactions involve dissolution and precipitation processes, where mass transfer can control the reaction rate (mineral leaching, crystallization)
• Interphase mass transfer and reaction kinetics are characterized by dimensionless numbers
  • Damköhler number compares the reaction rate to the mass transfer rate: $Da = \frac{\text{reaction rate}}{\text{mass transfer rate}}$
  • Effectiveness factor quantifies the actual reaction rate relative to the rate without mass transfer limitations: $\eta = \frac{\text{actual reaction rate}}{\text{reaction rate without mass transfer limitations}}$
• Mass transfer considerations are crucial in reactor design and optimization
  • Packed bed reactors require analysis of axial dispersion and radial gradients to ensure efficient mass transfer and reaction (trickle bed reactors, fixed bed catalytic reactors)
  • Fluidized bed reactors involve complex bubble dynamics and mixing patterns that affect mass transfer and reaction rates (gas-solid fluidized bed reactors)
  • Multiphase reactors, such as bubble columns and slurry reactors, rely on effective mass transfer and reaction coupling for optimal performance (Fischer-Tropsch synthesis, hydrogenation reactions)