7.3 Interphase mass transfer

Interphase mass transfer is all about stuff moving between different phases. It's crucial in chemical engineering, from oxygen absorption in fermentation to pollutant removal from wastewater. Understanding this process helps engineers design better equipment and optimize industrial processes.

The rate of mass transfer depends on concentration differences, interfacial area, and mass transfer coefficients. Engineers use various models like two-film theory and penetration theory to predict and improve mass transfer rates in different systems.

Interphase Mass Transfer Principles

Fundamentals of Interphase Mass Transfer

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• Interphase mass transfer involves the movement of a component from one phase to another due to a concentration gradient or driving force
• Mass transfer occurs across the interface between two immiscible phases, such as gas-liquid (oxygen absorption in fermentation), liquid-liquid (solvent extraction of antibiotics), or solid-fluid interfaces (adsorption of pollutants on activated carbon)
• The direction of mass transfer is always from the phase with higher concentration to the phase with lower concentration of the transferring component
• Equilibrium is reached when the chemical potentials of the transferring component are equal in both phases, and no net mass transfer occurs

Factors Influencing Interphase Mass Transfer Rates

• The rate of interphase mass transfer is influenced by factors such as the concentration difference, interfacial area, and mass transfer coefficients
• Concentration difference: The larger the concentration difference between the phases, the higher the driving force for mass transfer
• Interfacial area: Increasing the interfacial area (e.g., using packed columns, trays, or dispersed systems like bubbles or droplets) enhances the mass transfer rate
• Mass transfer coefficients: Higher mass transfer coefficients, which depend on fluid properties (density, viscosity, diffusivity) and hydrodynamic conditions (flow regime, mixing), indicate faster mass transfer rates

Mass Transfer Rates Across Interfaces

Gas-Liquid Mass Transfer

• Gas-liquid mass transfer occurs when a soluble gas is absorbed into a liquid or a volatile component is stripped from a liquid into a gas phase
• The rate of gas-liquid mass transfer is influenced by the solubility of the gas, the interfacial area, and the mass transfer coefficients in both phases
• Examples include oxygen absorption in fermentation processes, CO2 absorption in gas treating, and air stripping of volatile organic compounds from wastewater

Liquid-Liquid Mass Transfer

• Liquid-liquid mass transfer occurs when a solute is transferred from one liquid phase to another immiscible liquid phase
• The rate of liquid-liquid mass transfer depends on the distribution coefficient of the solute, the interfacial area, and the mass transfer coefficients in both liquid phases
• Examples include solvent extraction processes, such as the extraction of antibiotics from fermentation broths or the removal of contaminants from wastewater

Solid-Fluid Mass Transfer

• Solid-fluid mass transfer occurs when a solute is transferred between a solid phase and a fluid phase (gas or liquid)
• The rate of solid-fluid mass transfer is influenced by the solubility of the solute, the surface area of the solid, and the mass transfer coefficient in the fluid phase
• Examples include adsorption processes, such as the removal of pollutants from gas streams using activated carbon, or the leaching of valuable components from solid materials

Modeling Interphase Mass Transfer

Two-Film Theory

• The two-film theory assumes that mass transfer resistance is concentrated in two thin films on either side of the interface, with bulk phases being well-mixed
• The theory considers that the mass transfer rate is controlled by the diffusion through these films, and the concentrations at the interface are in equilibrium
• The overall mass transfer rate is determined by the sum of the resistances in both films, represented by the reciprocal of the overall mass transfer coefficient

Penetration and Surface Renewal Theories

• The penetration theory assumes that fluid elements from the bulk phase come into contact with the interface for a short time before being replaced by fresh fluid elements
  • During this contact time, the solute penetrates the fluid element by unsteady-state diffusion, and the mass transfer rate is determined by the contact time and the diffusivity of the solute
• The surface renewal theory is an extension of the penetration theory, considering that the fluid elements have a random distribution of contact times at the interface
  • The mass transfer rate is determined by the average contact time and the diffusivity of the solute

Film-Penetration Theory

• The film-penetration theory combines the concepts of the two-film theory and the penetration theory
• It assumes that mass transfer occurs by both steady-state diffusion through the films and unsteady-state diffusion in the bulk phases
• This theory provides a more comprehensive description of the mass transfer process, accounting for both film and bulk phase resistances

Factors Influencing Interphase Transfer

Interfacial Area and Specific Interfacial Area

• The rate of interphase mass transfer is directly proportional to the interfacial area between the phases
• Increasing the interfacial area through the use of packed columns, trays, or dispersed systems (e.g., bubbles, droplets, or particles) enhances the mass transfer rate
• The specific interfacial area (interfacial area per unit volume) is a key parameter in the design of mass transfer equipment

Phase Equilibrium and Driving Force

• The distribution of the transferring component between the phases at equilibrium determines the driving force for mass transfer
• The equilibrium distribution is described by phase equilibrium relationships, such as Henry's law for gas-liquid systems or partition coefficients for liquid-liquid systems
• The departure from equilibrium, or the concentration difference between the bulk phases and the interface, drives the mass transfer process

Mass Transfer Coefficients and Correlations

• The mass transfer coefficients in each phase depend on the physical properties of the fluids, such as density, viscosity, and diffusivity, as well as the hydrodynamic conditions, such as flow regime and mixing
• Higher mass transfer coefficients indicate faster mass transfer rates and are favored by increased turbulence, smaller diffusion distances, and higher diffusivities
• Correlations and empirical equations, such as the Sherwood number correlations, are used to estimate the mass transfer coefficients based on dimensionless groups and system properties

Temperature Effects

• Higher temperatures generally increase the diffusivity and decrease the viscosity of the fluids, leading to enhanced mass transfer rates
• However, the effect of temperature on the equilibrium distribution and the solubility of the transferring component should also be considered
• Optimal temperature selection for interphase mass transfer processes requires a balance between kinetic and thermodynamic considerations