Mass Transfer Principles

• Mass transfer is the net movement of mass from one location to another
• Mass transfer occurs in many processes, such as absorption, evaporation, drying, precipitation, membrane filtration, and distillation

Driving Forces in Mass Transfer

• Concentration difference is a primary driving force
• Mass moves from high to low concentration areas
• Other driving forces include pressure, temperature, and electrical potential differences

Fick's Law of Diffusion

• Describes diffusive mass transfer
• The mass flux is proportional to the concentration gradient
• J = -D (dC/dx), where J is mass flux, D is diffusivity, C is concentration, and x is distance
• Diffusivity depends on temperature, pressure, and the nature of the substances

Convective Mass Transfer

• Mass transfer happens between a surface and a moving fluid
• Rate depends on fluid properties, geometry, and flow rate
• Mass transfer coefficient (k) is used to quantify convective mass transfer
• Flux = k (C_bulk - C_interface), where C_bulk is bulk concentration and C_interface is interface concentration

Interphase Mass Transfer

• Mass transfer happens between two phases (e.g., gas and liquid)
• Equilibrium is established at the interface
• Two-film theory describes resistance in each phase
• Overall mass transfer coefficient relates to individual coefficients and equilibrium

Multiphase Systems

• Systems with two or more phases (gas, liquid, solid)
• Examples include gas-liquid absorption, liquid-liquid extraction, and solid-liquid leaching
• Design involves considerations for equilibrium, mass transfer rates, and hydrodynamics

Gas-Liquid Mass Transfer

• Important in processes like absorption and stripping
• Solute transfers between gas and liquid phases
• Equilibrium described by Henry's Law: p = H * C, where p is partial pressure, H is Henry's constant, and C is concentration

Liquid-Liquid Extraction

• Separation of solutes from one liquid phase to another
• Based on differences in solubility
• Distribution coefficient (K_D) determines solute partitioning: K_D = C_1/C_2

Solid-Liquid Mass Transfer

• Occurs in leaching and dissolution processes
• Solute transfers from solid to liquid phase
• Rate influenced by particle size, agitation, and temperature
• Mass transfer coefficient affected by fluid flow around particles

Mass Transfer Equipment

• Includes packed towers, tray towers, and stirred tanks
• Packed towers: Gas and liquid flow counter-currently over packing material
• Tray towers: Gas and liquid contact on trays with specific designs
• Stirred tanks: Enhanced mixing improves mass transfer rates

Absorption

• Removal of a gas component by dissolving it in a liquid
• Examples: CO2 removal from flue gas using amine solutions
• Design involves determining tower height and liquid flow rate

Stripping

• Removal of a dissolved gas from a liquid
• Opposite of absorption
• Examples: Removal of volatile organic compounds (VOCs) from wastewater using air

Distillation

• Separation of liquid mixtures based on boiling points
• Vapor and liquid phases are in contact
• Relative volatility determines ease of separation
• Common equipment: distillation columns with trays or packing

Extraction

• Separation of a solute from one liquid phase to another using a solvent
• Example: recovery of valuable compounds from natural products
• Equipment: mixer-settlers, extraction columns

Drying

• Removal of moisture from a solid material
• Mechanisms: evaporation, diffusion
• Equipment: dryers, such as spray dryers, fluidized bed dryers

Membrane Separation

• Separation using a semi-permeable membrane
• Processes: reverse osmosis, ultrafiltration, microfiltration, gas permeation
• Driving force: pressure, concentration, or electrical potential
• Membrane characteristics: selectivity, permeability, fouling

Key Parameters in Mass Transfer

• Temperature: Impacts diffusivity and equilibrium
• Pressure: Affects gas solubility and equilibrium
• Flow rate: Influences convective mass transfer coefficient
• Interfacial area: Larger area increases mass transfer rate

Dimensionless Numbers

• Sherwood number (Sh): Ratio of convective to diffusive mass transfer
• Schmidt number (Sc): Ratio of momentum to mass diffusivity
• Reynolds number (Re): Ratio of inertial to viscous forces
• These numbers help correlate mass transfer coefficients

Applications of Mass Transfer

• Chemical reactors: Mass transfer of reactants and products
• Environmental engineering: Treatment of wastewater and air pollution control
• Biochemical engineering: Fermentation and bioseparations
• Food processing: Drying, extraction, and concentration

Mass Transfer Modeling

• Mathematical representation of mass transfer processes
• Uses differential equations and empirical correlations
• Computational fluid dynamics (CFD) can simulate complex systems

Enhancing Mass Transfer

• Increasing interfacial area
• Improving mixing and turbulence
• Optimizing temperature and pressure
• Using additives to enhance solubility or reaction rates