8.1 Mass transfer coefficients and boundary layers

Mass transfer coefficients and boundary layers are key concepts in understanding how substances move between fluids or surfaces. They help quantify transfer rates and identify where resistance occurs, crucial for designing efficient systems.

These concepts apply to various processes like absorption and membrane separation. By grasping how factors like fluid properties and flow conditions affect transfer rates, we can optimize industrial applications and solve complex multiphysics problems.

Mass transfer coefficients

Definition and role

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• Mass transfer coefficients quantify the rate of mass transfer between a fluid and a surface or between two fluids
• Defined as the ratio of the mass flux to the driving force, typically the concentration difference
• Higher mass transfer coefficients indicate faster mass transfer rates, while lower values suggest slower mass transfer

Applications and factors affecting mass transfer coefficients

• Used to calculate the mass transfer rate in various applications (absorption, desorption, membrane separation processes)
• In convective mass transfer, the mass transfer coefficient depends on:
  • Fluid properties
  • Flow conditions
  • Geometry of the system

Boundary layers in mass transfer

Concept and characteristics

• Boundary layers are thin regions near a surface where the fluid velocity and concentration gradients are significant
• In mass transfer, the concentration boundary layer is the region where the concentration of a species changes from its value at the surface to its bulk value in the fluid
• The thickness of the concentration boundary layer depends on:
  • Fluid properties
  • Flow conditions
  • Geometry of the system

Mass transfer mechanisms within and outside the boundary layer

• Within the concentration boundary layer, mass transfer occurs primarily by molecular diffusion
• Outside the boundary layer, convective transport dominates
• The concept of boundary layers is crucial for understanding and modeling mass transfer processes, as it helps to identify the regions where mass transfer resistance is significant

Coefficients vs boundary layer thickness

Inverse relationship

• The mass transfer coefficient is inversely proportional to the concentration boundary layer thickness
• As the boundary layer thickness increases, the mass transfer coefficient decreases, indicating a slower mass transfer rate

Dimensionless numbers and correlations

• The relationship between the mass transfer coefficient and the boundary layer thickness can be expressed using dimensionless numbers:
  • Sherwood number (Sh): represents the ratio of convective mass transfer to diffusive mass transfer and is proportional to the mass transfer coefficient
  • Schmidt number (Sc): ratio of momentum diffusivity to mass diffusivity and characterizes the relative thickness of the velocity and concentration boundary layers
• Correlations relate the Sherwood number to the Reynolds number (Re) and the Schmidt number, allowing the estimation of mass transfer coefficients based on boundary layer characteristics:
  • Dittus-Boelter equation for turbulent flow
  • Leveque equation for laminar flow

Convective mass transfer problems

Problem-solving approach

• Identify the relevant mass transfer coefficients and boundary layer characteristics for a given convective mass transfer problem
• Use appropriate correlations or experimental data to estimate the mass transfer coefficients based on the system's flow conditions, fluid properties, and geometry
• Apply the mass transfer coefficients to calculate the mass transfer rate, flux, or concentration profile in the system

Considerations and analysis

• Consider the effects of boundary layer development (entrance length, flow separation) on the mass transfer process
• Analyze the impact of changing flow conditions, fluid properties, or system geometry on the mass transfer coefficients and boundary layer characteristics
• Utilize dimensionless numbers (Sherwood number, Schmidt number) to scale up or optimize mass transfer processes in industrial applications (cooling towers, gas-liquid contactors)

Multiphysics problems

• Combine the principles of mass transfer coefficients and boundary layers with other transport phenomena (heat transfer, fluid dynamics) to solve complex multiphysics problems
• Example: Analyze the simultaneous heat and mass transfer in a cooling tower, where water evaporation and air humidification occur alongside heat exchange between water and air streams