Mass Transfer

Why it matters

Mass transfer is a critical aspect of many industrial processes, such as drying, distillation, and absorption. Understanding mass transfer helps engineers design efficient systems for chemical processing, environmental control, and energy production.

Key ideas

• Mass Transfer Mechanisms: Mass transfer occurs through diffusion and convection. Diffusion is the movement of molecules from high to low concentration, while convection involves bulk movement of fluid.
• Fick's Laws of Diffusion: These laws describe how diffusion occurs. The first law relates the diffusive flux to the concentration gradient, and the second law predicts how diffusion causes the concentration to change over time.
• Mass Transfer Coefficient: This is a measure of how easily mass is transferred from one phase to another. It is influenced by factors such as fluid velocity, viscosity, and temperature.
• Dimensionless Numbers: Important in mass transfer analysis, including the Schmidt number (Sc), Sherwood number (Sh), and Peclet number (Pe), which help characterize the flow and diffusion processes.

These simple relations assume Fickian diffusion on a consistent concentration basis. If concentrations are in mol/m³, the resulting flux is mol/(m²·s), not kg/(m²·s). Interphase transfer requires equilibrium/partition relations when converting concentrations between phases. Total species flux may also include bulk advection. Sc = ν/D, Sh = k_c L/D, and mass-transfer Pe = VL/D = Re Sc.

Formulas

• J = -D (dC/dx)
  • J: Diffusive flux (kg/m²·s)
  • D: Diffusion coefficient (m²/s)
  • dC/dx: Concentration gradient (kg/m⁴)
• N = kc (C1 - C2)
  • N: Mass flux (kg/(m²·s)); multiply by area to obtain rate in kg/s
  • kc: Mass transfer coefficient (m/s)
  • C1, C2: Surface and bulk concentrations on the same phase/basis (kg/m³)

Worked example

Given:

• Diffusion coefficient, D = 2.5 × 10⁻⁵ m²/s
• Concentration gradient, dC/dx = 0.1 kg/m⁴

Find: Diffusive flux, J

1. Use Fick's first law: J = -D (dC/dx)
2. Substitute the given values: J = -(2.5 × 10⁻⁵ m²/s)(0.1 kg/m⁴)
3. Calculate: J = -2.5 × 10⁻⁶ kg/m²·s

Answer: -2.5 × 10⁻⁶ kg/m²·s

Common mistakes

• Confusing the direction of diffusion; the simple Fickian model here gives diffusion down the concentration gradient.
• Misapplying Fick's laws by not considering the correct concentration gradient.
• Ignoring the effects of temperature and pressure on the diffusion coefficient.

For GATE ME

Questions often involve calculating mass transfer rates using Fick's laws or determining dimensionless numbers. Practice problems on diffusion in gases and liquids, and understand the impact of different parameters on mass transfer.

Quick check

1. What is the primary mechanism of mass transfer in a still fluid?
2. Name a dimensionless number relevant to mass transfer.
3. What does the mass transfer coefficient depend on?

Answers: 1. Diffusion 2. Schmidt number 3. Fluid velocity, viscosity, temperature