Mass Transfer
Comprehensive guide to mass transfer principles, mechanisms, and applications in engineering.
Fick's First Law of Diffusion
Fick's First Law relates the diffusive flux to the concentration gradient. It states that the flux goes from regions of high concentration to regions of low concentration, with a magnitude proportional to the concentration gradient:
J = -D × (dC/dx)
Where:
- J = diffusive flux (mol/(m²·s))
- D = diffusion coefficient (m²/s)
- dC/dx = concentration gradient (mol/m⁴)
Fick's Second Law of Diffusion
Fick's Second Law predicts how diffusion causes the concentration to change with time:
∂C/∂t = D × (∂²C/∂x²)
Where:
- ∂C/∂t = rate of change of concentration with time (mol/m³/s)
- D = diffusion coefficient (m²/s)
- ∂²C/∂x² = second derivative of concentration with respect to position (mol/m⁵)
Mass Transfer Coefficient
The mass transfer coefficient is used to describe the rate of mass transfer between phases:
N = k × (C₁ - C₂)
Where:
- N = mass flux (mol/(m²·s))
- k = mass transfer coefficient (m/s)
- C₁ = concentration at interface (mol/m³)
- C₂ = concentration in bulk fluid (mol/m³)
The mass transfer coefficient depends on the flow conditions, geometry, and fluid properties.