Mass Transfer Calculator

Calculate diffusion coefficients, mass transfer rates, and concentration profiles for engineering applications.

Diffusion Coefficient
Mass Transfer Rate
Concentration Profile

Understanding Mass Transfer

Mass transfer is the net movement of mass from one location to another. It plays a crucial role in many industrial processes including distillation, absorption, extraction, and drying.

Key Insight: Mass transfer rates depend on the driving force (concentration gradient) and the resistance to mass transfer, which is inversely related to the mass transfer coefficient.

Fundamental Equations

1

Fick's Law of Diffusion: Describes diffusion driven by a concentration gradient:

J = -D · (dc/dx)

Where J is the diffusion flux, D is the diffusion coefficient, and dc/dx is the concentration gradient.

2

Mass Transfer Coefficient: Relates the mass transfer rate to the concentration difference:

N = k · A · ΔC

Where N is the mass transfer rate, k is the mass transfer coefficient, A is the area, and ΔC is the concentration difference.

3

Sherwood Number: Dimensionless number representing the ratio of convective to diffusive mass transfer:

Sh = (k · L) / D

Where L is the characteristic length and D is the diffusion coefficient.

Diffusion Coefficient Estimation

Method Application Key Parameters Accuracy
Wilke-Chang Liquid systems Solvent viscosity, solute molar volume ±10-15%
Fuller et al. Gas systems Molecular volumes, temperature, pressure ±5-10%
Stokes-Einstein Large molecules in liquids Solvent viscosity, molecular radius ±10-20%

Typical Diffusion Coefficients

System Temperature (°C) D (m²/s) Conditions
O₂ in water 25 2.10 × 10⁻⁹ Dilute solution
CO₂ in water 25 1.92 × 10⁻⁹ Dilute solution
Ethanol in water 25 1.24 × 10⁻⁹ Dilute solution
O₂ in air 25 2.01 × 10⁻⁵ 1 atm
CO₂ in air 25 1.64 × 10⁻⁵ 1 atm

Mass Transfer Correlations

Different geometries and flow conditions require different correlations for mass transfer coefficients:

Flat Plate (Laminar Flow): Sh = 0.664 · Re¹/² · Sc¹/³

Flat Plate (Turbulent Flow): Sh = 0.037 · Re⁴/⁵ · Sc¹/³

Sphere: Sh = 2 + 0.6 · Re¹/² · Sc¹/³

Pipe Flow: Sh = 0.023 · Re⁰·⁸ · Sc¹/³

Applications of Mass Transfer

  • Chemical Reactors: Mass transfer limitations can affect reaction rates
  • Separation Processes: Distillation, absorption, extraction, and adsorption
  • Environmental Engineering: Air and water pollution control
  • Biomedical Engineering: Drug delivery and artificial organs
  • Materials Processing: Drying, crystallization, and coating

Frequently Asked Questions

Diffusion coefficients are influenced by temperature (increases with temperature), pressure (decreases with pressure for gases), molecular size (larger molecules diffuse slower), and the nature of the medium (viscosity, molecular interactions).

Turbulence enhances mass transfer by reducing the boundary layer thickness and increasing mixing. This results in higher mass transfer coefficients compared to laminar flow conditions.

Diffusion refers specifically to the movement of molecules due to a concentration gradient. Mass transfer is a broader term that includes diffusion but also encompasses convection (bulk movement) and other mechanisms of mass transport.

The penetration theory is applicable to mass transfer at interfaces where the contact time is short, such as in gas-liquid contactors, falling films, and bubble columns. It assumes unsteady-state diffusion into a semi-infinite medium.

The choice of correlation depends on the geometry (flat plate, sphere, cylinder, etc.), flow conditions (laminar or turbulent), and the nature of the interface (fluid-fluid or fluid-solid). Always check the Reynolds and Schmidt numbers to ensure the correlation is applicable to your specific conditions.