Converters & Calculators
Mass Diffusivity: Equation And Applications
What is Mass Diffusivity?
The mass diffusivity, often denoted by DD, describes the rate at which particles or molecules of one substance spread within another, usually in a liquid medium. This physical property quantitatively measures the ability of a substance to diffuse from a region of high concentration to one of lower concentration. Diffusion occurs as a result of random molecular motion and concentration gradients. Mass diffusivity is critical in many industrial and scientific fields, such as chemical engineering, biology, and environmental science.
Equation of Diffusivity (Fick's Law)
The most frequently utilised model to describe mass diffusion is Fick's law of diffusion. This law relates the diffusion flux – the amount of substance that diffuses per unit area per unit time – to the concentration gradient.
The equation for the first Fick's law is:
J=-D⋅(dC/dx)
where:
- J is the diffusion flux (mol/m2·s), representing the rate of diffusion.
- D is the mass diffusivity (m2/s), indicating how easily a substance diffuses.
- dC/dx is the concentration gradient (mol/m3 per m), which shows the change in the diffusing substance's concentration with distance.
The negative sign indicates that the flux is directed from regions of high concentration to regions of lower concentration, thereby reducing the concentration gradient. Fick's law assumes a steady-state diffusion process, wherein the concentration profile remains constant.
For non-steady (time-dependent) diffusion, Fick's second law is used:
∂C/∂t = D*∂^2C/∂x^2
This equation accounts for temporal changes in concentration and is frequently applied in contexts such as diffusion in biological systems or in non-steady heat or mass transfer in engineering applications.
Factors Affecting Mass Diffusivity
Several factors affect the diffusivity of a substance:
1. Temperature: Generally, the diffusivity increases with temperature, since molecules move faster at elevated temperatures, thereby promoting diffusion.
2. Viscosity of the medium: A higher viscosity (for example, in syrup) impedes molecular movement, reducing diffusivity compared to a lower viscosity medium (such as water).
3. Molecular size: Larger molecules generally diffuse more slowly than smaller ones because their greater size and mass diminish mobility.
4. Concentration gradients: A larger concentration difference between regions leads to a higher diffusion rate; however, as the gradient decreases, the rate of diffusion is reduced.
5. Nature of the diffusing substance: The chemical characteristics (e.g. polarity, solubility) influence the substance's diffusion behaviour.
6. Properties of the medium: The medium's attributes, such as porosity or density, affect diffusivity. For instance, gases generally show higher diffusivity than liquids due to weaker intermolecular forces.
Applications of Mass Diffusivity
Mass diffusivity plays a crucial role in various scientific and industrial applications:
1. Chemical Engineering: Diffusion is essential for processes such as mixing, separation, and reaction kinetics. In reactors, the rate of diffusion directly impacts the efficiency of chemical reactions, especially in catalytic processes.
2. Pharmaceutical Industry: Mass diffusivity is vital for developing drug delivery systems. Controlled-release formulations depend on the manner in which drugs diffuse through membranes or other biological barriers.
3. Biological Systems: Understanding mass diffusivity is imperative for studying processes such as oxygen and nutrient transport within cells and tissues, as well as the diffusion of signalling molecules in organisms.
4. Environmental Science: Diffusion governs the dispersion of pollutants in both air and water. Accurately modelling how substances spread in natural systems enables better predictions of environmental impact and informs remediation strategies.
5. Materials Science: Diffusivity is relevant to processes such as sintering, coating, and material fabrication where the diffusion of substances within a material affects its properties.
Values of Diffusion Coefficients
Diffusion coefficients vary significantly depending on the substance and the medium. For example:
- Water: Diffusion coefficients for common substances in water range from 1 × 10-9 to 1 × 10-6 m2/s.
- Air: In air, gases such as oxygen or carbon dioxide typically exhibit diffusivity values in the range of 1 × 10-5 to 1 × 10-4 m2/s.
- Solids: Diffusion coefficients in solids are typically much lower, ranging from 1 × 10-15 to 1 × 10-10 m2/s.
Table 1: Diffusion Coefficients in Water
|
Substance |
Diffusion Coefficient (DD, m2/s) |
|
Oxygen (O₂) |
4.3×10-9 |
|
Carbon Dioxide (CO₂) |
1.6×10-9 |
|
Sodium Chloride (NaCl) |
1.3×10-9 |
|
Glucose |
6.0×10-10 |
|
Urea |
1.5×10-9 |
Table 2: Diffusion Coefficients in Air (at 25°C)
|
Substance |
Diffusion Coefficient (DD, m2/s) |
|
Oxygen (O₂) |
1.94×10-5 |
|
Nitrogen (N₂) |
1.78×10-5 |
|
Carbon Dioxide (CO₂) |
1.60×10-5 |
|
Water Vapour (H₂O) |
2.3×10-5 |
|
Ammonia (NH₃) |
1.4×10-5 |
Table 3: Diffusion Coefficients in Solids (at 1000°C)
|
Substance |
Diffusion Coefficient (DD, m2/s) |
|
Iron (Fe) |
4.8×10-14 |
|
Copper (Cu) |
7.2×10-14 |
|
Aluminium (Al) |
3.0×10-14 |
|
Silicon (Si) |
1.1×10-15 |
Table 4: Diffusion Coefficients in Polymers
|
Polymer |
Diffusion Coefficient (DD, m2/s) |
|
Polyethylene (PE) |
2.5×10-13 |
|
Polystyrene (PS) |
1.0×10-13 |
|
Polyvinylchloride (PVC) |
3.0×10-13 |
|
Polypropylene (PP) |
1.3×10-13 |
Table 5: Diffusion Coefficients in Gases (at 1 atm and 25°C)
|
Gas |
Diffusion Coefficient (DD, m2/s) |
|
Hydrogen (H₂) |
6.2×10-5 |
|
Methane (CH₄) |
4.6×10-5 |
|
Nitrogen (N₂) |
1.9×10-5 |
|
Oxygen (O₂) |
1.9×10-5 |
|
Carbon Dioxide (CO₂) |
1.5×10-5 |
Further information is available at Stanford Advanced Materials (SAM).
Frequently Asked Questions
1. What is the difference between mass diffusivity and thermal diffusivity?
Mass diffusivity refers to the spread of particles within a medium, whereas thermal diffusivity describes how heat is conducted through a substance. Both phenomena concern transport processes; however, mass diffusivity focuses on species transport, while thermal diffusivity pertains to heat transport.
2. How does the molecular weight of a substance affect its diffusivity?
Typically, heavier molecules diffuse at a slower rate than lighter ones because increased molecular weight and size reduce mobility.
3. Can the mass diffusivity in a system remain constant?
In many cases, mass diffusivity is treated as a constant under steady-state conditions. However, in inhomogeneous systems or systems with temperature gradients, diffusivity may vary.
Chin Trento
