Steady State Diffusion of Gases and Liquids through Solids

Definition

Steady-state diffusion is a mass transfer process where the concentration gradient (the change in concentration over distance) remains constant over time. In this state, the flux of the diffusing species (gas or liquid) through a solid barrier does not change, meaning the rate of diffusion entering one side of the solid is exactly equal to the rate of diffusion exiting the other side.

Main Content

1. Fick’s First Law of Diffusion

This fundamental law governs steady-state diffusion, stating that the flux (J) is proportional to the concentration gradient.
Mathematically expressed as $J = -D (dC/dx)$, where 'D' is the diffusion coefficient and 'dC/dx' is the concentration change over distance.

2. Concentration Profile and Flux

In steady state, the concentration profile within the solid remains linear over time, ensuring a constant driving force.
If the concentration at the source (side 1) is $C_1$ and at the sink (side 2) is $C_2$ across a thickness 'z', the flux remains uniform throughout the solid.

3. Mechanism of Transport

Diffusion occurs as particles move from regions of high chemical potential to low chemical potential.
In gases, molecules often dissolve into the surface of the solid (adsorption) before diffusing through the lattice structure (interstitial or vacancy diffusion) and eventually desorbing on the other side.

Concentration (C)
  ^
C1|-------.
  |        \
  |         \
  |          \
C2|           -------
  +----------------------> Distance (x)
  0          z

Representation of a linear concentration gradient across a solid thickness 'z'.

Working / Process

1. Adsorption at the Interface

The gas or liquid molecules come into contact with the surface of the solid material.
The molecules "dissolve" or soak into the surface layer of the solid, reaching an equilibrium concentration determined by the solubility of the substance.

2. Internal Diffusion

Molecules migrate through the solid matrix driven by the concentration gradient.
This process is highly dependent on the temperature and the structure of the solid; denser solids typically result in lower diffusion rates.

3. Desorption at the Exit

Once the molecules reach the opposite face of the solid, they leave the solid matrix.
They enter the surrounding medium or space (the sink) where the concentration is lower, completing the transition through the barrier.

Advantages / Applications

Membrane Separation: Used in gas separation processes, such as removing carbon dioxide from natural gas streams using polymer membranes.
Packaging Industry: Vital for designing food packaging materials that control the diffusion of oxygen and moisture to extend shelf life.
Pharmaceuticals: Controlled drug delivery systems often rely on steady-state diffusion to release medication into the body at a constant, predictable rate.

Summary

Steady-state diffusion describes a balanced mass transfer process where the rate of flow remains constant because the concentration gradient within the solid does not change with time. It is primarily defined by Fick's First Law and is essential for designing materials for separation, storage, and controlled release.

Key Terms: Flux (rate of transfer), Diffusion Coefficient (ease of movement), Concentration Gradient (driving force), Solubility (amount absorbed), and Steady State (time-independent flow).