Edited by Aimie Carlson || By Janet White || Published on March 9, 2024

## Key Differences

Steady state diffusion is characterized by a constant concentration gradient, leading to a uniform rate of diffusion over time. This means that the amount of substance entering a region is equal to the amount leaving, resulting in no net accumulation. In contrast, unsteady state diffusion occurs when the concentration gradient changes over time, leading to a variable rate of diffusion. This dynamic process can be observed during the initial stages of diffusion, where concentration gradients are not yet stabilized.
In steady state diffusion, the diffusion flux (the amount of substance diffusing per unit area per unit time) remains constant because the driving force, the concentration gradient, does not change with time. This condition is often achieved in systems where the diffusing substance reaches an equilibrium. Conversely, unsteady state diffusion deals with situations where the diffusion flux changes over time as the concentration gradients evolve, reflecting a non-equilibrium state that gradually moves toward equilibrium.
Steady state diffusion is typically described by Fick's first law of diffusion, which assumes a constant concentration gradient. This simplifies the analysis of diffusion processes in materials, such as the permeation of gases through membranes or the diffusion of solutes in a solvent. Unsteady state diffusion, however, requires Fick's second law, which accounts for the time-dependent change in concentration gradients, making it suitable for analyzing transient diffusion phenomena, such as the cooling of materials or the drying of paints.
Applications of steady state diffusion are prevalent in industrial processes where constant conditions are maintained for uniform product quality, such as in the steady delivery of drugs through certain medical devices. Unsteady state diffusion is crucial in understanding and designing processes like annealing in metallurgy, where the properties of a material change over time due to variable diffusion rates.
The mathematical modeling of steady state diffusion is generally simpler, using linear equations, while unsteady state diffusion models are more complex, often requiring differential equations to describe the time-dependent changes. This complexity reflects the dynamic nature of unsteady state processes, where initial and boundary conditions significantly influence the diffusion behavior.

## Comparison Chart

Constant over time
Changes over time

Constant
Variable

### Governing Law

Fick's first law
Fick's second law

### Mathematical Complexity

Relatively simple
More complex due to time dependency

### Application Examples

Gas permeation through membranes, drug delivery
Annealing in metallurgy, drying processes

The equilibrium state of diffusion in a closed system.
In a sealed container, the steady state diffusion of gas molecules results in uniform distribution.

A scenario where diffusive flux changes as the system evolves.
The drying of paint involves unsteady state diffusion as the solvent evaporates over time.

A scenario where the diffusive flux across a boundary is unchanging.
The steady state diffusion of nutrients through soil is crucial for plant growth.

Diffusion characterized by time-dependent concentration profiles.
Unsteady state diffusion is observed when a sugar cube dissolves in water, gradually disappearing.

Diffusion with a constant concentration gradient across the material.
Oxygen diffuses through a cell membrane at a constant rate in steady state diffusion.

Diffusion process where concentration gradients vary with time.
During the initial mixing of two gases, unsteady state diffusion occurs until equilibrium is achieved.

The process where the rate of diffusion does not change over time.
In industrial filtration, steady state diffusion ensures consistent separation efficiency.

The process describing the approach to equilibrium in a diffusive system.
Cooling of molten metal shows unsteady state diffusion as temperature gradients even out.

A condition in which the system's properties remain constant in time.
Perfume molecules disperse throughout a room at a steady rate once equilibrium is reached.

The transient phase of diffusion before reaching equilibrium.
In unsteady state diffusion, the concentration of a solute in solvent changes rapidly at first.

## FAQs

#### What defines unsteady state diffusion?

A diffusion process where concentration gradients and rates change with time.

It changes over time until equilibrium is reached.

#### Can steady state diffusion occur in all materials?

Yes, but only under conditions where the concentration gradient does not change.

#### What is steady state diffusion?

A diffusion process with a constant concentration gradient and rate over time.

#### What factors influence unsteady state diffusion?

Temperature, concentration gradients, and material properties.

It remains constant, ensuring a uniform diffusion rate.

#### How do you model steady state diffusion?

Using Fick's first law, which assumes a constant concentration gradient.

Yes, a system can transition from unsteady to steady state as it reaches equilibrium.

#### How does temperature affect steady state diffusion?

It can influence the diffusion coefficient but does not change the steady state nature.

#### What mathematical approach is used for unsteady state diffusion?

Fick's second law, accounting for time-dependent concentration changes.

#### Can steady state diffusion be achieved instantly?

No, it requires time for the system to reach a balance where the gradient stabilizes.

#### How do boundary conditions affect steady state diffusion?

They define the concentration gradient and thus the rate of diffusion.

#### What role does temperature play in unsteady state diffusion?

It affects the rate of concentration change and diffusion speed.

The diffusion coefficient can apply to both but is used differently depending on time-dependency of the concentration gradient.

#### What are practical applications of steady state diffusion?

Controlled drug release and membrane filtration are common examples.

#### Where is unsteady state diffusion commonly observed?

In processes like annealing and drying, where conditions change over time.

#### How can unsteady state diffusion be controlled?

Through temperature regulation and modifying the diffusion environment.

#### Can steady state diffusion rates be manipulated?

Yes, by altering the concentration gradient or diffusion medium properties.

#### What impact do boundary conditions have on unsteady state diffusion?

They influence how concentration profiles evolve over time.