Rate of Diffusion

Diffusion is termed as the movement of molecules of a substance in a mass unit from a higher concentration zone to a lower concentration zone allied with an active force due to concentration (the ratio of a substance in a compound mixture) difference. 

The migration of the molecules persists until the state of equilibrium (the sum of all forces is zero when the nature of the body is at rest or is in uniform motion) is achieved between two different concentration zones. The factors that influence the rate of diffusion are temperature, viscosity, and mass (particle size) of the substance.

Applications of diffusion

• Absorption of a drug released in the body (tablets, powders, ointments, injections)
• Excretion process through kidneys
• Changes of gases in alveoli

Factors affecting rate of diffusion

• Temperature
• Concentration difference
• Electrical potential
• Osmosis pressure

Fick’s law of diffusion

The process of diffusion explained by Adolf Fick states that diffusion is the movement of molecules from a higher concentration to a lower concentration region. Fick’s Law of Diffusion was proposed in 1855. He categorised the process under two conditions:

1. Normal diffusion: The process of diffusion that follows Fick’s rules is called normal diffusion. It is often known as Fickian diffusion.
2. Irregular diffusion: This is a process of diffusion that does not follow Fick’s rules. It is also known as non-Fickian diffusion.

Adolf Frick explained two inter-related laws; using the first the development of the second law is possible, which is comparable to the diffusion equation. The coefficient of diffusion ‘D’ can be solved using Fick’s law of diffusion.

According to the law, “the molar flux due to diffusion is proportional to the concentration gradient”. In this, flux refers to the molecular transportation from one zone to another, and gradient means a change in any one of the variables, i.e concentration, pressure, or temperature.

Fick’s first law 

It explains that across a concentration gradient, the migration of solutes is from a higher concentration to a lower concentration.

J = −D(dϕ/dx),

 where 

J: Diffusion Flux

D: Diffusivity

Φ: Concentration

X: Position.

Fick’s second law

Fick’s second law explains that in the process of diffusion, the time elapsed and the square of the period over which diffusion occurs have a fundamental relationship. For accurate numerical modelling of diffusion, it is critical to comprehend this relationship.

If the coefficients are equal and independent of temperature, pressure, and other variables. The process ensures that mass migration equations in the modelled domain are linear, as well as making correlations with known diagnostic bounds easier. Once the behaviour is established with all the same diffusion coefficients, the assumption can be discarded.

The law states that “prediction of change in concentration along with time due to diffusion”, or it can be claimed that the change in concentration in a region over time is proportional to the difference in concentration gradient at the moment of measurement.

∂ϕ/∂t= D(∂2ϕ/∂x2), 

where

D: Diffusivity

t: Time

ϕ : Concentration

X: Position

Application of Fick’s law 

• Medicinal/drug usage
• Food industries
• Semiconductor fabrication for integrated circuit panel-making
• Biological usage, flux = -P(C1 – C2) where P: Permeability, C1 – C2: Concentration difference

Permeability

• Consider two compartments of division cell of thickness ‘h’ and cross-section area ‘a’
• Consider C1 and C2 the concentration of donor and receptor respectively
• Replace C1 and C2 with the partition coefficient, i.e K= C1/C2
• Therefore P= DK/h
• Where P: Permeability, K: Coefficient of partition, h: Thickness of partition barrier.

Diffusion modelling

Diffusion cell modelling is used for the measurement of diffusion.

• Movement of particles from the donor cell to the receptor until equilibrium is achieved.
• The donor cell has a high concentration of solute while the receptor has a lower concentration level.

A diffusion cell is:

• Mostly made up of clear plastic or glass
• Enables easy maintenance and is handy to use
• Has provisions for external temperature rise
• Provides sample collection technique in the receptor cell
• Chromatology is used for analysis

Fick’s law concept

The principles controlling the mass migration of molecules through the process of diffusion were firstly coined by Adolf Fick. Fick’s work was inspired by Thomas Graham, who was unable to present the fundamental laws, making Fick famous for his results. The monitoring of salt concentrations and fluxes that were diffusing between two reservoirs via water tubes was his major focus.

Conclusion

Diffusion results in a progressive blending of materials. The process of diffusion will finally lead to a complete mixing in a phase with constant temperature and no external net forces acting on the molecules. The applications of diffusion can be observed in various fields of biology and chemistry explaining the exchange of substances for necessary life processes including medicine absorption to oxygen, carbon dioxide, and nitrogen changes in alveoli, in various food organisations, and so on. Fick’s law explains the principle of diffusion in liquids but is limited when it comes to solid diffusion as it was not possible during his time.