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Fick’s Law of Diffusion


Diffusion is the movement of particles when the difference in concentration occurs. To be specific, diffusion occurs whenever there is a concentration gradient. Diffusion is one of the most vital processes in living beings. It helps in the movement of wastes from our bodies and transfers food within our bodies. This food is transferred in our bodies from higher concentrations to lower concentrations. Liquids and gases undergo diffusion more than solids. Solids have very little negligible diffusion.

Various processes like dialysis, osmosis, etc., use the concept of diffusion to pass ions and molecules through a semipermeable membrane from higher to lower concentrations. Area of interaction, temperature, size of the particle and the concentration gradient affect diffusion.
We see diffusion in our daily lives. For example, the preparation of tea, smell from an incense stick, dissolving sugar, etc., all work on the principle of diffusion.

Fick’s first law of diffusion

Fick’s law of diffusion is widely used in science, particularly chemistry, to determine the movement of molecules from a higher concentration to a lower concentration. Adolf Fick described the law of diffusion in the year 1855. The compounds obeying Fick’s law are called Fickian diffusion or normal diffusion.

According to Fick’s law of diffusion, the molar flux due to diffusion is proportional to the concentration gradient.
Also, the rate of change of concentration of a compound is directly proportional to the second derivative of concentration.

Mathematically, Fick’s law is defined as,
J = -D dφdx
Where J = diffusion flux, known as amount of substance per unit area per unit time.
D = diffusivity, measured in area per unit time.
φ = concentration, measured per unit volume.
x = position, expressed in units of length.

D is dependent on temperature, size of particles (according to the Stokes-Einstein relation) and viscosity, and is proportional to the squared velocity of the diffusing particles.

The diffusion may range from (0.6–2) × 10−9 m2/s at room temperature to 10−10 to 10−11 m2/s in biological molecules.

Fick’s second law of diffusion

Fick’s second law of diffusion states that the concentration of a compound changes over time due to diffusion.
Mathematically, it is denoted by:

Where D = diffusion coefficient in dimensions of [length2 time−1], example m2/s
t = time in seconds
φ = concentration in dimensions of [(amount of substance) length−3], example mol / m3; φ = φ (x, t) is a function that depends on location x and time t.
x = position in meters

Diffusion in multiple compounds

The diffusion coefficient cannot be treated as a constant when diffusion occurs in two or more substances or substances with a higher amount of concentration. This is because the interactivity in such cases is so prevalent that we cannot ignore the physical inter-molecular dependencies. Due to the presence of such prevailing nature of particles, as a result, the coefficient of diffusion cannot be taken as a constant.

In cases like gas mixtures, water in a fuel cell cathode, etc., Maxwell-Stefan description of diffusion comes into effect. The diffusive mass flux of each species is expressed based on mass fractions. Mass fractions use multi-component diffusion coefficients, which are symmetrical so that the n-component system requires n (n-1) / 2 independent coefficients to define the component’s diffusion rate.

To make a uniform composition, a driving force acts on various intermolecular particles and species. This driving force acts vigorously on substances that are made with two or more chemicals or compounds. The diffusive flux is proportional to the composition gradient if a mixture contains only two types of molecules.
This proportionality is known as Fick’s law of diffusion. It is a mass transfer analogue of Fourier’s law of heat conduction and Newton’s law of viscosity.

Application of Fick’s law

1. Biological application
    Flux = −P (c2 − c1) flux = −P (c2 − c1) (from Fick’s first law)
    Where, P: permeability, c2 - c1: difference in concentration

2. Liquids: Fick’s law of diffusion comes into effect at the macroscopic level if the diffusion takes place between two               miscible liquids, which when brought closer to each other.

3. Fabrication of semiconductors: Fick’s law is used to fabricate integrated circuits.

4. Fick’s law is used widely in pharmaceutical industries to determine the concentration of medicines.

5. It is widely used in model transport processes in food industries and to balance the flavours.

6. It is commonly used in neurons, porous soils, biopolymers, population dynamics, semiconductor doping, plasma physics     and nuclear materials.

7. The theory of voltammetric methods is based on Fick’s law of diffusion.

8. Fick’s law is used to find terms that fluctuate in hydrodynamics.

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