# Fick’s Law of Diffusion

## Introduction

Diffusion coefficient of Oxygen can be explained by Fick’s laws. Fick’s laws of diffusion describe or explain diffusion, and it was derived in the year 1855 by scientist Adolf Fick. This law can be used to solve for the diffusion coefficient, denoted by “D”. Fick’s first law can be used to obtain or derive Fick's second law, which in turn is identical to the diffusion equation.

There are two major laws of Fick, and they are - Fick’s first law, which relates the diffusive flux to the gradient of the concentration. It postulates that the flux goes from regions of high concentration to regions with low concentration, and with a magnitude that is proportional to the concentration gradient. And, Fick’s second law of diffusion predicts how diffusion causes the concentration to change with respect to time. Also, there are various uses or applications of Fick’s law.

## What is Fick’s Law of Diffusion?

Fick’s law of Diffusion is a diffusion law that describes or elaborates on the diffusion process, and this law was given by the scientist Adolf Fick in the year 1855. They can be used to solve or find the diffusion coefficient, which is denoted by the symbol D.

Fick’s law is a combination of Fick’s first law of diffusion as well as Fick’s second law of diffusion. And the first law can be used to derive or find the second law, which in turn is identical or similar to the diffusion equation. A diffusion process that obeys or follows Fick’s laws is termed or called normal or Fickian diffusion; otherwise, it is termed or called anomalous diffusion or non-Fickian diffusion. There are certain uses or applications of Fick’s law in various fields.

Christopher Rowley, The mean square displacement as a function of time of an oxygen molecule diffusing water and pentane, CC BY-SA 4.0

## Fick’s First Law

Fick’s first law relates the diffusive flux to the gradient of the concentration. It postulates that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient also called spatial derivative, or it can be described as the concept that a solute will move from a region of high concentration to a region of low concentration across a concentration gradient. In one dimension or a spatial dimension the law can be written or expressed in various forms, and the most common form is in a molar basis −

$$\mathrm{J=-D \frac{\text{d}φ}{\text{d}x}}$$

Here,

J denotes the diffusion flux; it measures the amount of substance that will flow through a unit area during a unit time interval.

D denotes the diffusion coefficient or diffusivity

𝝓 is used for denoting the concentration, and x is the position, whose dimension is length.

## Fick’s Second Law of Diffusion

Fick’s second law of diffusion predicts how diffusion causes the concentration to change with respect to time. It is a partial differential equation which is in one dimension, reads −

$$\mathrm{\frac{\partial φ}{\partial t}=D\frac{\partial ^2 φ}{\partial x^2 }}$$

Here,

φ denotes the concentration in dimensions of [(amount of substance length-3)],

t denotes the time

D is the diffusion coefficient in dimensions of [length2 time-1]

x is the position or length

Fick’s second law has the same mathematical form as the Heat equation and its fundamental solution is the same or similar to the Heat Kernel, except for switching thermal conductivity with the diffusion coefficient.

## Multi-Component Diffusion

The problem of defining an average diffusion coefficient of a particular gas arises in the application of the film resistance model for mass transfer to the systems involving multicomponent mixtures of simultaneously diffusing gases and in the application of mass, momentum, and heat transfer analogies in such systems. It is also shown that in some cases, integration of the diffusion equation with an average value of the diffusion coefficient will not be valid. An approximate solution of the diffusion equation is obtained with the concentration dependence of the diffusion coefficient taken into account.

## Applications of Fick’s Law

The following are some applications of Fick’s law −

• It has pharmaceutical applications.

• Fick’s law is used or applicable for two miscible liquids when they are brought in contact and diffusion takes place at a macroscopic level.

• Also, the diffusion equations from Fick’s law are used to fabricate integrated circuits.

• Fick’s law also found uses in food industries.

## Importance of Fick’s Law

As we know that the gases dissolved in liquids move randomly throughout the liquid in a thermodynamic process which is well described as diffusion. We know that the diffusion rates of a gas within a continuous body of liquid are constant, the presence of a barrier within the liquid can substantially affect the diffusion rate of the gas. The rate at which gases can diffuse across the membranes is an essential aspect of respiratory physiology, as oxygen and carbon dioxide must cross the alveolar membrane during the gas exchange process. This law describes the rate at which a dissolved gas diffuses across a membrane given certain properties of the membrane and gas.

## Concept of Fick’s Law of Diffusion

Adolf Fick first reported or found the laws governing the transport or motion of mass through diffusive means. Fick's work was inspired or guided by Thomas Graham, who fell short of proposing the fundamental laws for which Fick would become popular. Fick's law is analogous to the relationships discovered at the same epoch or object by other eminent scientists. Fick's experiments always dealt with measuring the concentrations and fluxes of salt, diffusing between two reservoirs through tubes of water. It is well observed that Fick's work primarily concerned diffusion in fluids because, at the time, diffusion in solids was not considered generally possible.

## Conclusion

Fick’s laws of diffusion, which describe or explain diffusion, were derived in the year 1855 by scientist Adolf Fick. There are two major laws of Fick, and they are - Fick’s first law which relates the diffusive flux to the gradient of the concentration. It postulates that the flux goes from regions of high concentration to regions with low concentration, and with a magnitude that is proportional to the concentration gradient. These laws can be used to solve for the diffusion coefficient, denoted by D. Fick’s first law can be used to obtain or derive Fick's second law, which in turn is identical to the diffusion equation. Also, a diffusion process that obeys Fick’s law is termed or called normal or Fickian diffusion; otherwise, it is termed or called anomalous diffusion or non-Fickian diffusion.

## FAQs

### 1. Define diffusion.

Diffusion is defined as the net movement of anything generally from a region of higher concentration to a region of lower concentration.

### 2. What is the diffusion coefficient?

Diffusion coefficient or diffusivity is defined as a proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration of the species.

### 3.What do you mean by miscible liquids?

Miscible liquids are liquids that dissolve in each other to form a homogeneous mixture or solution.

### 4.What is diffusive flux?

Diffusive flux, denoted by J is defined as the measure of the amount of substance per unit area per unit of time.

### 5.Describe thermal conductivity.

The thermal conductivity of a material is defined as the measure of its ability to a particular material to conduct heat. It is denoted by the k or kappa.

Updated on: 02-Feb-2024

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