What is diffusion?

The term diffusion has been obtained from the Latin word “diffundere,” which implies spreading out. When the molecule of a substance goes from a region of its high concentration to a region of its low concentration, the method is recognized as diffusion. It is a kind of passive carrier of molecules because it is inevitable.

Overview of diffusion

It is a general practice that if a teaspoonful of salt is added to a glass of water, after some time, the water, on the whole, becomes salty. This indicates that salt is spread to every part of the water. This spreading out of salt molecules throughout the breadth and length of the water content of the glass is termed diffusion. It occurs because of the concentration variation between the two sections in water.

The movement of a particle occurs near a negative concentration gradient, such that from a large to moderate concentration. The diffusion theory is not only suitable in chemistry, science, and biology but also in economics, business, and sociology. For instance, the fast-food series McDonald’s was initially restricted to its geographic position, but it progressively spread to the whole world. The spread was due to the demand gradient.

The diffusion method can occur in liquids as well as in a gas. The diffusion is considered passive transport, which suggests that it is spontaneous. The force that pushes this kind of transport is termed as entropic force because, in this event, the system's entropy is increasing. It is distinct from the bulk flow of material. For example, the majority of water moves from high to low pressure. It is a fast process. Diffusion is a slow method. It takes place from high to low concentration.

Sometimes the bulk moment of material and diffusion co-occurs. When one breathes in, the air moves in the lungs due to the pressure gradient between the outside air and the air in the lungs. Inside the lungs, there is a concentration gradient of oxygen among the air in the lungs and the blood in the blood capillaries of the lungs. Therefore, oxygen diffuses from the lungs to the blood. At the same time, carbon dioxide diffuses from the blood to the air in the lungs.

Factors affecting diffusion

Temperature

When salt is added to warm water, it dissolves comparatively prompter. Therefore, a raised temperature can improve the rate of diffusion.

Size of molecules

The small-sized molecules diffuse quicker than large-sized molecules. For instance, hydrogen gas will diffuse in the air 4.5 times quicker than carbon dioxide gas.

The magnitude of concentration gradient

If we add some salt to water's solution that is previously salty, the rate of dissolution of salt in the solution is slow. But if we add water to the salty solution, the rate of dissolution accelerates. It is because, in the previous situation, the concentration gradient was of small magnitude, but upon adding water, the concentration gradient rises, and so does the diffusion rate.

Phase in contact

The diffusion of a gas into a different gaseous medium occurs very quickly. Due to its lower molecule weight, the obnoxious odor of ammonia gas is felt in the air instantly. Since ammonia is lighter than air, it mixes up quickly. Likewise, liquid nitrogen also diffuses into the air very fast. However, in liquids and solids like water, this method is more gradual.

Area of interaction

When we supplement a large lump of salt to the water, it dissolves gradually. But if it is dissolved in water after being split into tiny parts, it gets dissolved fast. Therefore, the rate of diffusion rises as the area of interaction raises.

What are the types of diffusion?

There are the following two types of diffusion:

• Simple diffusion
• Facilitated diffusion

Simple diffusion

When the diffusion method occurs without the aid of any carrier molecule, it is recognized as simple diffusion. Simple diffusion takes place within a semi-permeable membrane. Examples of simple diffusion are minor nutrients consumed by bacteria and the movement of carbon dioxide from the air into plant leaves.

Facilitated diffusion

When diffusion occurs with the aid of a carrier molecule, it is recognized as facilitated diffusion. The carrier molecule is termed a facilitator. In a facilitated diffusion method, passive transfer of molecules takes place. Examples of facilitated diffusion are osmosis and dialysis. It happens when the size of the molecule under diffusion is quite large. 

Fick’s laws of diffusion

In 1856, Adolf Fick introduced the laws for the diffusion method recognized as Fick’s laws of diffusion. Fick presented two laws for the diffusion method in a fluid. Fick’s law is not true for solid particles. Fick’s law is appropriate only for liquid or gas.

If a diffusion method obeys Fick's law, then it is identified as normal diffusion. If it does not obey Fick’s law, then it is known as anomalous diffusion.

Fick’s first law

Fick's first law builds a relationship between concentration and diffusion flux under a constant state. Fick’s derived an equation that states that the diffusion flux is directly proportional to the concentration gradient or, in other words, the net movement of particles (molecules, for a fair understanding) in a confined area of study, in a given time, is directly proportional to the steepness of gradient. The mathematical equation for Fick's first law is as follows:

$J=-D\frac{d\rho }{dx}$

In the above equation, J represents the number of molecule pass through a location per unit area per unit seconds, D represents the diffusion coefficient or diffusivity, $\rho$ represents the concentration, and x represents the distance.

According to the above equation, the diffusion coefficient (D) is the measure of area per unit time; thus, the unit of the diffusion coefficient is meter square per second. The diffusion coefficient is also recognized as the proportionality factor of Fick’s law. The negative sign in the equation shows that the diffusion occurs in the direction opposite to the concentration gradient. Hence, it occurs in the direction where there is decreasing concentration.

The rate of diffusion of a gas into a liquid is directly proportional to the partial pressure of the gas above the liquid and inversely proportional to the thickness of the membrane.

Fick’s second law

Fick's second law builds a relationship between concentration and diffusion flux under an unsteady state. Fick’s second law equation indicates the variable is changing with time, or the time to diffuse increases with the square of distance x. The equation for Fick's second law is as follows:

$\frac{d\rho }{dt}=D\frac{d^2\rho }{d{x}^2}$

In the above equation, t represents the time, D represents the diffusion coefficient or diffusivity, $\rho$ represents the concentration, and x represents the distance.

Under the steady-state condition, the equation for Fick’s second law can be written as:

$\frac{d\rho }{dt}=0$

In the above equation, t is the time and $\rho$ is the concentration.

Therefore, the equation for Fick’s second law can be written as:

$D\frac{d^2\rho }{d{x}^2}=0$

In the above equation, D represents the diffusion coefficient or diffusivity, $\rho$ represents the concentration, and x represents the distance.

Factors affecting Fick’s law of diffusion

Surface area

The greater the surface area, the greater is the rate of diffusion. This occurs because the number of points present on the surface also increases where the new molecules can come and join the cell.

The thickness of the membrane

The thinner the membrane, the smaller is the time needed by the molecules to diffuse across it. This is because the path of diffusion reduces.

Concentration difference

The higher the difference of concentration over the membrane, the quicker is the rate of diffusion.

Applications of Fick’s laws

• The transfer of gases inside and outside the body also obeys Fick's law.
• Fick’s law is suitable in the carburization method.
• Fick's law is adopted to prevent nuclear garbage from diffusing outside.
• Fick’s law is helpful in creating semiconductors. Semiconductors are created when one material is doped into the other material with various valencies. The doping method is carried out by diffusion.
• Fick’s law is helpful in hydrodynamics studies.

Common Mistakes

Students get confused between simple diffusion and facilitated diffusion. Simple diffusion is a process that transports molecules from a higher concentration region to a lower concentration region without the aid of any carrier molecule. In comparison, facilitated diffusion is a process that transports molecules from a higher concentration region to a lower concentration region with the aid of any carrier molecule.

Students get confused between bulk flow material and diffusion. The bulk flow is the movement of a mass of fluids down a pressure gradient, while diffusion is the movement of a substance from a greater concentration section to a lower concentration section.

Context and Applications

The topic of Fick’s law of diffusion is very much significant in the several professional exams and courses for undergraduate, diploma level, graduate, and postgraduate. For example:

• Bachelor of Technology in Mechanical Engineering
• Master of Technology in Mechanical Engineering
• Bachelor of Science in Physics
• Master of Science in Physics
• Bachelor of Science in Biology
• Master of Science in Biology

Related Concepts

• Dissolution
• Graham’s law of diffusion
• Osmosis
• False diffusion
• Advection

Practice Problems

Q1: The dimension of the diffusion coefficient is:

(a) ${\mathrm{ML}}^{-2}\mathrm{T}$

(b) ${\mathrm{LT}}^{-1}$

(c) ${\mathrm{L}}^2{\mathrm{T}}^{-1}$

 (d) ${\mathrm{MLT}}^{-2}$

Correct option: (c)

Explanation: The diffusion coefficient unit is a centimeter square per second. It will include the length (L) square and time (T) powered (-1). It is independent of mass (M). From the above options, option (c) includes the same relation.

Q2: In diffusion method, the molecules flow from a section of ___ to a section of ____.

(a) Low, high

(b) Low, medium

(c) High, medium

(d) High, low

Correct option: (d)

Explanation: The molecules will flow from higher to lower sections in the diffusion process. The spreading out of molecules and their motion occurs from higher to lower regions. Fick's law can describe this process.

Q3: Among the four samples, which of the following sample would diffuse the quickest?

(a) Salt into tap water

(b) Saltwater into saltwater

(c) Saltwater into tap water

(d) Salt into saltwater

Correct option: (a)

Explanation: Generally, gases will show a diffusion process faster than other states as the molecules can move freely in any direction. But in the above sample, the salt into the tap water will diffuse very fast compared to other samples.

Q4: The method of diffusion can happen in:

(a) Gas

(b) Liquid

(c) Solid

(d) All of the above

Correct option: (d)

Explanation: The diffusion process can occur in all states like liquid, solid, and gases. Diffusion consists of two processes, namely normal diffusion and anomalous diffusion. It involves the movement of various molecules from one region to another.

Q5: The most influencing factor of diffusivity is:

(a) Lattice structure

(b) Presence of defects

(c) Temperature

(d) Diffusing species

Correct option: (c)

Explanation: The most influencing factor is temperature. When an increase in the temperature takes place, the kinetic energy of all molecules will increase. Diffusion highly depends on temperatures for the solids.