Fick’s Law of Diffusion is an important principle in physics and chemistry. This law describes the rate at which particles (such as molecules, atoms, or ions) diffuse through a medium. It was formulated by Adolf Fick, a German physiologist, in the 19th century. It helps us understand how molecules move and diffuse in space, and in which direction they migrate.
In simple words, Fick’s law states that molecules diffuse in space from a point of higher concentration to a point of lower concentration. In this article, we will learn about all related topics to Fick’s Law of Diffusion. This article includes both the first and second laws along with their derivations. Additionally, we will discuss some common applications of this law.
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What is Diffusion?
Diffusion is the net movement of particles or molecules from a region of higher concentration to a region of lower concentration. This process is driven by a concentration gradient.
The process of diffusion is affected by various factors such as temperature, concentration gradient, particle size and characteristics of the medium. Some examples of diffusion are:
- Diffusion in Water: When any food colour is added to water, due to diffusion the entire water turns into the colour of the food colour.
- Diffusion in Air: When we sprinkle perfume on one side of the room, its fragrance spreads throughout the room.
Who is Adolf Fick?
Adolf Eugen Fick (1829-1901) was a German physiologist and physician, born in Kassel, Germany. He studied medicine at the University of Marburg and graduated in 1851. Fick is known for his contributions to the fields of physiology and biophysics, particularly for Fick’s laws of diffusion, which govern the diffusion of a gas across a fluid membrane, and for the Fick principle, which allows the measurement of cardiac output.
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What is Fick’s Law of Diffusion?
Fick’s law of diffusion tells that the diffusion processes movement of molecules from a higher concentration to a lower concentration region.
A diffusion process that obeys Fick’s laws is called normal diffusion or Fickian diffusion whereas a diffusion process that does not obey Fick’s laws is known as Anomalous diffusion or non-Fickian diffusion.
The law is based on two principles:
- Fick’s First Law of Diffusion
- Fick’s Second Law of Diffusion
Let’s discuss these principle in detail as follows:
Fick’s Law of Diffusion Formula
1. Fick’s First Law: The formula for Fick’s First Law describes the diffusion flux as proportional to the negative gradient of concentration:
J = -D \frac{\partial \varphi}{\partial x}
Here:
- J is the diffusion flux ([amount of substance] per unit area per unit time),
- D is the diffusion coefficient ([length^2] per unit time),
- φ is the concentration ([amount of substance] per unit volume),
- x is the position.
2. Fick’s Second Law: Fick’s Second Law describes how the concentration changes over time due to diffusion:
\frac{\partial \varphi}{\partial t} = D \frac{\partial^2 \varphi}{\partial x^2}
In this equation:
\frac{\partial \varphi}{\partial t} represents the rate of change of concentration with time,
\frac{\partial^2 \varphi}{\partial x^2} is the second spatial derivative of concentration, indicating how the concentration profile changes with space.
Fick’s First Law of Diffusion
Fick’s First Law of Diffusion is a scientific principle that describes the movement of particles from an area of high concentration to an area of low concentration.
Fick’s First Law of Diffusion states that the rate of diffusion of a substance through a medium is directly proportional to the concentration gradient i.e., rate change of concentration with respect to position, of the substance in that medium.
Formula for Fick’s First Law
Mathematical formula for Fick’s first law of diffusion is:
J = -D dϕ/dx
Where,
- J is a diffusion flux,
- D is diffusivity,
- Φ is concentration, and
- x is position.
Fick’s Second Law of Diffusion
Fick’s Second Law of Diffusion describes the time-dependent behavior of the concentration profile during diffusion. It states that the rate of change of concentration with respect to time is proportional to the second derivative of concentration with respect to position with the diffusion coefficient (D) as the proportionality constant.
Formula for Fick’s Second Law
According to the second law of diffusion the prediction of change in concentration along with time due to diffusion.
∂ϕ/∂t = D ∂2ϕ/∂x2
Where,
- D is diffusion coefficient or diffusivity,
- t is time,
- x is position, and
- Φ is concentration.
Application of Fick’s Law of Diffusion
Some of the common applications of Fick’s Law of Diffusion are:
- Biological Systems: Fick’s Law is an essential concept in gas exchange study which enable us to look into the exchange of oxygen and carbon dioxide across the respiratory membranes.
- Pharmaceutical Sciences: Fick’s Law is used for modelling the release of drugs and their diffusion processes in the situation of drug delivery systems.
- Chemical Engineering: Fick’s Law plays a role in the diffusion process in chemical reactors and according to it various reaction systems can be designed.
- Food Science: Fick’s Law is a very instrumental tool in determining and managing mass transfer processes which relate to food processing and dewatering technologies.
- Materials Science: The legal profession is the source and driver of the ideas which are evolving into technologies for gas and liquid permeability like in the design of membranes used for separation.
Conclusion
In conclusion, Fick’s Law of Diffusion provides a fundamental understanding of the process by which substances move through a medium. By establishing a quantitative relationship between the rate of diffusion, the surface area, the concentration gradient, and the diffusion distance, this law has wide-ranging applications in various scientific and engineering fields.
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Sample Problems on Fick’s Law of Diffusion
Problem 1: A membrane has a diffusion coefficient (D) of 1 × 10−5cm2/s. The concentration gradient (dx/dc) across the membrane is 2 × 10−3mol / cm4, and the cross-sectional area (A) is 2cm2 . Calculate the diffusion flux (J).
Solution:
Given: D = 1 × 10−5cm2/s
dx/dc = 2 × 10−3mol / cm4
and A is 2 cm2
J = −D⋅A⋅ dx/dc
⇒ J = −(1 × 10−5cm2/s) × (2cm2) × (2 ×10−3mol/cm4)
⇒ J = −4 × 10−8 mol/s
The negative sign indicates that the substance is moving in the direction of decreasing concentration.
Problem 2: Suppose a gas with a diffusion coefficient (D) of 4 × 10−6 m2/s is diffusing through a sheet of material with a thickness (x) of 0.02m. The concentration gradient (dx/dc ) across the sheet is 2 mol/m4, and the area (A) is 0.1 m2. Calculate the diffusion flux (J).
Solution:
Given: D = 4 × 10−6 m2/s
dx/dc = 2 mol/m4
and A is 0.1 m2
J = −D⋅A⋅ dx/dc
⇒ J = −(4 ×10−6m2/s) × (0.1 m2) × (2mol/m4)
⇒ J = −8 × 10−7mol/s
The negative sign indicates the direction of decreasing concentration.
Practice Problems
Problem 1: A gas with a diffusion coefficient (D) of 3×10 −6 m 2/s is diffusing through a barrier with a thickness (x) of 0.01m. The concentration gradient (dx/dc) across the barrier is 4mol/m 4 , and the area (A) is 0.03m 2. Calculate the diffusion flux (J).
Problem 2: If the diffusion flux (J) is 2×10−8mol/s and the other parameters are the same as in Practice Problem 1, calculate the concentration gradient (dx/dc).
Problem 3: A liquid with a diffusion coefficient (D) of 1×10 −8m 2/s is diffusing through a membrane with a thickness (x) of 0.02m.The concentration gradient (dx/dc) across the membrane is 3mol/m4 , and the area (A) is 0.05m 2 . Calculate the diffusion flux (J).
Fick’s Law of Diffusion – FAQs
What is Fick’s Law of Diffusion?
Fick’s Law describes the process where molecules diffuse from a region of higher concentration to a region of lower concentration. It is expressed mathematically in two main forms: Fick’s First Law relates diffusion flux to the concentration gradient, and Fick’s Second Law predicts how concentration changes over time due to diffusion
What are typical units used in Fick’s equations?
In Fick’s equations, the typical units are:
- V (volume flux): amount/time
- P (concentration): amount/volume
- A (area): length²
- D (diffusion coefficient): length²/time
- T (thickness): length
What does Fick’s Law of Diffusion State?
Fick’s Law of Diffusion states that the flux of a substance through a medium is directly proportional to the concentration gradient of the substance within the medium.
What is the Difference between Fick’s First and Second Law of Diffusion?
Fick’s First Law of Diffusion describes the rate at which atoms move, which is proportional to the concentration gradient, with the diffusion coefficient as the constant of proportionality. On the other hand, Fick’s Second Law generalizes the first law to a wide range of situations and is called the diffusion equation.
What Factors affect Fick’s Law?
Several factors can affect Fick’s Law of Diffusion, including:
- Concentration Gradient
- Temperature
- Medium Properties
- Boundary Conditions
What are some practical applications of Fick’s Law?
Fick’s Law is crucial in fields like medicine, engineering, and environmental science. It helps in understanding processes like gas exchange in lungs, pollutant spread in ecosystems, and the operation of various industrial processes
Can Fick’s Law be applied to gases only?
No, Fick’s Law applies to the diffusion of substances in liquids and gases, and under certain conditions, even in solids, particularly when dealing with impurities or doping in solid-state physics
What is Equation for Fick’s First Law?
Equation for Fick’s first law is given by J = -D dϕ/dx.
What is the Equation for Fick’s Second Law?
Equation for Fick’s first law is given by ∂ϕ/∂t = D ∂2ϕ/∂x2