What is Fick’s Law of Diffusion?
Fick’s law of diffusion tells that the diffusion processes movement of molecules from higher concentration to lower concentration region. A diffusion process that obeys Fick’s laws is called normal diffusion or Fickian diffusion. A diffusion process that does not obey Fick’s laws is known as Anomalous diffusion or non-Fickian diffusion.
There are two laws are semiconductors i.e. Fick’s first law is used to derive Fick’s second law which is similar to the diffusion equation. According to Fick’s law of diffusion, “The molar flux due to diffusion is proportional to the concentration gradient”. The rate of change of concentration of the solution at a point in space is proportional to the second derivative of concentration with space.
Fick’s First Law
Movement of solute from higher concentration to lower concentration across a concentration gradient.
\[ J=−D \frac{d\phi} {dx} \]
Where,
J: diffusion flux
D: diffusivity
\[\phi\] : concentration
x: position
Fick's Second Law of Diffusion
The second diffusion law of Fick is a linear equation with the dependent variable being the concentration of the chemical species under consideration. The spread of each chemical species occurs independently. These properties make it simple to simulate numerically the mass transport systems described in Fick 's second law.
When modeling diffusion, it is often a good idea to start with the assumption that all diffusion coefficients are equal and independent of temperature, pressure, etc. Such simplification guarantees the linearity of mass transport equations in the modeled domain and also allows for easier correlations with known analytical limits. This assumption can be relaxed once the behavior of the system with all the same coefficients of diffusion is well understood.
The dimensional study of Fick 's second law shows that there is a fundamental relationship in diffusive processes between the time elapsed and the square of the period over which the diffusion takes place. Understanding this relationship is very important for precise numerical simulation of diffusion.
Fick’s Second Law
Prediction of change in concentration along with time due to diffusion.
\[\frac{\partial{\phi}}{\partial{t}}\]= D \[\frac{\partial^{2}\phi}{\partial x^{2}} \]
Where,
D: diffusivity
t: time
x: position
\[\phi\] : concentration
Multi-Component Diffusion
In the case of condensed liquids or gas mixtures where more than one chemical species is present in large mass fractions, the coefficient of diffusion can no longer be viewed as constant or composition-independent. The interaction of molecules of different species with each other is too prevalent for a physical description to ignore these intermolecular dependencies. The coefficient of diffusion thus becomes a tensor and the equation for diffusion is modified to link the mass flux of one chemical species to the concentration gradients of all chemical species present. The requisite equations are formulated as the Maxwell-Stefan distribution description. They are often used to describe gas mixtures, such as syngas in a reactor, or the mixture of oxygen, nitrogen, and water in a fuel cell cathode.
In Maxwell-Stefan diffusion, the rational choice of dependent variables is not species concentrations, but species mole or mass fractions (xi and ωi respectively).
The diffusive mass flux of each species is, in turn, expressed on the basis of mole gradients or mass fractions using Dik multi-component diffusion coefficients. They are symmetrical so that the n-component system requires n(n-1)/2 Independent coefficients to parameterize the diffusion rate of its components. Such amounts are often unknown for four-component or more complex mixtures. Simplifications can be applied to Maxwell-Stefan equations in order to use the equivalent Fick law diffusivity. Systems, most often, involving concentrated mixtures require convection and retention of momentum (fluid flow) to be resolved by diffusion.
In a material composed of two or more chemical species in which there are spatial inhomogeneities of the composition, there is a driving force for the interdiffusion of the various molecular species in order to make the composition of the material uniform. In a mixture of just two molecules, the diffusive flux of each molecular species is proportional to the gradient of its composition. This proportionality is known as Fick's Law of Diffusion and is, to a small degree, a mass transfer analogue of Newton's Law of Viscosity and Fourier 's Law of Heat Conduction
Bird(1960)
Bird(1960). The mathematical formulation of Fick's Law must be carried out with considerable caution, because there are a variety of ways in which the structure of the substance can be represented and because it is important to administer it.
Application of Fick’s Law
Biological application:
flux=−P(c2−c1) (from Fick’s first law)
Where,
P: permeability
c2-c1: difference in concentration
Liquids - Fick 's law refers to two miscible liquids when they come into contact and the diffusion takes place at a macroscopic point.
Fabrication of semiconductor-Diffusion equations Fick's law is used for the manufacture of integrated circuits.
Pharmaceutical application
Applications in food industries.
Importance of Fick's law
As we know, the gasses 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 gasses can diffuse across membranes is an essential aspect of respiratory physiology as oxygen and carbon dioxide must cross the alveolar membrane during the gas exchange process. It is important to know the physical laws which govern the diffusion of dissolved gas across membranes as they heavily inform our understanding of the gas exchange process at the alveolar membrane. Fick's 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 the laws governing the transport of mass through diffusive means. Fick's work was inspired by Thomas Graham, who fell short of proposing the fundamental laws for which Fick would become famous. Fick's law is analogous to the relationships discovered at the same epoch 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.
Now we can say that Fick's Laws form the main to understand diffusion in solids, liquids, and gasses.
When a diffusion process does not follow Fick's laws then it is referred to as non-Fickian.
FAQs on Fick’s Law of Diffusion
1. What is Fick's first law of diffusion?
Fick's first law states that the rate of diffusion, or diffusion flux (J), across a surface is directly proportional to the negative of the concentration gradient across that surface. In simple terms, it describes how particles move from an area of higher concentration to an area of lower concentration at a steady rate. This fundamental principle is crucial for understanding various transport phenomena in physics, chemistry, and biology. For a complete overview, you can refer to Fick's Law of Diffusion & It's Applications.
2. What is the formula for Fick's first law of diffusion?
The mathematical formula for Fick's first law of diffusion is expressed as:
J = -D (dφ/dx)
Where:
- J is the diffusion flux, representing the amount of substance moving per unit area per unit time.
- D is the diffusion coefficient or diffusivity, a constant that depends on the temperature, fluid viscosity, and size of the particles.
- dφ/dx is the concentration gradient, which is the change in concentration (φ) over a given distance (x).
The negative sign indicates that the diffusion occurs in the direction of decreasing concentration. This process is a key aspect of general diffusion.
3. What is the main difference between Fick's first and second laws of diffusion?
The primary difference lies in the conditions they describe:
- Fick's First Law applies to steady-state diffusion, where the concentration gradient and diffusion flux are constant over time. It answers the question, "How much substance moves across an area?"
- Fick's Second Law applies to non-steady-state diffusion, where the concentration at a point changes with time. It is a partial differential equation that helps predict how the concentration profile evolves over time, answering, "How does the concentration change at a specific point?"
Essentially, the first law describes the 'what' (the flux), while the second law describes the 'how' (the change in concentration over time). It is one of the key Theories in Physics that explains material transport.
4. What are the key factors that influence the rate of diffusion according to Fick's law?
According to Fick's law, several factors directly influence the rate of diffusion:
- Concentration Gradient: A steeper gradient (a larger difference in concentration over a short distance) results in a faster rate of diffusion.
- Surface Area: A larger surface area available for diffusion allows more particles to move across, increasing the overall rate.
- Diffusion Coefficient (D): This intrinsic property depends on the diffusing substance, the medium it is diffusing through, and the temperature. Higher temperatures generally increase the diffusion coefficient and thus the rate.
- Membrane Thickness: The rate of diffusion is inversely proportional to the thickness of the membrane the substance is crossing. A thinner membrane leads to faster diffusion.
5. How is Fick's Law applied in biological systems, such as in respiration?
Fick's law is fundamental to understanding how gases are exchanged in the lungs. During respiration, oxygen moves from the alveoli into the blood, and carbon dioxide moves from the blood into the alveoli. The efficiency of this process is maximised by factors that align with Fick's law:
- Large Surface Area: The lungs contain millions of alveoli, creating a massive surface area for gas exchange.
- Thin Barrier: The alveolar and capillary walls are extremely thin, reducing the diffusion distance (dx).
- High Concentration Gradient: Continuous blood flow and breathing maintain a steep partial pressure (concentration) gradient for both oxygen and carbon dioxide.
This biological design ensures a high rate of diffusion, making the exchange of gases rapid and efficient.
6. What are some real-world examples of Fick's law outside of biology?
Fick's law describes many processes beyond biological systems. Some notable examples include:
- Material Science: In semiconductor manufacturing, Fick's law is used to model the process of 'doping', where impurity atoms are diffused into a silicon wafer to alter its electrical properties.
- Pharmacology: The release of medication from a transdermal patch through the skin into the bloodstream is governed by the principles of Fick's law.
- Food Science: The process of salting meat or preserving fruit in sugar relies on diffusion, where salt or sugar molecules move into the food to draw out water and prevent spoilage. The movement of these particles can be related to the diffusion of a colloidal solution.
7. What are the limitations or conditions where Fick's law might not apply accurately?
While powerful, Fick's law is an idealised model and has limitations. It may not be accurate under the following conditions:
- High Concentrations: At very high concentrations, interactions between diffusing particles can affect their movement, which is not accounted for in the simple model.
- Heterogeneous Media: The law assumes the diffusion medium is uniform (isotropic). In complex, non-uniform materials, the diffusion coefficient (D) may not be constant.
- Presence of Other Transport Mechanisms: If there is bulk flow (convection) or transport due to an electric field, Fick's law alone is insufficient to describe the total flux.
- Anomalous Diffusion: In some systems, like diffusion in porous or crowded environments, the movement does not follow the linear relationship predicted by Fick's law.
