How to Calculate Diffusion Coefficient:Detailed Facts and Problems on It

How to calculate diffusion coefficient: It is very useful concept in science.

The diffusion coefficient can be obtained either by calculation or graph. The formula of diffusion coefficient J = -D dφ/dx

The straight line graph is available to obtain diffusion coefficient.

J = -D Δφ

-Δφ is the driving force for a one-dimensional quantity of dimensional, and it is the concentration gradient for the ideal mixture.

As per the diffusion coefficient equation, we should be aware of the units of flux density and units for the gradient, and then we should talk about the units for the Diffusion coefficient.

Flux density is the net rate at which particles move through a certain area. Now, in-unit, there is a term length2 which suggests the unit of area, and it is related to the flux density.

How to find diffusion coefficient from a graph?

As per normal graph and slop calculation, we can calculate the diffusion coefficient from a graph

As we know, the basic relation for any normal graph is y = mx. If we consider it a negative slope, the equation can be written as y = -mx.

The calculation of the diffusion coefficient from the graph, we have to know about this basic relation.

This equation shows that flux is a dependent variable and gradient is an independent variable.

But we should know the biological meaning of the slope. Here we have to find a diffusion coefficient named D, which differs in each unique situation.

For example, in water, the coefficient of oxygen distribution is a constant value at room temperature. D rises with temperature, so as water is heated, D is raised, which means oxygen faster dissipates at a higher temperature. And for cold water, D is decreased means oxygen is less dissipated in the water.

As the function is like y = -mx and Negative D is the slope in it, all quantities related to this are directly proportional to each other according to Fick’s law. For different values of D, there is a different value of the slope, like a different amount of diffusion coefficient for glucose than the water.

Now it is time to define the actual meaning of diffusion, which describes how long any substance is to move through a particular medium. Diffusion coefficient C describes the oxygen or proteins to move through a particular medium.

Diffusion coefficient definition

The diffusion coefficient is defined as the capacity of any substance that can be diffused into another substance.

The diffusion coefficient is defined as an in-unit cross-section per unit time;

The quantity of a substance diffusing from one region to another region passes through when the volume concentration gradient is unit. This is also known as diffusivity.

Diffusion coefficient Formula

The diffusion coefficient formula gives the value of Diffusion flux

The equation of diffusion coefficient J = -D dφ/dx

In this equation,

J = diffusion flux which is the amount of substance per unit area per unit time

D = Constant or the diffusion coefficient or diffusivity, measured in area per unit of time.

φ = concentration for theoretical mixtures, and its unit is the amount of substance per unit volume.

x = position, which is measured in length.

Now, if we try to put the value of the gradient of equation means,

 = Δφ in that equation,

Fick’s law of Diffusion

A scientist name Adolf wick described a law in 1955 about diffusion and said that diffusion and diffusion coefficient has two types of law.

Fick’s law of diffusion gives the diffusion coefficient formula, and said that diffusive flux is related to gradient concentration.

Fickian Diffusion is a well-known property that defines the diffusion process that obeys Fick’s law of diffusion. And anomalous diffusion is the process that does not follow this law.

how to calculate diffusion coefficient
Fick’s law Credit Wikipedia

The diffusive flux is related to the concentration gradient said to Fick’s first law. It defines that flux goes to the regions of low concentration from regions of high concentration.This value is proportional to the concentration gradient or, in simplistic terms. This law can be written in different types of forms in which. The most known form is on a molar basis.

Now think about Fick’s law of diffusion as the gradient gets steeper and flux changes as the distance changes. As distance is not the dependent variable, anyone should use a different version of Fick’s first law.

Distance is not the dependent variable, so the equation is an example of inverse variation.

If the distance is very small, then the magnitude of the flux is very high and vice versa. This means distance is near about zero, then flux is maximum, and if the distance is near maximum, then flux is zero.

For example, if anyone is there in the room with the latest favourite perfume, then the radiant between you and the rest of the room is steep; no one in the room is with the same perfume. A mosquito right next to the ears is buzzing, and it gets a noseful almost immediately, so diffusion is created very fast in a very short time.

Diffusion coefficient unit

Unit of the diffusion coefficient is termed as (length)2/time. In the CGS unit system, the unit of D is represented in cm2/s.

Unit of diffusion coefficient D is m2/s in the SI unit system.

With the help of dimensional analysis of the physics concept, we can derive the unit of the diffusion coefficient in which we can use basic simple rules of an equation in which units should be balanced on each side of the equation.

The dimensional analysis method from a simple physics concept makes it so easy to derive units of the flux density and concentration gradient. However, still, this is a little complicated, and so in starting, we have a faulty unit of it, and if you know the initial units, then the process is just required to manipulate it.

Diffusion coefficient of water

It is used for providing the values of self-diffusion coefficients of water with the related temperature

The reference values for testing and calculation of distribution parameters like magnetic resonance imaging (MRI) with a weight of diffusion.


Many publications at different temperatures provide Self-diffusion coefficients of water. These data are interpolated and extrapolated using the dependence between log D and 1/T.

We can calculate the self-diffusion coefficient and temperature both from each other. List of the estimated data points that are of temperature, diffusion coefficients. These all data can be expanded or shortened.

For example, it may be deleted data for low temperature, which is less than -5o C and greater than 50 0C.

There is no linear relationship in the Arrhenius plot followed by any diffusion coefficient of water.This is accounted for by the quadratic fit option that results in a very good agreement of measured data points and fit function. The quadratic fit must be used to find the diffusion coefficient.

In the Arrhenius structure, the water distribution coefficient does not follow any line relationship. So a quadratic fit option is calculated by this, which gives output in the best way for limited data points and measurement function. So Quadratic fit must be used to calculate distribution coefficients.

Diffusion coefficient of gases

In the gas form, the normal diffusion coefficient of any molecule is between 10-6 to 10-5 m2/s.

The range of normal diffusion coefficient values is 10-10 to 10-9 m2/s in an aqueous solution. Fluid circulation is always dominated by convection, and it is slowed down on a daily length scale.

Instead, this dispersion of molten molecules slows down.

Diffusion coefficient of an oxygen

In this section, the diffusion coefficient of oxygen is explained and provides an overview of its general concept and equation.

The Diffusion coefficient of oxygen is calculated by one equation in which Absolute temperature, one related quantity of solvent water, a molecular weight of water, viscosity of water and molar volume of oxygen should be known to solve it.

The diffusion coefficient of oxygen means in water, and it can be explained by a relation given by Wilke and Chang, 1995, and it is developed using the Stokes-Einstein equation.

A rigorous theoretical foundation is lacking in this equation, and this foundation is used to develop the equation of gas mixtures. This equation for gas mixture is accurate to plus or minus ten per cent for a dilute solution of non-dissociating solutes.

We can neglect the effect of dissolved substrate and microorganisms to analyse this mixture. We also can assume that the solvent is water. To calculate the diffusion coefficient of oxygen, we can substitute the given values in the equation. In a specified range of temperatures, the calculation result is common in compositing solutions.

Deepakkumar Jani

I am Deepak Kumar Jani, Pursuing PhD in Mechanical- Renewable energy. I have five years of teaching and two-year research experience. My subject area of interest are thermal engineering, automobile engineering, Mechanical measurement, Engineering Drawing, Fluid mechanics etc. I have filed a patent on "Hybridization of green energy for power production". I have published 17 research papers and two books. I am glad to be part of Lambdageeks and would like to present some of my expertise in a simplistic way with the readers. Apart from academics and research, I like wandering in nature, capturing nature and creating awareness about nature among people. Let's connect through LinkedIn - Also refer my You-tube Channel regarding “Invitation from Nature”

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