Diffusion Coefficient And Viscosity: Relationship And Impacts


Diffusion Coefficient simply refers to the rate or how fast one matter diffuse into the other and Viscosity is the resistance to any flow. Here we will discuss about the relationship between Diffusion Coefficient and Viscosity.

The Initial requirement for understanding of this article is to know both the terms Diffusion Coefficient and Viscosity. After that we can properly visualize the relationship among them and also the impacts on each other.

What Is Diffusion Coefficient?

Including Fick’s first and second law, Diffusion coefficient is an important parameter in lots of equations in Physics and Chemistry.

Diffusion Coefficient depicts the diffusion mobility, the higher the Diffusivity or Diffusion coefficient of a substance in comparison to the other in a pair of species, the faster they mix into each other.

Diffusion coefficient is the parameter which measures how quickly one matter diffuses into the other. The S.I unit of Diffusivity is m2/s.

We can get the mathematical expression for Diffusion Coefficient from Fick’s laws.

From Fick’s first law, we know that molecules move from a region of higher concentration to lower concentration that means it relates directly the diffusive flux to the gradient of concentration.

Where J: diffusion flux

            D: diffusivity

             x: position

From Fick’s second law, calculation of concentration change of a fluid with respect to time period is possible.

Where,    D: diffusivity

                t: time

                x: position

What Is Viscosity?

 Viscosity is resistive force experienced by a particle against its motion.

Viscosity is experienced during the relative motion between two layers of a fluid. It is the frictional resistance when layers of fluid slide over each other during their motion.

Diffusion of two liquids with different viscosity; Image Credit: Wikipedia

When a fluid is used as a lubricant and at the time of transporting through pipelines Viscosity plays a major role to determine the forces which might be overcome. In certain processes like surface coating, spraying and injection moulding etc Viscosity controls the flow of the fluid.

How does Viscosity affect Diffusion?

Viscosity is a parameter which determines the rate of Diffusion.

Diffusion is the spreading out of molecules or atoms from a higher to lower concentration region and Viscosity depicts the intermolecular friction of a fluid which restricts it’s motion. Since Diffusion is nothing but the movement of molecules and Viscosity is the restriction towards movement, so Viscosity directly affects Diffusion.

Diffusion of Ink in Water: Image Credit:flickr

Diffusion Coefficient And Viscosity
Cup of tea with pouring honey; Image Credit: Unspalsh

In case of a fluid(may be liquid or gas)with high viscosity, the intermolecular friction or collision among the particles also high which prevents the free movement of particles resulting a low rate of diffusion.

On the other hand if the fluid is less viscous, the intermolecular space among the particles is more and they can move or diffuse more easily, the rate of diffusion automatically goes up.

Diffusion Coefficient Viscosity Relationship

Diffusivity or Diffusion coefficient(D) is influenced by various factors, one among those is Viscosity.

Diffusion takes place due to the random motion of particles inside a system and Diffusion Coefficient refers how fast theses molecules move to attain equilibrium condition. Viscosity results due to the interaction of molecules of a fluid in the form of an internal frictional force that slows down the overall relative motion of the particles.

Viscosity and atomic diffusion are the inter related properties which govern fluid dynamics.Stokes Einstein relation is generally used to calculate the diffusion coefficients of atoms or molecules of a liquid from the viscosity and vice versa.

Where, kB = 1.38×10-23J/K is the Boltzmann constant

             D is Diffusion Coefficient.

             r_{H}  is its hydrodynamic radius.

is the viscosity solvent.

             T is the absolute temperature.

From (1),

Polymer Diffusion Coefficient and Viscosity

Diffusion process in polymer is critical and the rate of diffusion should lie between solid and liquid.

Non newtonian fluids have high viscosity than ordinary fluids, hence possess low diffusion coefficent.

Study of migration of small molecules in polymaric material such as in drying polymaric packaging, controlled drug delivery, formation of films and membrane separation is important.

Because it would help to estimate the diffusion coefficient at a specific concentration and temperature which otherwise have to be measured experimentally on case to case basis.

Diffusion Coefficient and Concentration

Diffusion of a matter happens mainly due to the differences of concentration throughout the mixture or solvent.

A steeper concentration gradient results quicker diffusion in a solution. Molecules from higher concentration region move faster towards the lower concentration region to attain an equilibrium condition.

As the solutes distribute evenly throughout the solution(attains an equilibrium condition),the rate of diffusion also slows down.

Concentration of a solution is the amount of one solute present in a particular amount of solvent. For example in a mixture of sugar and water, the amount of sugar is its concentration. Concentration plays a crucial role to decide many properties of the solution.

Diffusion coefficient is associated with the random motion of the solute which is mainly governed by the difference in concentration throughout the solution.

So we can say Diffusion Coefficient(D) is directly proportional to Concentration gradient.

Diffusion Coefficient and Concentration Relationship

Diffusivity or Diffusion Constant(D) is the constant of Proportionality encountered in Fick’s Law which gives a direct relationship between Diffusion Coefficient and Concentration.

According to Fick’s First law of diffusion, the molar flux due to diffusion is proportional to the concentration gradient where molar flux refers to the amount of substance flow through a unit area within a unit time interval and concentration gradient is the change in the value of quantity.

From Fick’s first law we get the following equation:

Where J: diffusion flux

            D: diffusivity

             x: position

Why do Higher Concentrations Diffuse Faster?

Concentration gradient is the main parameter of Diffusion mechanism.

The movement of particles within a solution is influenced by the number of molecules in a particular amount of solvent or its concentration in that region. Particles always tend to move from higher concentration region to lower concentration region until they diffuse evenly in the solution.

No energy input is required for this purpose, the concentration gradient itself behaves like stored potential energy which enhances the motion of the particles.

Diffusion; Image Credit: Wikipedia

How does size affect Diffusion Coefficient?

Molecular size of diffusing matter is one of parameter that affects Diffusion Coefficient.

In a solution the lighter particles faster than the heavier one. So it is oblivious that in a solution consisting of particles of different sizes move with different speed. A lighter particle moves faster and attain the equilibrium state within a shorter period of time.

Diffusion Coefficient depicts the rate of Diffusion or time taken by the molecules inside a system to distribute evenly. If we consider two solutions Xand Y and solution X has more smaller particles in comparison to solution Y then solution X will attain the equilibrium state within a shorter period of time than solution Y .  

To know more about diffusion coefficent (Click Here)

Sangeeta Das

I am Sangeeta Das. I have completed my Masters in Mechanical Engineering with specialization in I.C Engine and Automobiles. I have around ten years of experience encompassing industry and academia. My area of interest includes I.C. Engines, Aerodynamics and Fluid Mechanics. You can reach me at https://www.linkedin.com/in/sangeeta-das-57233a203/

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