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It states that the movement of particles diffusion flux from a region of high concentration to a low concentration region is directly proportional to the magnitude of the concentration gradient of the substance.

It is proportional to the squared velocity of the diffusing particles, which depends on the temperature, viscosity of the fluid, and the size of the particles.

The negative sign of the equation indicates that diffusion occurs in a direction opposite to that of the increasing concentration. Hence, diffusion occurs in the direction of decreasing concentration of the diffusing substance, and thus, the diffusion flux is a positive quantity.

It is derived from the first law, to predict how diffusion causes a change in concentration with respect to time. After a certain time, the room is found to be filled with the perfume odor.

This occurs because the perfume molecules have diffused from one side of the room to the other, from a region of high concentration to a region of low concentration to attain a state of equilibrium or become even throughout.

However, in this context, it becomes inaccurate when the diffusion constant is low, and the radiation becomes limited by the speed of light rather than by the resistance of the material the radiation is flowing through.

In such situation a flux limiter is used. Article was last reviewed on Saturday, July 11, Your email address will not be published.

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For two or more dimensions, more complex equations are given. In gases and liquids, diffusion does not create a stress field.

But in solids, a particular stress is created due to the presence of swelling penetrants. This stress can cause even cracks, which in other words, morphological changes are induced.

Then these swelling and stress fields can affect the diffusion. The effects of swelling and stresses can be:. A fundamental criterion of Fickian diffusion is that the surface concentration attains its equilibrium value immediately upon a change in conditions and remains constant through the sorption process.

For example, in a resin matrix system, the polymer chain segments at the surface must instantaneously reach saturation. Fickian diffusion is rarely observed for the transport of a liquid through a glassy polymer.

If the mass uptake M can initially be represented by,. In , the concept of the non Fickian diffusion was brought forward during the discussion held on swelling and shrinking by Faraday Society.

This concept states that in some polymer systems, sharp boundaries that move linearly with time exist between the swollen and un-swollen regions.

There are four types of non Fickian diffusion as given below. Figure 1: Molecular Diffusion. Fickian Diffusion: Fickian diffusion is a form of diffusion that obeys the Fickian laws.

Non Fickian Diffusion: Non Fickian diffusion is any form of diffusion that does not obey the Fickian laws. Fickian Diffusion: No boundaries can be observed in Fickian diffusion.

Non Fickian Diffusion: A sharp boundary that separates the highly swollen region from a dry, glassy region can be observed in non Fickian diffusion.

Fickian Diffusion: A sharp front is absent in Fickian diffusion. Fickian and non Fickian diffusion are two forms of diffusion.

An extremely simple model of this process, which has the merit of containing all the essential physics, is a molecule making a random walk on a one-dimensional number line: To further simplify our life, this model molecule moves only at every clock tick, and sits peacefully waiting for the clock tick.

At each clock tick, it moves left or right by one unit, with equal probability 50 percent of moving in each direction. What will happen to it in the next time ticks?

After the next tick, the molecule is equally likely to be at 3 or 5. That changes the probability distribution to the following.

Thus, although we don't know exactly where it will be, we know that the expected value of x is still 4.

Pause the video here, and find the expected value after one more tick -- that is, two ticks after it was known to be at 4.

You should have found that the expected value is still 4. Here is the probability distribution. It has a one-fourth chance to be at 2, a one-half chance to be at 4, and a one-fourth chance to be at 6.

In short, the expected value never changes. Alone, it is thus not a good way of characterizing how the molecule wanders. We also need to characterize the spread in its position.

Thus, we use a higher moment, the second moment, the expected value of x-squared. What about after one clock tick?

Pause the video here and work out You should have found that We find that the expected value of x-squared equals Hmm, it seems like the expected value increases by 1 with every clock tick.

That's true in general, no matter how many ticks you wait, or where the molecule started. Thus, for a molecule starting at the origin at 0 , the expected value of x-squared is just the number of clock ticks.

This equality is fascinating, because it contains the difference between this kind of walk, a random walk, and a regular walk. The random walk is fundamentally different, and that fundamental difference will explain, among a vast number of physical phenomena, why you wear a jacket in the winter, and why some animals have circulatory systems.

Now, instead of speaking of counting clock ticks, let's measure actual time. Instead of counting units left or right, let's measure actual distance.

If each clock tick takes time tau, and each distance unit is lambda, instead of one, as before, then these relationships here change slightly to include the dimensions and units.

For the regular walk, x is lambda times the number of ticks. Let's see how "fast" a random walk goes, in comparison with a regular walk. Suppose that the molecule has to cross the narrow gap between two neurons, a synaptic cleft, which has width L.

If we wait long enough, until How long do we wait on average? Thus, the "speed" of the random walk is something like the distance divided by this time t, and that time t is the distance squared divided by the diffusion constant.

So this speed is the diffusion constant divided by distance. Again we see the fundamental difference between a regular and a random walk.

A regular walk has a constant speed here of lambda over tau, as long as lambda and tau don't change. In contrast, in a random walk, the speed is inversely proportional to the gap L.

This result explains the structure of Fick's Law for the flux of stuff. Flux is particles per area per time. How are the flux and diffusion velocity connected?

Well flux is also equal to the concentration n times the speed. But where did the dx here and the dn here come from? What do those have to do with n and L?

Imagine two regions. One with concentration n1 and another with concentration n2, separated by a distance delta x.

So this is the concentration of neurotransmitter here at one end and concentration of neurotransmitter here at the other end of say, a gap.

We could use this same model for oxygen in a circulatory system. Then the flux in one direction is this and in the reverse direction, it's this.

So we've explained the d and the delta x in Fick's law over here. What about the dn? Well n2-n1 is the difference in n, or just dn, so this piece here is dn.

This is dx, and this is D. So we arrive at Fick's Law based on the realization that flux is concentration times speed, and the speed here in a random walk is the diffusion constant divided by L.

And that's why you wear a coat, rather than a thin shirt, in the winter. The thin shirt has a dx of maybe 2 mm. But the winter coat may be 2 cm thick.

That reduces the heat flux by a factor of 10 through your coat compared to the shirt. And you can stay warm just using the heat produced by your basal metabolism -- about Watts.

For our final calculations, let's return to the neurotransmitter and then discuss circulatory systems.

How long would it take a neurotransmitter molecule to diffuse across a 20 nm synaptic cleft? Pause the video here and make your estimate of the time.

You should have found that the time is about 4 microseconds. Is that time short or long?

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