 # Mass Transfer Equations: Fick's Law

So far we have discussed the concept of mass transfer. We said that mass transfer is the movement of matter from a high concentration to a low concentration. This means that the matter wants to "get away" from the other similar matter and go to a place where there is open space. Let's relate this to an example. Everyone has sprayed air freshener before. When you spray the air freshener, it does not just smell where you sprayed it, but rather the smell spreads throughout the room. The air freshener (matter) moves from an area of high concentration (where you sprayed it) to an area of low concentration that is far from the place that it was sprayed. This movement of the material is called diffusion. Diffusion can be represented by a basic equation. The equation that we are about to study is often referred to as Fick's Law. Our task is to introduce Fick's Law and dissect it into understandable parts.

J= -D * D C/Dx

Every symbol stands for a different quantity.

• J– The Mass Flux – Flux is the movement of objects from one point to another in a given time. The flux is what we are measuring when studying diffusion.
• Units: the units of moles / (time * area)

Note: area has units of length*length (or length2)

Example: mol/(h*ft2), mol/(s*m2)

• D– Diffusivity – The diffusivity is the constant that describes how fast or slow an object diffuses.
• Units: the units of area / time

Example: ft2/h, or cm2/s

• D - Delta - Delta is the Greek letter that represents the words "change in." When the symbol D is used, it refers to subtracting the beginning value from the final value of the symbol following the D .
• For example: D C = C2 – C1 = the last C – the first C, where C represents concentration.
• C – Concentration – Concentration is the amount of mass in a given volume.
• The symbol D C refers to the change in concentration from when the object had not diffused at all, to the final concentration when the object was done diffusing.
• Units: the units of amount of substance / volume

Note: volume is the representation of size in three dimensions. Therefore it has the units of length*length*length (or length3)

Example: mol / cm3, mol/L

• x – Distance – This refers to the distance that the object is diffusing.
• The symbol D x refers to the distance between where the object started and where it ended up after it diffused.
• Units: the units of length

Example: m, cm, ft

Therefore, returning to the equation,

J = -D * D C/D x

It was described that the flux was equal to the negative diffusivity times the change in concentration divided by the change in distance.

How about doing an example using Fick's Law?