# Fick's law

#### knickers

I have a sealed container which will be stored in a humid environment. The container has a small lid, which is opened briefly once a day. I would like to calculate how much water vapour will enter my container through the following transfer mechanisms;
1) Permeation of water vapour through the plastic
2) Water vapor entering through the opening each time the lid is opened.

I’ve calculated the (1) using Fick’s law of diffusion. I found the diffusion coefficient for the plastic that my container is made from. I then use this together with the thickness of the material, exposed surface area and differences in water vapour concentrations to work out the mass flow of water into the container when it is closed.

I’m now trying to figure out the mass flow of water into the container each time the lid is opened (2). I have found a diffusion coefficient for water in air at my temperature range of interest. I also know the surface area of the opening. The problem is that the Fick’s law formula I am working with seems to require a “membrane thickness”. In my case I have no membrane – just an opening. Can this formula still be applied? Is there another formula I should be looking at? How can I go about calculating how much moisture makes its way into the container each time it is opened?

#### benit13

I’m now trying to figure out the mass flow of water into the container each time the lid is opened
I'm not sure using Fick's law will give you the best result in a situation where mixing occurs (i.e. fluid inside the container mixes with fluid outside of the container). You'll probably get better results using some kind of advective mass transfer equation.

For example, if you consider the total mass of water vapour inside the container to change, then you have an equation:

$$\displaystyle \frac{dM}{dt} = -\dot{m}A$$

where $$\displaystyle \dot{m}$$ is the mass flux (in kg/(s.m2)) and A is the surface area of the opening.

You might also gain some insight by looking into psychrometrics, which deals with humidity of air based on different transitions along a chart. It gives a set of formulae to deal with changes in humidity based on different kinds of processes.

1 person

#### knickers

Thanks benit13.
I looked up psychrometrics and ended up using a moisture balance equation to get a rough number. The hard part is knowing how much of the air in my container will be replaced with the humid air from outside. I guess I can either take a punt, and say 20-30%, or for the worst-case scenario assume 100% of the air is replaced with outside air. The volume of high-humidity air outside my container is sufficiently large compared to the volume of my container that it can be considered infinite.

#### Woody

I remember someone once asking what the speed of a fart is,
by which they meant how long between the emission and someone across the room complaining about the smell.

I can't remember what the answer was,
but it basically depends of the speed of diffusion of one gas into another.