Model:

The basic assumptions of the model for the chemo-repellent are:

- There are no forces except diffusion:
> Chemo-repellent concentration in the sample is relatively low and does not cause osmotic pressure.
> The changes in pressure due to loading the sample is negligible.
> No other significant external forces (for example, moving the chip while in use).
- The bacteria do not consume the chemo-repellent and its concentration does not change in time. This is not case with chemo-attractants.
- We expect to detect small proteins and molecules (those are the materials bacterial receptors bind to). The diffusion coefficient for such materials is about 10^-9 [m²/s].
- Because of the geometric properties of the channel and the expected diffusion coefficient, this is approximately a half-infinite one dimensional problem.
- The starting conditions: no chemo-repellent in present (a) and in all times, at infinite distance the concentration is also 0 (b).

We modelled the change in concentration of chemo-repellent based on "Top Hat Function" for a diffusion problem:

v[M] is the chemo-repellent concentration, D[m²/s] is the chemo-repellent diffusion coefficient,
N[mol] is the number of repellent atoms,
A[m²] is the cut section of the channel,
x[m] is the distance on the channel,
t[s] is time.
The solution for this problem is:

In our problem, we want the diffusion to start from . Also, we take into account only the positive distance:

The change in value of the diffusion limit between times 0 to 15 minutes, is relatively big. As the time passes the change lowers.
* This is the diffusion coefficient for potassium permanganate (see "Comparison to Experiment").
** h = (Sample_volume)/(Reservoir_cut_section).

Comparison to Experiment

Most diffusion experiments need a dedicated system that is based on the diffusion of an isotope or a fluorescent material that can be detected easily and very pre-cisely. In this case, as explained in the opening, our goal is showing that the overall system behaves as we expect.

The experiment ran as shown in the "Introduction" section where we replaced the bacterial medium with water and the repellent with potassium permanganate in the following amounts:

Motility buffer is mostly water (98%) and can be modelled by it. Potassium perman-ganate is a salt with a known diffusion limit and acts as most of the materials we want detect using our system. Also, it has a very distinct pink color in low concentra-tion, so the diffusion limit can be seen easily.

We ran the experiment 4 times, with a standard roller to measure the distance of the diffusion limit.

As expected by the mathematical model, the diffusion limit starts moving relatively fast and its speed decreases rapidly. The difference in distance between the model to the experiment (average of 2.5[mm] fro, T=0) can be explained by:
- The actual diffusion limit is in too low concentration of potassium permanganate to be seen in the naked eye. If the visible con-centration is about 0.000015 [M] the experiments results lines up with the model (Graph 2.2).
- The roller is a crude measuring tool. Its mistake is +/- 0.5 [mm]. - Difficulties loading the sample in a uniform way, especially in low volumes. Mistakes in loading the sample inside the bacterial fluid and not on, or sticking the drop of sample to one of the entry slot walls will cause uneven diffusion.