Do minerals and/or metals found in water tend to settle to the bottom?
I have experimented with this phenomenon and found that allowing water to sit for a day may have a non-trivial effect on the TDS gradient in the water. This effect could be due to various reasons, however.

Materials: Glass pitcher, plastic &amp; porcelain &amp; glass containers; tap water from near Chicago, IL, USA; TDS meter

Methods: I poured tap water into various containers and allowed the water to stand for about 30 hours. I then measured the TDS at the top of the water. Then I stirred the water vigorously and let the water sit for about a minute. I took a TDS reading again at the top of the water. I repeated the experiment a total of 4 times.

Results (Updated 12/23/2016): 
$$\begin{array}{ccc} 
 &amp; \text{TDS Before Stirring} &amp; \text{TDS After Stirring} \\ \hline
\text{Glass} &amp; 138 &amp; 141 \\ 
\text{Plastic} &amp; 150 &amp; 146 \\ 
\text{Porcelain} &amp; 153 &amp; 152 \\ 
\text{Glass} &amp; 147 &amp; 149 \\ 
\end{array}$$

Conclusion: The results are interesting. I will discuss a few possible reasons behind the results, but I'm not certain.


TDS (after) was higher both times for glass. Maybe this is because when the water sits, a small number of ions adsorb to the glass surface. 
For plastic and porcelain, TDA (after) was lower for both plastic and porcelain. This may be due to dust that settled and dissolved into the water, as I did not cover the containers (looking back, covering the containers would probably have made the experiment more controlled). In addition, maybe ion adsorption happens less with porcelain and plastic.