Surface Tension
The effect of surface tension has the potential to seriously hinder the effective and accurate dosing of alum in AguaClara plants. Surface tension is caused by the cohesive forces of liquid molecules at the water surface. The concept of surface tension can be visualized by the figure below.
Figure 1: The effect of surface tension
As can be seen in the figure above, a certain head, h, is required to overcome surface tension and form a water droplet. The graph above indicates this relationship between the height required to form the water droplet and the diameter of an orifice subject to the water head. Any value beneath of the line indicates that there is not sufficient head to form a water droplet, and no flow will occur. If the head subject to a set orifice size is above the line, there is adequate water height to cause flow.
The relationship shown in the graph above is represented by the formula:
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$$
\Delta h = {{2\sigma } \over {\rho g
Unknown macro: {d over 2}
}} - 2{d \over 2 \over 3}
$$
where:
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$$\Delta h$$
= the height of water above the orifice
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$$\sigma $$
= Surface tension, force/length
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$$\rho $$
= density of alum, mass/volume
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$$d$$
= Diameter of the orifice, length
The effect of surface tension can manifest itself in errors in the calculated head values in the dosing system. A certain headloss on the lever arm corresponds to a certain flow rate of alum. If surface tension increases the necessary head required to achieve this flow rate, underdosing will result. This concept can be shown in the figure below:
Figure 2: Headloss error caused by surface tension
The error caused by this difference is especially prevalent in lower plant flow situations where the head between the orifice and water level in the constant head tank is small. Another words, at lower concentration scale positions, ex. 5 mg/l, the effects of surface tension will be especially prevalent.
The affect of surface tension has not been integrated into the generation of the dosing scales yet, but several solutions are proposed to minimize the error caused by surface tension.
Solutions
There are two proposed solutions to mitigate the affect of surface tension, they are presented below:
Option 1:
The creation of a three scale range which has a narrower concentration range than the dual scale, will allow us to adequately handle surface tension. The narrower range permits for a smaller orifice size for that range, which allows for a higher head to drive this flow. The higher head driving the flows leads to less of an effect of surface tension on the effectiveness of the doser.
Figure 3: Three scale
Shown in the figure above is the three scaled orifice and the corresponding orifice sizes for each scale. For instance, if raw water coming in from the river were really turbid then the highest and largest orifice size would be chosen and the higher dosing scale would be followed.
Option 2:
The addition of a submerged orifice inline between the constant head tank and the opposite end of the tube eliminates the need to correct for surface tension affects. The submerged orifice has water on both sides of orifice opening and thus is not subject to an open atmosphere, and a vena contracta. This submerged orifice would be much easier to use since it would not require a custom scale to be made for every AguaClara plant. This would allow for a standard scale with which the only thing which would change is the size of the hole in the submerged orifice.
Figure 4: Submerged orifice
This would be a robust mechanism for dosing as long as the major losses contributed by the submerged orifice insert were kept to a minimum. The main downside is the ease with which the submerged orifice would be implemented. Current models have been difficult to slide in and out and might not be easy for the operator to change the orifice sizes. Further research will be done to find an easy way to change the orifice sizes.