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:
Unknown macro: {latex}
$$
\Delta h = {{2\sigma } \over {\rho g
Unknown macro: {d over 2}
}} - 2{d \over 2 \over 3}
$$
where:
Unknown macro: {latex}
$$\Delta h$$
= the height of water above the orifice
Unknown macro: {latex}
$$\sigma $$
= Surface tension, force/length
Unknown macro: {latex}
$$\rho $$
= density of alum, mass/volume
Unknown macro: {latex}
$$d$$
= 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 head loss 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, under dosing 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. The effects of surface tension will be especially prevalent at lower concentration scale positions, ex. 5 mg/l,.
The effect 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 effect 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 are the three scales and the corresponding orifice sizes for each scale. For instance, if raw water coming in from the river was really turbid then the highest and largest orifice size would be chosen and the higher dosing scale would be followed. For the Agalteca plant the recommended orifice sizes are 1, 1.41, and 2 mm. The scale has been calculated by the following file, and is shown below:
Scale, cm
6.46
9.29
12.66
16.53
20.92
25.83
31.25
In a three scale system that covers a range from 10 mg/L to 88 mg/L the total dynamic range is 8. This dynamic range is divided equally between the 3 scales. Thus each scale has a dynamic range of 8^1/3 or 2. With a dynamic range of 2 the minimum dosing position on the scale is at (1/2)^2 or ¼ of the total scale length. The lever arm is 40 cm long and thus the minimum dosing position is at 10 cm from the pivot point.
In a two scale dosing system with a dynamic range of 9 (to make the math easy...) the dynamic range for each scale is 9^1/2 or 3. The minimum dosing position on the scale is at (1/3)^2 or 1/9 of the total scale length. The lever arm is 40 cm long and thus the minimum dosing position is at 4.4 cm from the pivot point. Thus adding a 3rd scale more than doubles (10cm/4.4cm) the amount of head that is available to drive the smallest flow rates.
The following graph shows the measured results which have been taken using the new triple scale.
Figure 4: Results from triple scale testing
The graph above shows that the actual measured flows of alum for each scale are very close to ideal flow rates. There averaged error for each of these dosing ranges is around 10%, and is an acceptable amount of error for AguaClara dosing systems. This is very promising results and is the most promising option for future AguaClara plants.
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 effects. The submerged orifice has water on both sides of orifice opening and thus is not subject to an open atmosphere. This would allow for a standard scale where the only thing which would change is the size of the orifice in the submerged piece.
Figure 4: Submerged orifice
This would be a robust mechanism for dosing as long as the major losses contributed by the walls leading up to the submerged orifice in the insert were kept to a minimum. Major losses have been neglected in this design, so any further contribution of major losses would introduce further dosing error. The main downside to the submerged orifice insert is the ease with which it 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. In addition, it is difficult for the operator to see if the submerged orifice has become clogged. Further research will be done to find an easy way to change the orifice sizes as well as permit the operator to readily clean and maintain the submerged orifice insert.