Gas Dilution With The Equal Capillaries Technique
The advantages of the equal capillaries technique are surprising and leads to reach accuracy values of one order of magnitude higher than all the other dynamic dilution techniques. This comparison will be supported by analyzing the accuracy available with two different techniques.
Nozzles (sonic or non-sonic) technique
With this technique, a series of different size nozzles is used to provide, applying a constant pressure, a flows series complying with the 2n progression. That means if the smaller nozzle is involved by a flow q, the flow through the next is 2•q, through the next again is 4•q, and so on. Combining in parallel more nozzles, all of the integer multiples of q may be obtained. Supplying one part of the nozzles with the gas to be diluted and the remaining with the diluting gas, all the possible dilutions are obtained at intervals whose distance depends upon the number of used nozzles.
For example, with 3 nozzles 8 dilutions are possible (0, 1/7, 2/7, 3/7….6/7, 7/7) , with 4 are possible 16 and so on, according to the progression 2n . The advantage of this technique is in the fact that using few nozzles many dilution ratios are possible. The image on the left shows the proportions of equivalent capillaries with growing size, giving the 2n progression on the flows. It’s important to verify how much the selection of the nozzles may be accurate before they are installed in the diluter in a way that the wanted flows progression be complied. The series of four targets here shown gives an idea of the proportions between the required flows measurements: Having 4 nozzles, 4 flows must be measured and the targets diameters are proportional to the relevant flows.
The flow meter is necessarily selected in a way that the higher flow to be measured is within the measuring range, and his uncertainty may be in the order of 0,2% of the range. Which is the uncertainty measuring the lower flow, 8 times lower ? Obviously it will be about 1,6% of the reading, because the reading is 8 times lower.
And then, why not to use more than one flow meter, each having a range more suitable to the measurement to be done ? In fact one reason may suggest to avoid this choice : the sole important requirement for a gas diluter is the correctness of the flows ratio, because the dilution factor is that. If the flows would be both double of the wanted value, the dilution ratio and the diluted concentration would be as wanted, just the output flow would be double, but this is not critical.
In the left image, the dilution diagram, we may see that, moving from point A to point B, the flows do change (maintaining the same proportions) but the dilution ratio don’t change. Performing all the measurements with the same instrument gives the advantage that the sensitivity error don’t affect the test : just a zero calibration, linearity and repeatability is required. Using multiple flow meters, traceable sensitivity calibration is required and despite what, the sensitivity errors mismatching become the most important uncertainty cause.
Equal capillaries technique
Also the technique of the equal capillaries may use the binary progression described above: instead of being obtained with elements of different cross-section it is realized by bringing together the capillaries in groups, according to the same progresssion: single capillary, group of two capillaries, group of 4, group of 8 etc. The advantage of grouping consists in the fact of reducing the number of flow shut-off elements (solenoid valves). The different capillaries that make up a group are arranged in parallel so that the flow corresponding to a group is equal to the sum of the flows affecting the capillaries of the group itself.
The disadvantage of this solution consists in the greater number of the required elements : to obtain 8 dilution ratios 7 capillaries are necessary against the 4 orifices of the case described above, and to obtain 16 dilutions 15 capillaries are necessary against 5 orifices and the ratio capillaries / orifices worsens dramatically for larger numbers. But let's consider the advantages: in the choice of the equal capillaries, the situation is quite different from the previous case. Chose a flow meter having a measuring range suitable for measurement of a capillary, all remaining are measured in a narrow scope of values, and if the deviation is excessive capillary is discarded. Returning to the analogy of the targets, the situation is illustrated by the example shown here, but the size of the targets should not lead us into error: the value of the flow to be measured can be increased (almost) at will, increasing the pressure applied, and the sensitivity of the meter can be freely selected so that all measures are in the top quarter of the measuring range of the instrument. So apart from the needs of space in printing, the 15 targets were to be represented by all size equal to the greater of the five targets of the previous case. If then the uncertainty of measurement of a flow is, as above, in the order of 0,2% of the measure itself, all the flows will be measured with the same uncertainty. When combining the groups, the uncertainty about the flow of a group, relatively to the sum of the flows in the capillaries of the group is even better, both for statistical reasons, and because the breeder can compensate for the elements 'poor' with those 'abundant'. But the fact of repeating almost equal measures has further advantages: short or medium term drifts in the measuring system are well controlled interspersing the extent of the capillaries to be selected with the measure of a comprehensive reference, selected, but not necessarily traceable, for the reasons already stated above
a) The linearity of the measuring system does not affect the test, precisely because the measures are in a close neighborhood of a point (the capillary that were to produce a stream that is more would anyhow be discarded)
b) Even in this case it is not required traceability of the measurement, because the objective is the search of the capillaries equal to each other, not of those that control (by applying a specific pressure) to a specific flow value.
In addition to the effectiveness of the capillaries equality, a second element plays an important role for the accuracy of the diluter : the pressures applied to the capillaries. Two different gas (the gas to be diluted and the diluting gas) affecting separately capillaries: a share of these is affected by the gas to be diluted and the remainder from the diluent gas. The allocation of the two quotas is managed by solenoid valves according to the desired dilution ratio.
All capillaries have in common the drain (output of the diluted gas), but it is necessary that the two incoming gases or mixtures have the same pressure so that the equality of flows is maintained even during the use of the diluter. Sometimes, it is the case of incoming gases with different viscosity, it is necessary (or desirable) unbalancing the pressures applied by virtue of the relationship between the different viscosity (applied pressure and viscosity have linear effect and inverse to each other on the flow in the capillaries).
Unfortunately, in a diluter, to vary the dilution ratio, while an input flow falls, the other grows and the differences between the applied pressures are additive.
In a diluter with capillaries, but same is with the orifices, the calibration of the pressures does not need traceability, in fact, a variation of the applied pressure affects the dilution ratio only when is not proportional : what counts is the ratio between the applied pressures.
To ensure the proportionality of the applied pressures, the reference sensors are calibrated by applying to them the same zero and the same span: to this aim, during the calibration procedure, the two inputs are closed, the reference pressure is applied from the output and the internal volume is placed in communication so that all three pressure sensors (two at the entrance and one exit) 'see' the same reference pressure. Also, to avoid that the variations of the back-pressure have influence on the proportionality of the pressures applied to the capillaries, the pressures control is of the differential type (input-output) on both sides (gas to be diluted and diluent gas).
Finally, to ensure uniformity of temperature across all the capillaries, these are 'embedded' between the two shells of solid material (fluorinated resin or stainless steel). This construction gives further advantages :
a) The ways of connection between the ends of the capillaries and other components (sensors and valves) are obtained from communicating holes and the risk of leakages is minimized.
b) The result is a compact and extremely robust, with very low dead volumes
The comparison between the two techniques (equal capillaries and scaled nozzles) would have led to the same conclusions by replacing the orifices with flow regulators: also in this case, for the determination of the polynomial correction of linearity, would have required the measurement of flows very different from each other so as to verify the flow regulators on the entire operating field, which generally covers almost a decade. Not for nothing, the MFC are always qualified in terms of accuracy relative to full scale and not to the value of actually regulated flow.
Until now it is highlighted, where possible, that traceable references are not required for selecting equal capillaries, but for 'legal' applications traceability is an essential condition. Among other things, when the diluter is assembled, the individual capillaries are no longer accessible or measurable individually: we know that they are nearly equal (if they were identical the dilution uncertainty would be limited to the uncertainty on the pressure applied), but to release a verification it is necessary to involve accredited laboratories that perform traceable measures on either inflows and the outflow using traceable instruments.