of gas diluters

## THE BetaCAP DESIGN

BetaCAP is a project that did evolve during the years, generating an high quality and diversified set of gas diluters. It was born about 20 years ago by some intuition immediately converted into drawings but just after long decantation converted into a prototype. It was different from the actual BetaCAP30, but it was possible to see the promises and the game become a work. Considering how much all the BetaCAP diluters series is known and used in Italy , but also how it’s generating interest (and some qualified User) in all the word, lets us to understand that we did match the performances technicians was waiting. All of this without a sales dept, just thanking the word of mouth and this web site. Our task is continuing that way, respecting our users requests and promoting the knowledge of BetaCAP advantages : as you will see it’s not difficult. Advantages list is:

- Using nearly equal capillaries
- Electronic pressures control
- Design and management of the diluter using the logical and analytical representation of the gas divider and associated capillaries physics
- Construction based on manifolds couples
- The range of gas dividers resulting from that project includes various models, each with specific functions and suitable for a defined user type. Now the family is growing again… you will see next.

## EQUAL CAPILLARIES

**Capillaries** are very thin holes where fluids flow in laminar mode (without vortexes) and with repeatable quiet flow value. Flows are induced by a differential pressure applied to capillary ends and are quantified by the Poiseuille formula where the additional parameters influencing the flow are the physical dimensions and the fluid viscosity. A simpler image of the capillary can be got using the Electrical analogy : Replacing Differential pressure with Voltage difference, the fluid flow with current flow and the capillary with a resistor, it’s evident the analogy of Poiseuille formula and Ohm law.

In the title it’s used the words couple “equal capillaries” : we know that equality does not exist in real word : the project identifies the ways to arrive very near to the equality result. Purchasing the capillaries lot, departure is not the best with 0,015 mm tolerance over 0,1 mm (the specified capillary diameter). Unfortunately the consequent mean deviation on the flow induced by a constant pressure is about 0,028 over an expected value of 0,05 L/min (that result is due to the fourth power elevation of diameter ). Hopefully selecting nearly equal capillaries by measuring the flow is very easy :

a) Lot classification. A first series of flow measurements (one or two thousands of capillaries) is selected with better than 0,1% accuracy. Different classes are located in different containers at 0,2% distance in flow one each other

b) To build BetaCAP30 gas dividers it’s necessary to have 5 capillaries groups, 1, 2, 4, 8 and 15 capillaries each group, to reach a total of 30 capillaries. Using a self made tool that can receive 36 capillaries and filling it with 36 capillaries taken from a single compartment of classified capillaries we start extracting the 30 capillaries required to produce one BetaCAP30 :

The 1 capillary group is formed by selecting one capillary having a flow measurement near to the mean value of flow measuring in the selected class. His flow measurement will be the internal reference for the next grouping. The groups containing more capillaries are composed using the same number of capillaries scarce and of capillaries abundant, where scarcity and abundance is calculated as a difference between the single capillary b) flow and the flow of capillaries to be selected. Sum of excesses and deficiencies must be null. If the result is very accurate for the single capillary group (about 0,2% related to the value), the groups containing more capillaries are even more accurate, because the flow value is the sum of the capillaries flows in the groups. It must be highlighted that whichever different technics using different elements or different flows from one element (MFC) can offer accuracy near to 0,2% of the value just for the upper values, but it decrease dramatically with the measuring value : at 10% measuring the accuracy is about 2% of the value

### ELECTRONIC PRESSURES CONTROL

As shown in the functional diagram, Input pressures (gas to be diluted and diluting gas) and output pressure (Diluited gas) are measured. The electronic function (hardware and firmware) handling the pressures control operated on differences P(TG1)-P(OUT) and P(TG0)-P(OUT) and setpoints come from calculations This is another key point of the project : being known the logical-mathematic function behind the diluter device and capillaries physics, the diluter can be driven as a conceptual object. This allows reaching unexpected results, like viscosities compensation, certified deviations correction and, last but not least … the continuous dilution range covering !

### MATHEMATICAL DESCRIPTION OF THE DILUTER

This subject is already mentioned in another section of this web site, but it’s so essential in BetaCAP project that we need to anticipate here some point. Dilution ratio is the target of the BetaCAP project function and it can be expressed in a numerical form as a flows ratio : gas to be diluted flow / total output flow.

Those contributions depends on capillaries partition in the diluter and from the physics of capillaries that we learned from Poiseuille. The resulting formula (one more equation is added to allow P(TG1) and P(TG0) calculation) show us that, changing the capillaries partition in the range 1/29 to 29/1, always it exists a couple of P(TG1) and P(TG0) giving the wanted dilution.

- To get the better accuracy and an easy handling of the diluter, capillaries partition is set in the best way, mainly depending on the viscosities ratio (typically some more capillaries are moved to the more viscous side). When the user sets a target dilution, the equations solution starts to recover viscosities, to fix N (capillaries crossed by measurand gas) and then calculating P(TG1) and P(TG0) : calculated pressures become the setpoints
- Certified deviations correction. In the metrological certificate, the gas to be diluted flow and the diluted output are measured and deviations are recorded for each of the main dilutions. Whichever dilution can be expressed as a ratio of gas to be diluted flows through some main capillaries group and the sum of all the main certified flows. This calculation gives the real dilution as measured by certifying body. The correction function moves the user dilution target in a direction opposite to the certified deviation in a way that this deviation restores the user dilution target.

- Extension of the step by step operating mode to the continuous uninterrupted mode typical of MFCs. Operating from the menu “Set Kdil.” we can just change the capillaries partition : in this case BetaCAP30 allows 31 different capillaries partition. If viscosities (η1 and η0) are very similar, P(TG1) is nearly equal to P(TG0) . We can imagine to increase P(TG1) : TG1 flow increase and the diluted concentration is higher. This is done basing on accurate measurements, than a control of all the dilution range is available.

### MANIFOLDS TYPE CONSTRUCTION

A big amount of junctions between the 30 capillari alternately to the gas to be diluted or to the diluting gas and all the devices in the functional diagram (five 3 ways solenoid valves, two proportional pressures controllers, three pressures sensors and the connections to two inlets and one outlet, did force us to search a method different from tubes and fittings. We saw in the past some “Manifold type” circuit connection and we did apply. Did use a couple of parallelograms in a way that capillaries are hod part in one and part in the second with an o-ring between the two faces sealing all the ways requiring not to leack The two pieces are hardly kept together by 4 or more screws. The other components are placed and fixed in caves on external faces. This solution assures a total capillaries protection (never had 1 broken) and a module very compact, rugged and easily assembled.

## Some of our clients

We collaborate with and supply companies in the sector all over the world.