# Low viscosity, low surface tension liquid for volume measurement

## General Case

This question concerns the general problem of accurate volume measurement of a given object. Among other techniques, that of liquid displacement is sometimes used for this purpose.

• In case of a solid material, the latter may be immersed in liquid, and its volume calculated by measuring the amount of fluid displaced in a graduated cylinder.

• In case of a hollow object, the latter may be filled in with a liquid which amount is accurately determined, either while filling in, or by emptying the object in a graduated container a posteriori (or - maybe more accurately - by weighing).

In both cases, the choice of the liquid is of crucial importance for the accuracy of the measurement.

## Specific Issue

I have a CO2 gas sensor with a complex hollow embodiment, also containing electronics, and since I wish to perform response time measurements, I would like to precisely know its inner volume. I came up with the idea of filling it with a liquid, as stated above. I do not have and cannot have accurate drawings of the inner sensor.

## Questions

1. Is there other methods to perform such a volume measurement which may be preferable?

Indeed, I came up with this idea because I find acceptable to sacrifice a sensor to perform such volume measurements. Alternatively, I also thought of placing the sensor in a closed, accurately known volume, along with some amount of chemical reagents that would produce a given amount of CO2. Then, by dilution and measurement of the CO2 percentage inside the enclosure, I may know the volume occupied by the sensor. However, I believe that there are far too many sources of errors in such procedure for it to yield accurate results. I may be wrong, though, and other variations of the latter idea may work well...

2. Which liquid may be the best for such measurement?

This is the main issue here. I would tend to say that such a liquid should have both a low surface tension and a low viscosity. Additionally, low volatility would be a plus, since it would prevent the amount of poured liquid to decrease with time. I find methanol or ethanol to be good canditates despite their high-volatility. I cannot use acetone because of the risk of plastic dissolution and the resulting leakage of the sensor's embodiment. Would you know of a more suitable liquid, possibly readily available in the lab?

3. Can surfactant be added to ethanol or methanol? If so, do they further decrease surface tension? Which are they?

A quick search in the literature revealed that methanol or ethanol are themselves considered as water surfactant. Their mixture with other surfactants is often analysed in emulsions of oil, or other chemicals, but not alone.

## Edit:

• As pointed out by Poutnik, low volatility and low viscosity are mutually incompatible with each other. Indeed, low viscosity tends to be positively correlated with high volatility, both of them being the consequence of low intermolecular forces. More resources on the topic are available here (saved version). The requirement on low volatility was not mandatory though, as it was just to ensure that not too much of the liquid evaporates during the filling of the sensor...
• Low viscosity and high volatility are two correlated attributes of low intermolecular forces, so these requirements go strongly against each other. You may found a liquid with good one value and acceptable other value, but it may be tough. Oct 9 '20 at 15:39
• @Poutnik, Indeed, I should have thought about that in the first place. Actually, the constraint on volatility is not that important. It was just to ensure that not too much of the liquid evaporates during the filling of the sensor... I edited my question accordingly, thanks :) Oct 12 '20 at 8:47

Air would be a convenient fluid. Fill your sensor with air at a known (atmospheric) pressure - well, it is probably filled with air already.

Then connect it to a vacuum chamber tube of known volume with a pressure sensor, i.e., a tube with two valves and a pressure sensor. Attach a vacuum pump to one valve and evacuate the tube; attach the $$CO_2$$ sensor to the other valve and then open it and measure the new pressure in the closed system. All the air will have been supplied by the sensor volume, and the new system volume will be the sensor volume plus the (known) tube volume. Doing it this way is likely to be less messy and more accurate than using liquids, and it won't sacrifice a sensor - and you can check every sensor!

A problem with liquids in a blind experiment (you cannot see the internals) is that there could be blind alleys that would be hard to detect and hard to fill with liquid (or which would not empty easily).

• 1 - Your idea may be good with a solid sensor with an inlet and outlet that may be easily connected with pipes but it is not the case (it is a sensor for free air measurement, with no in / out ports, rather a thin mesh exposed to ambient air). We could however place it inside a known volume enclosure and apply your method. Oct 12 '20 at 8:54
• 2 - Its main drawback, in my opinion, is that - while you are certain that no "dead space" remains (as could have been the case with liquid filling, with a hard-to-fill volume) - the accurate measurement of the volume of your pipe and valve is quite impossible. In other word, there are too many little uncertainties (is my pipe pushed enough on the nozzle, what is the gas volume at the entrance of the valve, etc.) that makes the global measurement inaccurate. It may work for big enough sensors though, given these inaccuracies are negligible compared to the inner sensor volume... Oct 12 '20 at 8:58
• The internal volume is secondary, if you want to find the response time. When you open the system and allow CO2 in, the output of your sensor will reach equilibrium after some time. Why do you need to know the volume? If holdup of gas in the sensor extends the response time by limiting diffusion, would putting the sensor into different CO2 concentrations establish a time to reach equilibrium easier than calculating from a volume? Oct 12 '20 at 14:32
• I would like to place the sensor against a medium which will produce (exhale) CO2. What I really want to measure in the end is the rate of production of CO2 by this medium at t=0. To do so, my idea was to place (air-tightly) the sensor against this medium, wait a few minutes and deduce the diffusion rate from the slope at t=0 which will be the quotient of the diffusion rate by the sensor's volume. Hence my need to know the sensor's volume... Oct 13 '20 at 11:56
• @mranvick: How about making "synthetic media": fill a balloon with CO2, fill another with air. Place your sensor against the one with CO2, plot response vs time, then against the one with air. The rate of CO2 production from a balloon will depend on how big you blow it up (pressure, thickness of membrane); it should be constant for several minutes. You can get the actual rate of CO2 production per cm^2 by weighing the balloon and calculating its total area. One liter of CO2 (a small balloon) weighs about 2 grams plus the balloon; the pressure inside is only about 10-20 mm Hg above atmospheric. Oct 13 '20 at 15:42