Math is Fun

February 27, 2012 7:02 PM

What are some ways to accurately measure the volume of very small amounts of liquid without complex equipment?

I need to accurately measure the volume of droplets between let's say 0.1 to 2 μL. I cannot use a calibrated micropipette tube because the smallest ones available (10μL) are too big for the liquid to sit evenly.

I tried placing the droplets on a wax surface and measuring diameter with a micrometer, but there's no way I know of to calculate volume with this diameter since the droplets aren't spheres when resting on a surface. I think I would need a contact angle goniometer to begin to analyze the geometry.

I guess I can try placing the drops in oil and calculating the area that way but in reality I've tried different types of oil and the drops don't stay in a nice easy shape.

I have access to basic chemistry glassware and equipment but nothing fancy.

posted by WhitenoisE to science & nature (23 answers total)

Do you know the density of the liquid? If you have a precision balance you can weigh and calculate the volume.
posted by inkisbetter at 7:05 PM on February 27, 2012 [1 favorite]

Seriously, I don't think you're going to be able to measure volumes that small accurately, or at all. My lab has 0.2 - 2 uL pipets, and at the low end even those aren't very accurate or reliable because it's such a tiny amount (I'm talking about 0.3 uL, which I had to pipet the last few days and don't really trust that it was accurate).
posted by imagineerit at 7:07 PM on February 27, 2012

Can you weigh the liquid? If is mostly water, you can use the weight along with the specific gravity (density) to calculate volume.
posted by nasayre at 7:08 PM on February 27, 2012

inkisbetter is right, but it would have to be very sensitive and accurate.. I know our 4 digit scale wouldn't work because it drifts by 4 millions of a gram sometimes.
posted by imagineerit at 7:08 PM on February 27, 2012

The only way I know of to do this even semi-accurately is with a 2uL pipetter. (Although I'd be willing to try for the 2uL with a 10 or even a 20. Heck, I was doing 0.4uL pipettes with a 20uL pipetter just a week ago and my reactions were coming out fine.) I've done 0.1uL with a 2uL pipetter many times before and it's been accurate enough for my purposes. I'm unaware of any better way to do it except with a better pipetter. I know there are fancy specialized models that are meant to perform better with problem liquids and such, but nobody in the labs I've worked in has ever mentioned using one.

What would the consequences be for your reaction if you were off by 0.1uL either way? As I parenthetically mentioned above, it's sometimes not actually that big a deal if your volumes are a tiny bit off. Of course, I don't know what actual application you're dealing with here, but most of the time if it were me I'd just get the best tool I had (the 10uL pipetter you mention) and just go for it. Just be as careful as possible and do my best with the tool available.
posted by Scientist at 7:18 PM on February 27, 2012

What are you trying to accomplish? The technique I would use is to periodically prepare a working stock (10 µL into 90 or even 990 µL) and then use 1 - 20 or 10-200 µL of that, but it depends on what you're doing and how well the stuff you're working with responds to dilution.
posted by Kid Charlemagne at 7:21 PM on February 27, 2012 [1 favorite]

Also the infuriating thing about trying to weigh 0.1uL of liquid is that even if you do manage to get the weight right, you're never going to pick all of that droplet back up again with your pipetter. Some residue is inevitably going to be stuck to the weigh paper (even if you use parafilm, as you should) and that will definitely throw off your volume. You're 22, I assume you're not the PI in your lab. What did your supervisor have to say about this?

Alternatively, what you might be able to do (depending on circumstances) is make a dilution of your reagent (say, a 1:100 dilution) and then you can move 10-200uL of your dilution instead of 0.1-2uL of the neat reagent. This obviously doesn't work for everything but you can do it a lot of the time.
posted by Scientist at 7:23 PM on February 27, 2012 [1 favorite]

The other option is you could place a lot of different drops (a hundred maybe?) on your wax paper at the approximate volume you describe, then try weighing that. Then divide your final number by the number of drops to get an average weight per drop. Which you can use density to then calculate volume.
posted by nasayre at 7:24 PM on February 27, 2012

I would do this by making serial dilutions, which allow you to simply measure larger volumes of water. Of course, this will only work if what you're actually determining is the concentration of a solute, not the water itself (which is a situation I haven't ever encountered...but this doesn't sound like a normal lab techniques problem).
posted by pullayup at 7:24 PM on February 27, 2012 [1 favorite]

Sorry, that should be amount not concentration of solute.
posted by pullayup at 7:26 PM on February 27, 2012

The ideas I have won't measure in absolute units, but should be good for sorting out relative amounts:

1. Get some paper or cloth that is of consistent density, and measure the diameter of the "stain" after it quits spreading.

2. Get some fine wicks. Fiberglass comes to mind. Separate out a known constant quantity of strands and measure the length of how much it wicks up.

IANAS
posted by markhu at 7:29 PM on February 27, 2012

My immediate reaction would be to measure mass, or dilute the liquid, etc., as everyone else has suggested. But, trying to think of a way to answer the question as posed: if you assume that there's a reasonably smooth, but unknown, relationship between the diameter of a drop viewed through a microscope and the cube of its volume, you could make a large number of sets of drops of various known average volumes, measure them, and work out that relationship. I assume it'll change a lot based on the liquid's surface tension and density, so, um… control for that I guess?
posted by hattifattener at 7:32 PM on February 27, 2012

Bear in mind here that 0.1uL is an unbearably tiny amount of liquid. It is a small enough amount that things that you would not normally worry about, like a little smear left behind on a weigh paper, or the amount that evaporates while you're trying to weigh it, or the tolerance/technique limits of even specialized scientific equipment become big deals. There aren't actually a lot of good ways to measure such a small amount of liquid, we are talking nearly microscopic quantities here. It can be done but if dilution is not a viable technique and the smallest pipetter in the lab is a 10uL pipetter and your measurement must be precise then I submit that the best thing to do would be to go down the hall to a different lab with a 2uL pipetter and ask if you can borrow it. I very much doubt you'd be refused.
posted by Scientist at 7:44 PM on February 27, 2012

Oh, or perhaps you could increase the volume of your total reaction to a size where the smallest amounts of liquid that you needed to move were within the tolerances of your equipment. May not be an option (again, hard to tell without knowing what exactly you're trying to do here) but then again it may be. Would it be OK to make the reaction 10x the size you need and then throw out 9/10ths of it, for instance?
posted by Scientist at 7:47 PM on February 27, 2012

I am really hoping that the OP comes back and tells us what he's trying to do that requires him to pipette 0.1uL of liquid. Not that it's an unreasonable thing to need to do, I'm just curious what he's up to!
posted by Scientist at 7:49 PM on February 27, 2012

What everyone else said about these being unworkably small volumes. If you have a balance that's sensitive enough to weigh 0.1 µl (which weighs 0.1 mg, or 100 µg), you will see the weight decrease steadily as the water evaporates.

However, you might be able to get an estimate of the volume of the droplets with a microscope and a hemocytometer. Put your droplet onto the grid, put the coverslip on and count how many squares the liquid occupies. This will give you the volume, approximately, since the chamber has a defined volume. Not terribly accurate, but maybe good enough.

Check your results using droplets of known size (go borrow a 2 µl pipettor from another lab). Hemocytometers run about $50 but they're the kind of thing that many biology labs have lying around, if you can't afford to buy one.
posted by Quietgal at 8:37 PM on February 27, 2012 [1 favorite]

I tried placing the droplets on a wax surface and measuring diameter with a micrometer, but there's no way I know of to calculate volume with this diameter since the droplets aren't spheres when resting on a surface. I think I would need a contact angle goniometer to begin to analyze the geometry.

It's possible to do this analytically. There are instruments which can do this, if it's really important to you, usually used for interfacial tension and contact angle measurements. Drop shape analyzers run in the 60 to 100k range, but most university mechanical engineering departments will have one or two. This really isn't what you want to do though.

I guess I can try placing the drops in oil and calculating the area that way but in reality I've tried different types of oil and the drops don't stay in a nice easy shape.

Again, that's drop shape analysis. Not easy.

Weighing at that level is really prone to balance uncertainty. Normal four decimal lab balances are calibrated only with uncertainties in the 0.1 to 0.3 µg range. That's really not good enough for you. To accurately do this needs a five decimal balance or better, and those are uncommon.

Is there any reason you can't buy a microlitre syringe? Hamilton makes low-volume syringes which can dispense down to 0.5 µL full scale. They cost about $100 each. A 20% fill would be plenty to ensure at least Class B accuracy. Syringes that small are fragile, but I've used a similar one now for four or five years manually without damaging it.

That said, when someone comes to me with this kind of problem, the best answer is often a rethink. Getting below the 10^-3 range is very hard without automation to do it for you---humans aren't precise enough and can't see well enough to do it well. If you actually do need to deliver a set amount of liquid at that volume, then you may want to reconsider your experimental scale. If you just need to deliver a quantity of material at low concentration, consider serial dilution.

Only if you have no alternatives should you consider trying to do this by hand. It's going to be difficult and you will have to accept that your volumes will not be well-controlled. If that's a problem, you need to consider automation---an autoinjector can do 0.1µL repeatably, but I've never met a human who could.
posted by bonehead at 9:14 PM on February 27, 2012 [1 favorite]

To follow up---if you need to do this accurately, find a cooperative analogical chemist with a gas chromatograph, ideally one with a combi-pal type rail system, though a standard Agilent or Varian turret will do. They can program the autoinjector to dispense 0.1µL aliquots into vials quite easily with the right syringes. Fortunately 1µL injection syringes are fairly common---0.1µL should be quite possible.
posted by bonehead at 9:20 PM on February 27, 2012

bonehead, the OP is trying to measure the drops, not dispense them...

totally agree with Quietgal...use a .1-2µL pipettor and lay down some scale drops (in the same material) and measure the diameter of those...then you just have to measure the sample drops diameter and the drop geometry should cancel out.
posted by sexyrobot at 9:47 PM on February 27, 2012

Gosh, sexyrobot, you are totally right. The question does not seem to be a matter of moving or dispensing liquid, but rather of simply measuring the droplets themselves which are, I guess, the result of some other process. I feel stupid for assuming things that weren't in the question.

I like Quietgal's hemocytometer method. If the droplet is already there it should be possible to move it with the 10uL pipetter, as long as the liquid isn't something nasty that would stick to the inside of the pipette tip. Pop it in the hemocytometer, count the squares, get your measurement. Might be too cumbersome if there are a lot of droplets involved... if so, I would hope that an average volume would be OK because then it would be possible to just weigh them all at once and take an average.
posted by Scientist at 10:06 PM on February 27, 2012

Check your results using droplets of known size (go borrow a 2 µl pipettor from another lab). Hemocytometers run about $50 but they're the kind of thing that many biology labs have lying around, if you can't afford to buy one.

Depending on how small you need to go, you might be better served by a counting chamber that's shallower than the usual haemocytometer (e.g. something like a Petroff-Hausser counter.) You can get them as shallow as 10µm, though of course those get rather more expensive than Quietgal's $50. People who work with bacteria are more likely to have these (people who work with eukaryotic cells are more likely to have a haemocytometer.)

Also, if you're trying to dispense 100nL quantities of something, you might want to consider automation. (Look for a high-throughput facility - for setting up large numbers of small-volume reactions, I've been using a machine from Labcyte that can dispense 2nL quantities of liquid. At the range you're looking at - as low as 100nL- a machine like that is apt to be more accurate than manual pipetting.)
posted by ubersturm at 10:16 PM on February 27, 2012

Hey guys, thanks for the answers.

What I'm trying to do is measure the amount that houseflies salivate when injected with serotonin. I don't know the exact composition of the saliva and the scales in the lab are only accurate to 1mg so I don't think weighing would work.

But the counting chamber/haemocytometer idea actually might work! I didn't think of that. I can transport the liquid in the 10ul pipette without too much trouble.

Thank you!
posted by WhitenoisE at 3:44 AM on February 28, 2012

Just brainstorming during my lunch break:

If the haemocytometer doesn't work, I think your next best bet would be the imaging approach. If you place the droplets on a superhydrophobic surface, they will be spherical - gravity won't have much of an influence compared to surface tension at these scales. Maybe even a simple windscreen coating spray would work.

Can you get a mirror/prism in your field-of-view to do a simultaneous side view through the microscope?

As other have mentioned, evaporation will be very significant at these scales. You could actually use this to your benefit: observe the descrease in droplet size visually and set up a simple mass transfer model. The rate of evaporation will be a function of the surface area (and thus mass) of the droplet. This would require some assumptions regarding the composition (but saliva is pretty complex, I assume).
posted by swordfishtrombones at 4:37 AM on February 28, 2012