Is your drop the same size as mine?

Have you ever wondered if the size of a drop is always the same? The short answer to the question of the size of a drop is that the volume of a drop usually does vary, in fact depending on 10 different factors. This is of course relevant to alt. proc. because recipes often specify “20 drops”, “20 gtt” or “20 gt” which also means drops.

Writer and photography / Mike Ware and Pradip Malde

Welcome to the sub-science of STALAGMOMETRY!
From the Greek: ‘Stalagma’ = a drop. (it has nothing to do with WWII POW camps or cave mineral formations!)

The short answer to this question is that the volume of a drop usually does vary. For water, it will be in the order of 0.06 milliliters.
This defines a very approximate unit of volume which apothecaries called a “minim”. A rough rule of thumb is “about 17 drops to the ml”.

The longer answer is to be found in Physical Chemistry. The actual volume of any drop depends on:

1. The radius of the dropper tube orifice
2. The material of the dropper tube
3. The shape of the dropper tip
4. The speed of expelling the liquid from the dropper (which may bring in the viscosity of the liquid)
5. The density (or specific gravity) of the liquid being dropped
   5a.The density of air (or other surrounding fluid)
6. The surface tension of the liquid
7. The nature and concentration of any solute, if the liquid is a solution or a mixture (often the case with our various sensitizer solutions)
8. The temperature (affects 5 and 6 slightly)
9. The force of gravity prevailing locally (- ask any astronaut!)

…and possibly more things that we haven’t thought of.

• 1, 2 and 3 can be made consistent by always using exactly the same type of dropper
• 4 suggests we should expel the liquid slowly -not squirt it
• 5, 6 and 7 mean that different liquids (or solutions) give different sized drops – even with the same dropper
• 6, the surface tension, is most important, and can vary greatly (e.g. the surface tension of water is about 3x that of alcohols).

The drop size is directly proportional to the surface tension of the liquid: this provides the basis for the ‘Drop Count Method’ for comparing the surface tensions of liquids, using an instrument called a Stalagmometer. (Google it.) I will refrain from citing the mathematical equations.
The use of any “wetting agent”, such as Tween20, will have a large effect on the surface tension – that’s why they’re called “surfactants”.

All this explains why I never attempt to measure out volumes of liquid by counting out lots of drops: when scaled up, the errors become huge.
To try to measure precious metal solutions this way is scientifically -and economically- ridiculous.

All this uncertainty is eliminated by using calibrated “disposable” plastic hypodermic syringes -without needles-, which are graduated with numerical volume markings. They have long been cheap and widely available, (and following the endeavours to stem the current pandemic, there should soon be an industrious re-cycling market of 1 ml and 5 ml syringes!)
Graduated glass pipettes are the more sophisticated -and fragile- option for the chemically-trained, and require a mechanical piston or rubber bulb to suck up the liquid, because – whatever the historical traditions of chemical practice – pipettes today are never used by mouth, for safety reasons.

The most modern and convenient way of measuring out pre-set volumes of liquids are adjustable micropipettes with disposable slip tips, but they are expensive. There is a practical advice section on measurement in Pradip Malde’s and my book on Pt/Pd printing see pp.67-69 and Figures 4.5 and 5.3.

Footnote: The only liquid I personally measure by a drop, is Tween20 solution, where low precision suffices.
I find that 20% v/v Tween20 solution does have a better shelf-life than more dilute solutions. One drop of 20% per 5 ml of sensitizer is a dilution of ~100x, giving a final Tween20 concentration of approximately 0.2% – a typical starting point for exploring its effect on sensitizer coating.

Dr. Mike Ware graduated in chemistry at the University of Oxford (1962). He is an Honorary Fellow in Chemistry, University of Manchester, UK, and a recipient of the Hood Medal of the Royal Photographic Society.
Pradip Malde graduated from the Glasgow School of Art (MA, 1980). He is a professor of Art at the University of the South, Sewanee, Tennessee, teaching photography and documentary studies.