Measuring a small volume of liquid is hard
Why accuracy gets worse as the volume gets smaller.
A given percentage error is invisible in a poured litre and can be larger than the entire target in a poured microlitre, because the physical sources of that error, a hanging drop, a warmed pipette tip, a trapped speck of air, do not shrink at anything like the rate the target volume does.
I spent my first weeks on a liquid-handling instrument certain that the electronics were at fault, since the machine dispensed a millilitre of water with no complaint and then missed a microlitre target by an amount that looked, on paper, like carelessness. It took a while to accept that nothing was broken, and that the difficulty was built into the physics of small volumes.
A splash of milk and a teaspoon of vanilla
Splashing a spoonful of milk while filling a large mixing bowl for a batch of pancake batter costs nothing worth noticing, since the bowl will hold a couple of litres and a spoonful lost or gained vanishes into that total. Splashing the same spoonful while measuring one teaspoon of vanilla extract is a different event entirely, because the same absolute splash is now as large as the whole quantity being measured. The splash never changed size. The target it was being compared against did, and a liquid-handling instrument dispensing microlitres works permanently at the vanilla end of that comparison, surrounded by drops, films and residues that would be rounding error at any larger scale.
Every volume is measured through something else
A volume is never measured directly. It is inferred from something else: the travel of a plunger, the weight on a scale, the position of a meniscus against a printed line. Each of those proxies carries its own small, mostly fixed error that has nothing to do with how much liquid is being measured. A plunger might repeat its travel to within a few thousandths of a millimetre whether it is dispensing a litre or a microlitre. A drop left clinging to an outlet by surface tension is roughly the same size whatever the target around it. None of these error sources knows what target it is attached to.
Most of them, a hanging drop, a tube's internal wetted film, the space taken by a trapped bubble, scale with surface area or with fixed geometry instead of with the target volume. Surface area falls off more slowly than volume as a droplet or a channel is made smaller. Shrink a droplet to a tenth of its diameter and its surface falls to a hundredth while its volume falls to a thousandth, so every film and residue clinging to that surface grows ten times larger relative to the liquid it belongs to. A tip that reliably leaves behind a droplet of a certain size is leaving a droplet whose share of the total keeps climbing as the total falls, and past a certain point that one retained droplet can exceed the instrument's entire quoted tolerance.
A microlitre weighs a milligram
Proving a small dispense correct is itself a hard problem. A litre jug can be trusted by eye against a printed line because the errors involved are too small to matter. A microlitre of water weighs one milligram, and checking it to within one percent means resolving ten micrograms. Small dispenses are therefore normally checked by weighing the delivered liquid on a balance sensitive enough to resolve a fraction of a milligram, since weight is one of the few proxies precise enough to catch an error no printed scale or human eye could. Switching from reading a volume to weighing one amounts to admitting that at this scale the measurement has become a harder engineering problem than anything the rest of the instrument does.
It follows that an instrument built to move small volumes reliably cannot treat volume as a single number to be hit and forgotten, the way a jug is filled to a line and left. Every stage that could leave behind a film, a drop or a bubble needs its own accuracy budget, because at small enough scale the sum of those leftover fractions makes up much of the measurement. Accounting for every place liquid can be lost or trapped along the way, one mechanism at a time, is what the rest of this set works through, starting with the force that dominates all of them at this scale.
Back to millilitres
Once volumes climb back towards the millilitre range and beyond, a stray drop or a thin wetted film really is the rounding error it looks like, and the old intuition about pouring carefully and reading a line on a jug is good enough again. The difficulty described here belongs to the regime where surface-bound losses and a useful measurement are close enough in size to be mistaken for each other, and outside it the ordinary rules of pouring liquid apply without complication.