What do we call the stream-like leftovers of water sticking to a glass surface?

From a Russian document:

Лабораторная посуда считается чистой, если вода, стекающая по стенкам, не оставляет капель или «ручейков».

Translation:

Laboratory glassware is considered clean when the water running down its walls doesn't leave drops or "rivulets".

But I'm not sure about "rivulets". What is meant in the original text are elongated, thread-like drops that would make the laboratory beaker hard to use, because these drops will make measurements imprecise.

I wonder what the natural-sounding English term would be for these.

From a website dedicated to titrations:

Laboratory glassware have to be perfectly clean before it can be used for any type of analytical work. There are two reasons for that. If the glass is not perfectly clean, water will not wet its surface, and it will be present on the glass surface in the form of droplets. It is impossible to account for volume of these droplets, so you will never know what volume of the reagent was used - and as the precision of the volume measurements is the basis of the precision of the volumetric methods, dirty volumetric glass means huge errors.

I think that rivulets is fine. Look at these examples:

Blue drops of rain trickles in rivulets on a black background. — Dreamstime Stock Video

Sun Tuff roofing with rain drops and rivulets — Alamy Stock Photo

Soap suds and rivulets of water on window glass of a red saloon car being washed in an automated car — Alamy Stock Photo

Alternatively, these can be called trails:

Vertical shot of a window with water trails and a blurred background — Stock Editorial Photography

The word is droplet

There is nothing wrong with using "droplets" as in the website you reference. A rivulet is a thin stream of water that is flowing. A droplet is a small drop that adheres to the surface.

Look at some of these images