General WHO recommendation says that handwash should last for 20 seconds or more.
Why not 15, why not 30?
What could be the biological relevance of the recommended time period?
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This is something people have been studying since 1847 when Ignaz Semmelweis hypothesized that childbed fever was caused by physicians assisting at deliveries without cleaning their hands (sometimes coming directly from autopsies or cadaver dissections).
Since then there have been thousands of experiments performed to find the best methods of hand sanitizing, including what cleaning chemicals to use, and how long, and how vigorously to wash. You can read a review of some of the relevant research in this publication from the CDC: Guideline for Hand Hygiene in Health-Care Settings.
The destruction of microbes by soap and water is due to chemical reactions. Chemical reactions take time, and of course there are many variables: What kind of microbe? How much soap is suspended int the water? How hot is the water? Are the hands covered in caked dirt or grease?
As with any numerical threshold, there is an element of arbitrariness about it. It's not an absolute guarantee, but people can't realistically respond to vague directives. If you simply tell people to 'wash their hands' some of them will simply stick their hands under a trickle of water for 5 seconds and call it good (I know this from when I was an 11 year old). From the experiments mentioned above we know this will leave lots of active microbes. On the other hand if you tell people to wash their hands for two hours, they won't be able to do it, and it would cause secondary issues like cracking and irritation of the skin.
So you do a bunch of experiments, and you pick an average time that is practicable, and that will prevent, say, 99% of infections from the microbes people are commonly exposed to.