In my world vampires own a kingdom with human slaves. They harvest human blood but how can they preserve it with medieval technology?
PS : I would like to preserve the blood in liquid state, but other methods are allowed.
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To keep blood in liquid state, they can use:
All the above methods rely on chemistry. The physical method employed to keep blood liquid to enable further processing when making blood sausage was to frequently stir it, to prevent the formation of the protein network induced by the coagulation. Harvest some snow to keep it cold (Hint: Snow mixed with straw can be stored in underground rooms all summer even in warm climates like the South of Italy.)
Carefully bred leeches -
They have anti coagulants in their saliva which would keep the blood fluid, and to a certain extend, fresh.
They're well known in medival times, and often feature in literature of the era in use in medicine. Something like the common leeches used in medicine could either be processed, or bigger leeches used to draw and possibly even store blood.
There are a few ways depending on the exact specification.
First of all, anti-coagulation (=keeping the blood liquid) can be achieved with some natural substances. They adress different reactions in the coagulation chain (you might want to read something about that for further background).
etc. (Google natural antikoagulants or see for example here).
Those prevent the blood from clotting, which keeps it liquid but they will be present in the blood afterwards so effects might be that the vampires have thin blood and their wounds don't heal / bleed a lot.
Of course, there is actually no need to do that, you could just let the blood clot and eat it like that.
Depending on what you want to achieve / what part of the blood you need filtering it would work too, but I'm not sure filters that good are available in the medieval ages. Centrifuges could be used to separate the bloodcells, they are pretty low tech but not exactly medieval, though with the necessary knowledge about cells they could be build with medieval tech I think. (https://en.wikipedia.org/wiki/Blood_fractionation)
Another way (a little out of the box) would be to breed hemophiliacs. That would allow for some interesting problems with keeping them safe.
(Btw. if you want to store the blood for a longer time you have to keep it clean from bacteria, fungus etc.)
I was thinking that destroying the thrombocytes (blood cells) might work too, but was told it probably wouldn't.
Blood is a pretty agressive liquid and even modern medicine has the problem of coagulation and storing it for longer times (you could look up how blood banks do it, they don't store blood more than 90 (I think) days though, so your medieval tech will probably not achieve that much unless you are okay with the blood going "bad" in the sense tat a human couldn't be infused with it anymore without severe consequences. But again, eating/drinking it allows for a lot more as the acid in the stomach will deal with most problems that would kill you if infused with the blood.
So my final suggestion, if you do not want to deal with that to a bigger extent, let it coagulate and the vampires spread it on bread, eat it as pie and invent many delicious dishes focussing on adding stuff before or after the coagulation.