Do I say "quenched my thirst" or "stilled my thirst" when I speak of something that I desire and not actual thirst? E.g. a thirst for a new car or something.
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Thirsts are always quenched or slaked, never stilled or silenced, even if they are metaphorical.
In contrast, desires, like beating hearts, are never quenched or slaked, but may be killed or calmed or assuaged. And they may, perhaps, be stilled or quelled.
You are perhaps more apt to appease desires than thirsts.