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See, take a piece of cloth and let some water spill over it. You see, it's not going to get darker immediately but slowly and gradually it does (as more and more water gets absorbed maybe!) Why? I mean why not immediately?

I have read answers on the internet which say that the liquid layer formed at the surface actually reflects back (only a small part gets out of the liquid surface via refraction at each step) the light which is reflected off the fabric surface back to the fabric. This goes on continuously and at each step a bit of the light gets absorbed making the fabric darker. That's a nice explanation. But it doesn't explain my question. The liquid layer is formed as soon as we spill the water. But still it only slowly gets darker not immediately.

user266637
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Other places have tackled the question of why pale things are pale and why wet things are dark. To answer the specific question of timing, consider that the darkening effect of moisture is more pronounced on materials who get their initial paleness from their porosity/fine surface-structure. The more porous a surface is, and the finer the pores are, the more time it will take water to penetrate/saturate the pores.

I expect that this accounts for the whole delay. It takes time for moisture to wick into a porous surface.