The crumpling effect you refer to is known in the paper industry as "moisture welts" or "weather wrinkling". Paper is made of plant fibers, which are long and narrow, like straws. Because of the way commercial paper is made, the fibers tend to orient themselves so that the paper has a grain. The grain is the direction the majority of the fibers are aligned with, and it is the reason that paper tends to tear straight in one direction and not in the other. When paper gets wet, the fibers absorb water and they get bigger around. This causes the paper to expand in the cross-grain direction more than in the grain direction, which creates the wrinkles.
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