Hospitals provide paper diapers while the infant is a patient. Babies going through withdrawal tend to very quickly develop diaper rash due to frequent stooling, and for some reason the stool is more tough on their skin. They also over-eat compared to non withdrawing babies. So, unless you have a ton of cloth handy, you might prefer to just go with the paper ones. I would invest in a gentle baby soap and your favorite diaper cream that is nice and pasty, maybe a zinc oxide one. Frequent soap and water bathing of the skin helps keep the breakdown from acidic stool at bay. Sometimes the nursing staff will think that water only wipes are better, but they don't remove all the acid from the skin that lets it get raw. I always push for minimum twice a day rinse with soap/water, from a peri bottle is easy in nicu, instead of holding baby over sink. But once the baby is stable and in the treatment of withdrawal only, it doesn't really matter what kind of diaper since mostly they are only counting pees and poops per day, not a strict intake measurement.
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