How does the wall of the collecting duct located in the renal papilla achieve impermeability to water given the fact that lipid bilayers are permeable?

The relative permeability of the papillary collecting ducts to water is dependent on the circulating levels of Antidiuretic Hormone (ADH). ADH is produced in the brain's hypothalamus and released from axons in the neurohypophysis (posterior part of the pituitary gland). In the kidney, this hormone acts to open water channels in the cells lining the papillary collecting ducts. The higher the circulating levels of ADH, the more permeable to water the papillary collecting ducts become.

The lipid bilayer is by its nature, only poorly permeable to ionic molecules like water. Water has difficulty passing through the hydrophobic (literally "water hating") region of the membrane and generally requires ionic channels to cross this barrier. ADH controls the valves on the main water channels in the cells lining the papillary
ducts. Because there is generally always some ADH in the circulation, these collecting ducts never really achieve complete impermeability to water. In the complete absence of ADH, all of the ADH-controlled channels would be closed and permeability to water would be severely restricted. However, even in such an unlikely case, some water would still be able to pass through other ion channels in the membranes.

The high solute concentration between the tubules in the papillary region of the kidney, draws water from the duct lumen, through the channels opened by ADH, and into the tissue between the tubules (the interstitium). This occurs by simple passive diffusion of the water down its concentration gradient into the water-poor interstitium when the channels are open. In this way, ADH promotes the retention of water in the body by reducing the amount released in the urine. By retaining
water in the body, ADH serves to increase blood volume, which, in turn, increases blood pressure as well. Blood pressure sensors in the carotid artery among others help provide signals to the hypothalamus to slow down ADH production when blood pressure is at proper levels.