A rilem tube is a method used across the industry to test the absorptivity of a wall surface. They are plastic or glass tubes that are lined up vertically to the dry masonry surface, the other end of the tube is attached to the masonry surface using a putty. Once attached, water is poured into the open end of the tube, and using the measurements on the side of the tube and a timer, you can measure how quickly a masonry surface can absorb water. Rilem tubes have been proven time and time again to be one of, if not the most reliable test for testing how much water is absorbed by a wall, and is used throughout the industry.
Using rilem tube tests, you can test the absorptivity of a particular wall to determine if certain products can be used on it, or see if there is a water drainage issue in the wall system if the water is drained exceptionally fast.
Rilem tubes were created as an absorptive test by Reunion Internationale des Laboratoires d’Essals et de Recherches sur les Materiaux et des Constructions (RILEM), a French standards organization similar to ASTM before ASTM Standards became international. While some sources say rilem tubes can be used on a variety of absorptive wall surfaces like concrete, they are intended for use only on masonry and mortar. Organizations and authorities on concrete say that rilem tubes are ineffective on their surfaces, so it's best to stick to only masonry, as far as rilem tubes are concerned. Other kinds of walls and materials have their own testing methods for absorptivity, we recommend using the accompanying standard for different kinds of materials.
We found a very good article by The Construction Specifier about testing rilem tubes effectiveness, and though it is a bit outdated as it was written in 2013, before the ASTM Standard for water absorptiveness was written, it's still loaded with great information, research and testing on the consistency of rilem tube results.