This Wikipedia page states that sawdust, cellulose etc. can be used to absorb water from azeotropic ethanol to produce anhydrous ethanol. How does this work? Why would the sawdust not simply absorb any liquid, not just water?
This is somewhat conjectural, but I think that sawdust is selective in terms of how polar the liquid is. Water and ethanol are both polar, but water significantly more so (ethanol is significantly less nonpolar at the CH3 end).
To determine if this is indeed the case, I tried pouring some very low-viscosity (so that it tends to ball up less) cooking oil on sawdust, and it rolled right off; high-concentration hydrogen peroxide was absorbed quickly, apparently all of it, so this seems fairly likely.
I cannot find sources confirming this (apart from some google books results, but those were all collections of wikipedia articles). Somewhat related is this source: "Dehydration of Ethanol-Water Mixture Using Activated Carbons from Sawdust and Palm Kernel Shells". The abstract says that the sawdust was chemically activated with ammonium chloride as catalyst, and was able to remove water from an azeotropic solution. Activated carbon is frequently used to filter distilled alcohol, without any effect on the water content, so this activated carbon probably had a very specific pore size.
That specific section of the wikipedia article has been tagged with a "needs additional citations for verification" message, the publication listed as source is not freely available, and there are indications that its contents are not accurately represented/summarized (for example writing about absorption by molecular sieves, instead of adsorption) . It's quite possible that the source mentions sawdust in the context of pressure swing adsorption. A whole range of materials are suitable for PSA dehydration of ethanol (like corn-grits, or see this source for canola meal), and sawdust would be a likely candidate, but pressure swing adsorption is a gas (vapor phase) purification process, not a simple filtering of liquids.
If sawdust would remove water from a liquid azeotropic alcohol-water mixture, I'd expect to find other sources mentioning it. But the "searchability" or "search specificity" of the topic is poor: Sawdust has been, and still is, used as feed source for the production of (bio-) ethanol (and even for distilled spirits: German Holzbranntwein). Water content and removal is a likely topic in those contexts as well, making it hard if not impossible to filter out non-relevant search results without potentially losing relevant ones; and should a page mention both applications (sawdust as feed source and as method to remove water), the short text extract google returns may not tell you so.
Zeolite molecular sieves (size 3A) seem to be the most popular method for "home made" absolute alcohol. A drying agent like CaO is also an option. No mention of sawdust however.