A general idea, when a stream is divided more and more finely but you don't want to drop more pressure, is to make the paths shorter and put more in parallel.
Maybe it doesn't adapt to chromatography - but maybe it does; this depends on how you wish to clean the column. For oil drying, it looks better. And it's perfect in a heat exchanger (if the fluids contain no particles) or to distribute oxygen and glucose to cells.
The perfect combination is to distribute the fluid through arteries, subdivided in arterioles and so on, down to many very short capillaries, then collect the fluid into veinules and so on, that end in a vein. With the proper tree you get as much fluid in capillaries as thin as desired, with a pressure drop as small as wished. Particle size if any, and manufacturing capability, are the only limits.
But then the engineer may have some sense of not being the original inventor.
As an alternative to the many disks rotating slowly, one can use fewer disks (one?) that spins quickly so that the oil film is really thin, like 5µm, so it dries quickly. Like a spinning disk reactor, but used with vacuum or a dry gas instead of a reactant.