Please keep in mind that that mesh size is listed as wires per inch (may be wires per cm in some parts of the world, but I don’t know). The wire takes up part of the spaces so the particles will have at least two dimensions that will fit through a hole that is smaller than the nominal mesh size. Caveat for the purists is that odd shaped particles can twist and turn their way through the not quite square hole.
For example, McMaster-Carr ( Screws | McMaster-Carr) lists several wire diameters for most of their different nominal mesh sizes. For example they list 4 wire sizes for 8x8 galvanized wire mesh with openings from 0.093 inch to 0.102 inch (2.36 to 2.59 mm) - the more expensive and longer lasting screens use heavier wire and have smaller openings. Most of us (including myself) would call this 0.125 (3.18 mm) and be done with it - I call it 3 mm.
As the mesh size (number for inch) increases the the wire size becomes less of a factor.
It would be interesting to know what Ryan feels is the smallest useful particle size in a soil - not in mesh size, but in actual dimensions - inches or mm does not mater since there is an exact conversion.