Size of "green water" algae
Green algae commonly implicated as the cause of "green water" are
Chlamydomonas, Carteria, Chlorogonium and Volvox. All are flagellated
green algae, and all are unicelluar except for Volvox, which is
actually a multi-celled spherical colony.
These unicelluar green algae are 5-10 microns in diameter, not
including the flagella (add an extra 10-30 microns for the flagella).
Volvox can get huge--up to 500 microns (half a millimeter--visible to
the naked eye).
A diatom filter claims to be able to filter out particles as small as
one micron, which explains why a diatom filter can clear up green
water in just a few hours.
I have no idea what particle size a conventional filter can handle,
but I can tell you my Hagen Aquaclear foam inserts were useless
against green water.