OK, let's be clear: I'm a software engineer (retired), not a physicist, hydrologist, or hydraulics person, so please be gentle.
In the process of developing an open source system for monitoring water column height in our well and of house / irrigation water usage (we're in N. CA), I discovered we had a substantial problem with sand and silt in our well water. We hadn't noticed it before because other components of the system (e.g. our 3,000 gal holding tank, ozone system, and calcite filter) were removing most of it before it came out of the kitchen tap. But that's not what they were meant to do. (Well, the ozone is sort of meant to help with clumping, but not the other 2.)
After going through several variations on filters -- paper, steel mesh, etc. -- it became clear that they all clogged up, requiring frequent flushing / cleaning.
After reading a lot of stuff which is waay outside my area of expertise, it is clear what we need is a hydrocyclonic filter. User rul30 mentioned Solid-Liquid Seperation by Ladislav Svarovsky. Chapter 6, Hydrocyclones appears to be exactly what I need. Except I don't know how to go from the formulas and academic description to a specific set of dimensions I could use with a 3D printer or other fabrication method.
I have a well pump that is throttled to 3GPM to minimize silt migration into the well. This flow level is substantially below what all commercial hydrocyclonic filters require (mostly 10GPM and higher). We have a mix of heavy sand (which is easy to get rid of with even a half-assed cyclonic filter), and a fair volume of material that is as small as 50 µm. I have plenty of pressure available, so we can create significant velocity, but the specific dimensions of the upper cylinder, the lower cone shape, and the depth of the vortex finder are based on equations that are beyond me.