When I make horchata or aqua frescas, I often have a large volume (quarts) of liquid that could benefit from straining.  Usually only the small fine mesh strainer can get out the fine particles that remain after running the juices through the blender.    I haven't really seen very fine mesh strainers that are bigger than a couple inches across; I'd like to be able to strain a large volume at once.  Are there any tricks of the trade? 
Frequently health food stores and asian markets will have "milk bags" that are used for straining soy milk and nut milks. They usually look either like a pillowcase with a drawstring at the open end, or occasionally a long cloth tube with a wire handle. Either way, you pour the liquid in and the fine mesh of the cloth holds the particles back, but the large surface area allows the liquid to drain quickly. You then rinse the cloth inside out and wash it before reusing. I've used them to make both nut milks and cold brewed coffee and they work a lot faster than a strainer of equivalent mesh size. Another advantage is that the cloth allows you to squeeze the liquid out of the pulp for maximum yield.  