Biliary sludge is not a very good description of the condition. One imagines that sludge is a sediment of granules and thick fluid. In reality biliary is a condition where small stones, usually less than 3 mm, have started to form in clumps. These clumps can vary in size from a few millimetres to a size that is equal to the volume of the gallbladder itself. This means that they can be larger than 'true' Gallstones which usually grow to about 10 mm in diameter. This sludge drastically alters the function of the biliary system and other mixed stones start to form. These are the familiar green pieces seen when you flush.
Here is a picture of biliary sludge
It is possible to expel this sludge through flushing but it is not for the weak hearted. In my experience you need more Epsom Salts and more of the flush potion to succeed.