There are many different methods of filtration, but all aim to attain the separation of two or more materials. This is achieved by some form of interaction between the substance or objects to be removed and the filter. In addition the substance that is to pass through the filter must be a fluid, i.e. a liquid or gas.
The simplest method of filtration is to pass a solution of a solid and fluid through a porous interface such that the solid is trapped, and the fluid passes through. This principle relies upon the size difference between the particles making up the fluid, and the particles making up the solid.
By extending this principle, it becomes possible to separate any two things with a significant or reliable size difference. For example an experiment to prove the existence of microscopic organisms involved the comparison of water passed through unglazed porcelain and unfiltered water. When left in sealed containers, the water passed through the porcelain took longer to go foul. In this way we can see that very small items (such as bacteria) can be removed from fluids.
In fact it is possible for other molecules to be removed from fluids using this method of filtration, as long as there is a size difference. However the smaller the channels through which the fluid that is being filtered must pass, the greater the physical interaction between the fluid and the filter. Thus the pressure required to achieve a flow through the filter rises very quickly.
A further disadvantage with the physical barrier method of filtration is that the substance being filtered from the fluid will block up the channels through the filter over time. Thus the filter becomes less and less efficient over time (for example, a vacuum cleaner bag). Thus methods have to be developed to prevent this from happening. Most methods involve replacing the filter. However, if you need the filter for a continuous process, this is highly problematic, so complex scraping and in-situ cleaning mechanisms have to be created.
To avoid all of this complication, other methods may be used:
For separating solids from fluids where there is a large size difference (such as dust from air) a cyclone may be used. Essentially this uses centrifugal force to separate the items. The air is forced around at high velocity in a tighter and tighter circle. The dust particles are forced to the edges by the centrifugal force, and clean air can be drawn off from the middle of the vortex.
For separation where there is a very small size difference, chemical filters may be used. These will use a filter that has properties such that undesirable items are attracted and retained by the filter, and the fluid from which it is to be separated is not. These most often take the form of electrostatic attractions. These form of filters again have the problem of either becoming clogged, or the active sites on the filter all become used by the undesirable. However, most chemical filters are designed so that the filter can be flushed with a chemical that will remove the undesirables and allow the filter to be re-used.