Filtration

Filtration is commonly the mechanical or physical operation which is used for the separation of solids from fluids (liquids or gases) by interposing a medium through which only the fluid can pass. The fluid that passes through is called the filtrate. Oversize solids in the fluid are retained, but the separation is not complete; solids will be contaminated with some fluid and filtrate will contain fine particles (depending on the pore size and filter thickness). Filtration is also used to describe some biological processes, especially in water treatment and sewage treatment in which undesirable constituents are removed by absorption into a biological film grown on or in the filter medium as in slow sand filtration.

Applications

Clarification and stabilization of wine

In winemaking, clarification and stabilization are the processes by which insoluble matter suspended in the wine is removed before bottling. This matter may include dead yeast cells (lees), bacteria, tartrates, proteins, pectins, various tannins and other phenolic compounds, as well as pieces of grape skin, pulp, stems and gums. Clarification and stabilization may involve fining, filtration, centrifugation, flotation, refrigeration, pasteurization, and/or barrel maturation and racking.

Clarifying wine

In wine tasting, a wine is considered "clear" when there are no visible particles suspended in the liquid and, especially in the case of white wines, when there is some degree of transparency. A wine with too much suspended matter will appear cloudy and dull, even if its aroma and flavor are unaffected; wines therefore generally undergo some kind of clarification.

Before fermentation, pectin-splitting enzymes and, for white wine, fining agents such as bentonite may be added to the must in order to promote the agglomeration and settling of colloids later. Pectins are structural molecules in the cell walls of fruits which have the important function of 'gumming' plant cells together. The pectin content of grapes increases steadily throughout ripening, reaching levels of about 1 g/l, although it varies by varietal and pre-fermentation handling processes. Large pectin molecules can affect the amount of juice yielded at pressing, ease of filtration and clarification, and extraction of tannins. Grapes contain natural pectolytic enzymes responsible for softening the grape berries during ripening, but these are not active under wine-making conditions (due to pH level, SO₂, and alcohol.) Therefore, fungal pectolytic enzymes are often added to white must to break up pectins, decrease the viscosity of the juice, and speed up settling. In red musts, this increases color and tannin extraction.

Filtration (mathematics)

In mathematics, a filtration is an indexed set S_i of subobjects of a given algebraic structure S, with the index i running over some index set I that is a totally ordered set, subject to the condition that

If the index i is the time parameter of some stochastic process, then the filtration can be interpreted as representing all historical but not future information available about the stochastic process, with the algebraic object S_i gaining in complexity with time. Hence, a process that is adapted to a filtration , is also called non-anticipating, i.e. one that cannot see into the future.

Sometimes, as in a filtered algebra, there is instead the requirement that the be subalgebras with respect to some operations (say, vector addition), but not with respect to other operations (say, multiplication), that satisfy , where the index set is the natural numbers; this is by analogy with a graded algebra.

Sometimes, filtrations are supposed to satisfy the additional requirement that the union of the be the whole , or (in more general cases, when the notion of union does not make sense) that the canonical homomorphism from the direct limit of the to is an isomorphism. Whether this requirement is assumed or not usually depends on the author of the text and is often explicitly stated. We are not going to impose this requirement in this article.