Filtration

This article is about Conventional Filtration, for crossflow filtration see Crossflow filtration.

Filtration is a process by which most or all solid particles in a liquid-solid suspension fluid are separated from the fluid by passing the fluid through a porous medium barrier. In conventional filtration (as opposed to crossflow filtration) the incoming fluid, or feed, flows perpendicular to the porous medium. A layer of solids continues to build with time over the surface of the medium, while the flux of the feed through the medium approaches a zero asymptote. In bioprocessing, filtration is an early processing step during the recovery phase. It may be employed, for example, to retrieve a target product in solution from an undesired solid mass of freshly ruptured cells. Filtration is of particular value because it allows for an effect means of volume reduction, a crucial tool in early processing.

The Processes
Filtration, as discussed above, deals with the separation of solids in suspension from liquids. A barrier, called the filter medium or septum, catches solid particles too large to pass through this medium on a first side as liquids and fine, very small solid particles pass to a second side side. On the first side, the solids form a continuously thickening layer known as a filter cake. As this cake increases in thickness, the flux of material, or filtrate, through the filter medium, decreases, approaching a horizontal asymptote at zero. It is therefore necessary to occasionally stop filtration and remove the cake, or systematically clean the filter during filtration, in order to continue a process of filtration for en extended period of time.

Design and Operation
Use lots of subsections here as you describe various aspects of the process.

There are four categories of filtration as divided by driving force: gravity, vacuum, pressure and centrifugal force. The last may also be considered a form of centrifugation, and will not be discussed in great detail here.

Principles and theory
In most cases of conventional filtration, a solid suspension fluid, or filtrate, is flowed against a porous medium by application of a pressure gradient across the medium, wherein the solids in the suspension too large to pass through the medium become trapped on one side of the medium, building up in a layer called a cake, of sometimes more specifically filter cake. The flow of the liquid filtrate through the porous medium, which is a bed of solids, may be described by Darcy's Law written in the form:


 * $$\frac{1}{A}\frac{dV}{dt} = \frac{\Delta p}{\mu_oR}$$

wherein A is the cross-sectional area of the medium through which the fluid flows, V is the volume of filtrate, t is the time, Δp is the change in pressures across the medium and cake, μo is the is the viscosity of the filtrate, and R is the combined (in series) resistance of the filter medium ("RM") and filter cake ("RC"), which is:


 * $$R = R_M + R_C$$.

The cake resistance may further be described in terms of the specific cake resistance α the the following form:


 * $$R_C = \alpha\rho_c\left ( \frac{V}{A} \right )$$

wherein ρc is the mass of dry cake solids per unit volume of filtrate.

Darcy's Law for the flow of the liquid filtrate through the bed of solids porous filter medium and cake may therefore be rewritten as:


 * $$\frac{1}{A}\frac{dV}{dt} =\frac{\Delta p}{\mu_o\left ( \alpha\rho_c\left ( \frac{V}{A} \right ) + R_M \right )}$$

This equation may be integrated with an initial condition of zero filtrate at time zero to yield:


 * $$\frac{t}{\frac{V}{A}} = \frac{\mu_o\alpha\rho_c}{2\Delta p}\left ( \frac{V}{A} \right ) + \frac{\mu_o R_M}{\Delta p}$$

which may also be rewritten in term of the filtrate density ρ, the ratio of the mass of dry cake solids to the mass of feed c, and the ratio of the mass of wet cake to the mass of dry cake w:


 * $$\frac{t}{\frac{V}{A}} = \frac{\mu_o\alpha\rho c}{2\Delta p\left ( 1-wc \right )}\left ( \frac{V}{A} \right ) + \frac{\mu_o R_M}{\Delta p}$$

History
This section should describe the invention and development of the process. If the section runs long, divide it into chronological subsections, for example:

Invention and early development
This subsection should provide some historical context for the development of your process, describe its invention, and name some early developers and/or applications.

Recent developments
This section should discuss new developments in the field. Don't hesitate to drop in brief mentions of processes or features you don't intend to discuss in depth. By so doing you are planting seeds of articles which will eventually be developed by others.

Applications
This section should discuss how the process is used in practice.

Examples
If you have used a lot of equations in your article, this may be a good place to show an example of how they are used. See the article on the Antoine Equation for an example.