Filtration

All unapproved Citizendium articles may contain errors of fact, bias, grammar etc. A version of an article is unapproved unless it is marked as citable with a dedicated green template at the top of the page, as in this version of the 'Biology' article. Citable articles are intended to be of reasonably high quality. The participants in the Citizendium project make no representations about the reliability of Citizendium articles or, generally, their suitability for any purpose. This article is currently being developed as part of an Eduzendium student project in the framework of a course entitled BEE 4640 Bioseparation Processes at Cornell University. The course homepage can be found at CZ:Cornell_University_2010_BEE_4640_Bioseparation_Processes. For the course duration, the article is closed to outside editing. Of course you can always leave comments on the discussion page. The anticipated date of course completion is 21 December 2010. One month after that date at the latest, this notice shall be removed. Besides, many other Citizendium articles welcome your collaboration! Note to course participants: Looking forward to some insightful and useful articles from your collaborations.

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 Process

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:

${\frac {1}{A}}{\frac {dV}{dt}}={\frac {\Delta p}{\mu _{o}R}}$

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, μ_o is the is the viscosity of the filtrate, and R is the combined (in series) resistance of the filter medium ("R_M") and filter cake ("R_C"), 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 ρ_c 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.

Design and Operation

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

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.