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 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 an extended period of time. Several methods and devices have been devised that allow for this filter cleaning while operating, as well as mechanisms permitting easy removal of filtered solids from the filtering machinery.

In mathematical modeling, filter cakes are often treated as non-compressible. Unfortunately, that is not the case. Several factors, including the pressure gradient of the driving force, if applicable, may cause the filter cake to partially collapse. This can make determining the height and resistance of the cake difficult, which in turn renders other variables such as flux and processing time indeterminate.

Design and Operation

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. Types of filtration may also be classified by mechanism (sorted by whether solids are stopped at the surface of a cake or trapped within pores of a medium), by objective (sorted by whether a dry solid, clarified liquid, or both are sought), by operating cycle (sorted by whether filtration is continuous or intermittent), or by nature of the solids. For simplification, only classification by driving force, with specific reference to exemplary machinery will be discussed here.

Gravity filtration

The simplest form of filtration uses only the force of gravity to drive a fluid through a porous medium. Because this driving force is relatively weak, the filtrate must be of low viscosity and generally dilute. The medium is placed orthogonal to the force of gravity and parallel to the ground. An excellent example of such filtration may be found in the common place household drip coffee filter, in which a layer of coffee grounds acts as a pre-established filter cake and the thin paper of the coffee filter is the the filter septum. Liquid coffee streams through the septum into a collecting pot below; coffee grounds remain trapped on the upper side of the septum. Such gravity filters my also be used in industry on a larger scale, for example, the sand gravity filter, however, with only gravity as the driving force, these filters tend to be too slow to meet the demands of industry.

Vacuum filtration

An example of a rotating drum vacuum filter from US Pat. 2,379,754

A vacuum filter operates by creating a lower pressure on the distal side of the medium with respect to the incoming feed. A vacuum may provide a substantial pressure difference sufficient to filter a filtrate too viscus for a gravity filter to handle. It can also produce a fairly dry solid and provide a means for washing the precipitate. Examples of vacuum filters include the leaf filter, the Buchner funnel, and rotating drum vacuum filters. Leaf filters are a staple of this design. Essentially, the leaf with a low internal pressure due to vacuum is immersed in the filtrate mixture until a think layer of cake has built up on the surface of the leaf. The leaf is then transferred to a washing tank, where wash is draw through the leaf until a slight internal pressure is applied to the leaf, removing the cake. In another example, drums with filter media on the outer face, and an internal vacuum, are partially immersed in and rotated through the filtrate mixture, picking up a layer of precipitate. As the drum rotates out of the mixture, the precipitate is washed off the surface and collected. Most vacuum filters operate continuously.

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:

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

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.

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.