Filtration

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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.

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

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Invention and early development

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Recent developments

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Applications

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Examples

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