Filtration

This article is about Conventional Filtration, for crossflow filtration see Crossflow membrane 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 in which flow is parallel) the incoming fluid, or feed, flows in a direction that is perpendicular to the porous medium. A layer of solids builds up over time on 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. Bioprocessing filtration may be employed, for example, to retrieve a target product that is in solution from an undesired solid mass of freshly ruptured cells. Filtration is particularly valuable in early processing because it allows for an efficient means of volume reduction. Filtration, dating back in its simplest form to water treatment around 2000 B.C.E., is well established in the fields of science and engineering. While very few changes were seen in filtration mathematical theory during the past century, improvements in materials and manufacturing processes have allowed steady incremental advances in the quality and efficiency of equipment associated with filtration.

A large Buchner funnel and small Buchner funnel situated in an air-tight flask attached to a pressure pump.

The Processes

Diagram of Conventional filtration (Left) showing feed entering a filter, depositing filter cake on a septum, and leaving the filter as permeate. (Right) Graph of conventional filtration showing building of cake and flux with respect to time.

Filtration deals with the separation of solids in suspension from the liquid of the suspension. A barrier, called the filter medium or septum, catches solid particles that are too large to pass through this medium on an upstream side, while liquids and very fine solid particles pass through the medium to a downstream side. On the medium's upstream surface the larger solids, caught by the filter medium, form a continuously thickening layer known as a filter cake. As this cake increases in thickness, the flux of material, or flow of filtrate through the filter medium, decreases, approaching a horizontal asymptote of 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 developed that allow for filter cleaning during operation, 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 in practice. Several factors, including the pressure gradient of the filtered fluid's driving force, if applicable, may cause the filter cake to partially deform. 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

The household coffee maker is a commonplace gravity filtration device.

There are four primary categories of filtration which are classified according to the driving force of the filtrate: 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 according to solids being stopped at the surface of a cake or trapped within pores of a medium), by objective (sorted by a dry solid, a clarified liquid, or both being sought), by operating cycle (sorted according to continuous or intermittent filtration), or by characteristics 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. Since this driving force is relatively weak, the filtrate must be of low viscosity and the slurry sufficiently 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 commonplace household drip coffee maker, in which a layer of coffee grounds acts as a pre-established filter cake and the thin paper of the coffee filter is 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. Gravity filters may also be used in industry on a larger scale, for example, the sand gravity filter used in drinking water treatment; however, with only gravity as the driving force, these filters tend to be too slow to meet the demands of most industries.

Vacuum filtration

An example of a rotating drum vacuum filter from US Pat. 2,379,754, issued July 3, 1945.

A vacuum filter operates by creating a lower pressure on the opposite side of the porous medium with respect to the incoming feed. A vacuum may provide a substantial pressure difference sufficient to filter a filtrate too viscous for a gravity filter to handle. A vacuum filter 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 vacuum filter design. Essentially, the leaf filter, with a low internal pressure (due to a vacuum), is immersed in a filtrate mixture until a thick layer of cake has built up on the surface of the leaf. The leaf is then transferred to a washing tank, where wash water is drawn through the leaf until an 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 solids. As the drum rotates out of the mixture, the precipitate is washed off the surface and collected. Most vacuum filters operate continuously.^[3]

Pressure filtration

Several plates and filters from an example of a filter press from US Pat. 2,390,628, issued December 11, 1945.

If a higher pressure is required than can be achieved via vacuum filtration, such as when an especially viscous liquid is being filtered or when filter aid (see below) cannot be used to ease the filtration, a pressure filter may be employed. In pressure filtration, the filtrate is driven through the filter by positive pressure on the feed side of the filter. While there are several forms of pressure filters, the filter press largely dominates the field. Often taking the form of the plate-and-frame filter or the similar plate filter, the filter press is comprised of a series of plates and frames between which the filtering medium is arranged such that the plates tightly stack one against the next, forming small chambers in between. Channels for filtrate and clarified fluid (or wash and soiled wash) run along the top and bottom of the plate stack. Near the top and bottom of each plate are holes which may alternately be shut to force filtrate or wash entering one hole to flow through the medium and exit an alternate hole on the side of the filter distal to the side from which the filtrate entered. After filtrate has run through the filter press for a time, cake builds up on one side of the filter medium. The holes may alternately be plugged and wash forced through the device so as to clean the cake from the filter press device. Pressure filtration has high energy demands and the device cleaning and cake removal process is often sloppy and messy, however, this form of filtration is capable of separating solid-liquid suspensions that other forms of filtration simply cannot handle.^[3]

Centrifugal force filtration

Traditional centrifuge devices, such as the basket centrifuge, may be adapted to act as a filter by placing a filter medium orthogonal to the centripetal force. Solids are caught by the medium and may generally be removed by the same arrangement used to remove solids from the traditional centrifuge, such as by stopping the centrifuge or by continuous removal from a rotating element.^[3]

Materials

The materials used in a given filtration process have a strong influence on the success of the process and affect several measurements thereof, including, but not limited to: efficiency of operation, quality of product, and economic requirements (e.g. cost).

Filter media

The filter medium, or membrane, or septum, is a porous barrier through which large particles suspended in the filtrate cannot pass, and are therefore trapped within the medium or on the surface of the medium forming a filter cake, while a clarified liquid passes through to the far side of the medium. It is necessary to replace and/or wash the filter medium regularly as media becomes damaged with extended use and unusable if coated with excessive filter cake.

Loose or Granular Medium

In one form, filters may comprise a vessel with a false or perforated bottom filled with granular matter of a size sufficiently small to catch particles in suspension. For example, crushed charcoal is used for drinking water purification. The absorptive qualities of charcoal also make it ideal for filtering heavy tar from pyroligneous acid (a product of destructive distillation of wood) and for removing impurities from raw sugar syrup. Coarse gravel, fine pebbles, and fine quartz sand, sometimes sitting atop canvas or cloth protected by metal grating, are examples of granular matter commonly used. Crushed marble or pure limestone may be used when filtering alkaline materials thereby stopping the alkaline materials through the utilization of both small channels and their tendency to adhere to the filter media. Cleaning may be achieved by passing water, as well as air, backward through the filter. Mechanical stirring may also be employed to produce additional agitation for cleaning.

Felted or Woven Medium

A felted or woven fabric of fibers is more practical when a large amount of solid particulate matter is present in the feed and/or it is desirable to recover this solid matter. Fabrics may be made from a variety or fibers, including vegetable (e.g. cotton, hemp, and jute for weak alkalis), animal (e.g. wool or horsehair for weak acids), and mineral, or from other materials altogether, such as metal wire when working with very caustic filtrates or requiring very high pressures. Metal wire fabrics, or screens, may be made from nickel, copper, brass, aluminium, steel, stainless steel, Monle, and other alloys, all of which are highly resistant to leaching and corrosion. Typically, the example devices discussed above under the vacuum and pressure filtration section, namely leaf filters, rotating drum vacuum filters, and filter presses, employ such felted or woven media.^[1],[4]

Rigid Porous Medium

Rigid porous structures having a large number of very small channels can be produced from materials such as sintered stainless steel, porcelain, plastic, and silica. These structures are easy to shape into any form desired and may be employed as filtering media. They are fairly strong, and can withstand vacuum driven filtrations. Furthermore, given the very small holes found in this media, it is useful for removing exceedingly small particles and is sometimes found in domestic water purification. Silica also has the further advantage of being capable of being cut into blocks for further versatility.^[1],[4]

Semi-permeable Medium

Dialysis, a technique in which a membrane allows some particles dissolved in solution to pass though but not others, may be employed in some separations. A stream of liquor and a stream of water are introduced to two chambers separated by a semi-permeable medium, through which the desired particle can pass to the water side but undesired impurities cannot. Both liquids are continuously drawn out of their chambers through separate exits.^[4]

Sterile Air Filtration

High Efficiency Particulate Air (HEPA) filters and vent filters are used for the sterile filtration of air. HEPA filters comprise compacted beds of pads of fibrous material such as glass wool. While HEPA filters are high throughput ventilation filters that collect microbes and other harmful particles in a room at a high flow rate, vent filters are used on equipment that needs to be filled or drained (e.g. product tanks). Vent filters are hydrophobic, asymmetric (pores are larger on one side than the other) membrane filters.^[1]

Filter aid

Two jars of diatomite filter aid with dishes of the filter aid powder in the foreground.

Filtration can be improved by adding filter aid, a kind of highly permeable powdered solid, to the feed side of the filter medium. When choosing a filter aid for a process, factors such as surface properties, chemical resistance, and compatibility with the product to be separated should be considered.

The filter aid may be mixed directly with the filtrate or a layer of filter aid may be applied directly to the medium. The objective of the former approach is to keep the pores in the filter cake open, to prevent compression of the filter cake, and to hasten the speed of filtration. In some instances of the latter approach, such as in rotary vacuum filters, the filter is operated with a layer of filter aid "precoat." When operating with a precoat, the filter medium is coated with a thick layer of filter aid and the solids being filtered penetrate into this layer of precoat by a small distance. An adjustable knife is used to cut away the layer of precoat containing the filtered solids, exposing a fresh layer of precoat. When the layer of precoat on the medium becomes very thin, a new, thick layer of precoat is reapplied in the manner described above and the process repeats.

Diatomite (kieselguhr or deatomaceous earth) and perlite are two of the prevalent filter aids in current use. Diatomite is made from the skeletal remains of diatoms, a kind of algae whose structure provides for high intrinsic permeability and whose chemical makeup of mostly silica allows for insolubility in both strong acids and alkalies. Perlite is a glassy volcanic material, having a high aluminium silicate content, whose high porosity comes from its ability to expand upon being heated during processing. Perlite is popular for rough filtrations where filtrate clarity is of low priority but high flow rates are preferred.^[1]

Principles and theory

In most cases of conventional filtration, a solid suspension fluid, or filtrate, flows against a porous medium by application of a pressure gradient across the medium, where 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, or 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:

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

where A (m²) is the cross-sectional area of the medium through which the fluid flows, V (m³) is the volume of filtrate, t (sec) is the time, Δp (Pa) is the change in pressures across the medium and cake, μ_o (kg/m*s) is the is the viscosity of the filtrate, and R (m^-1) 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 (m/kg),in the following form:

$R_{C}=\alpha \rho _{c}\left({\frac {V}{A}}\right)$

where ρ_c (kg/m³) 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:

${\frac {1}{A}}{\frac {dV}{dt}}={\frac {\Delta p}{\mu _{o}\left(\alpha \rho _{c}\left({\frac {V}{A}}\right)+R_{M}\right)}}$

For constant pressure operation, this equation may be integrated with an initial condition of zero filtrate at time zero to yield:

${\frac {t}{\frac {V}{A}}}={\frac {\mu _{o}\alpha \rho _{c}}{2\Delta p}}\left({\frac {V}{A}}\right)+{\frac {\mu _{o}R_{M}}{\Delta p}}$

© Image: Jean Hunter
Method for finding K and C for a filtration by graphing.

which may also be rewritten in term of the filtrate density ρ (kg/m³), the ratio of the mass of dry cake solids to the mass of feed c (kg/kg), and the ratio of the mass of wet cake to the mass of dry cake w (kg/kg):

${\frac {t}{\frac {V}{A}}}={\frac {\mu _{o}\alpha \rho c}{2\Delta p\left(1-wc\right)}}\left({\frac {V}{A}}\right)+{\frac {\mu _{o}R_{M}}{\Delta p}}$

A method of graphing may be used, as seen on the right, to find $K={\frac {\mu _{o}\alpha \rho c}{2\Delta p\left(1-wc\right)}}$ and $C={\frac {\mu _{o}R_{M}}{\Delta p}}$. The integrated Darcy's Law equation above is graphed to find the slope equaling K and the y-intercept which is C.^[1]

History

Filtration is a well known technology that is utilized in science and engineering. Simple methods of filtration were used by ancient civilizations, and are recorded in both Sanskrit writings and Egyptian inscriptions. As early as 2000 B.C.E. filtration through sand, coarse gravel, and charcoal were known methods of treating drinking water. In Greece, Hippocrates (460–354 B.C.E.) advised straining rain water after boiling through a cloth bag, called a “Hippocrates’ sleeve,” to prevent the water from smelling foul and causing hoarseness. During ancient times, wine-makers also used cloth-covered screens to removed unwanted impurities from wine.

The first modern description of sand filtration was in a 17^th century text by Italian physician Lucas Antonius Portius in which he described three pairs of sand filters, each having a downward-flow and an upward flow filter through which water was fed. In approximately 1703, La Hire, a Parisian scientist, brought a plan before the French Academy of Sciences in which he proposed the widespread use of rainwater cisterns and sand filters in every household to promote the use and availability of clean water. It would take another century until the technology he envisioned was utilized on a large scale.^[5]

In 1804, the town of Paisley in Scotland saw the first municipal water treatment plant consisting of a sand and gravel filter whose water was distributed by horse and cart. Shortly thereafter, Glasgow, Scotland began distributing water to its residents using a system of pipes. Robert Thom designed a slow sand filter, cleaned using backwash, which was put into use in Greenock, Scotland by 1827. James Simpson designed a similar filter, cleaned by scraping, which was used in London by 1829 and became the standard throughout the English commonwealth. Slow sand filters were the chosen method for cleaning municipal water supplies in the 19^th century, however, these filters were problematically large in size, with sand beds 2 to 3 feet (~ 0.5 to 1 meter) deep, areas covering several acres, and cleaning methods requiring scrapping with a shovel by brute effort. Given the rate at which cities were expanding and their increasing need for land, the slow sand filter could not produce a sufficient volume of water to justify its enormous size. In the 1880s, rapid sand filtration was developed in the United States of America by improving upon Thom's methods. The false bottom and reverse-flow wash of the slow sand filter was kept, but the rapid sand filter also used water jets or backwash to clean the filter medium and a mechanical agitator to loosen debris. Pretreatments (e.g. coagulation and settling) also became increasingly popular as a means to decrease the amount of actual sediment the filter would need to process and thereby effectively decrease the size requirements of the sand filters. Eventually, filtration through charcoal was used to improve the taste and odor of water, although this method was initially thought to be unfeasible for large municipal water supplies.^[5]

The theory behind filtration has been well established for over a century, and through mankind's trials with water purification via filtration, the use of filtration for separating other liquids and solids has been readily extrapolated. In the past century there really have not been any major changes in mathematical filtration theory, as such is already well understood. In addition to gravity, as primarily discussed above, pressure and centripetal force were also employed to drive filtrate through filter media as the technology and materials to harness these forces were developed. Incremental advances and innovations have been made in filtration equipment and materials in the past century so as to increase the efficiency and quality of filtration. However, the basic principles remain unchanged. A comparison of chemical engineering texts from 1937, 1952, 1997, and 2003, all reveal the same understanding of theory and point to very similar devices to illustrate example filters.