Theory of Filtration, Crop Process Engineering | Crop Process Engineering Notes - Agricultural Engg - Agricultural Engineering PDF Download

25.1 Filtration

 Depending on dispersing medium filtration is divided in two parts:

a) Gas filtration and b) Liquid filtration.

 25.1.1 Gas filtration

 It mainly includes filtration of aerosols and lyosols. Membrane filters and nucleopore filters are based on these below mechanisms.

 Mechanism of gas filtration

Diffusion deposition: The trajectories of individual small particles do not coincide with the streamlines of the fluid because of Brownian motion. With decreasing particle size the intensity of Brownian motion increases and, as a consequence, so does the intensity of diffusion deposition.

Direct interception: This mechanism involves the finite size of particles. A particle is intercepted as it approaches the collecting surface to a distance equal to its radius. A special case of this mechanism is the so-called sieve effect, or sieve mechanism.

Inertial deposition: The presence of a body in the flowing fluid results in a curvature of the streamlines in the neighbourhood of the body. Because of their inertia, the individual particles do not follow the curved streamlines but are projected against the body and may deposit there. It is obvious that the intensity of this mechanism increases with increasing particle size and velocity of flow.

Gravitational deposition: Individual particles have a certain sedimentation velocity due to gravity. As a consequence, the particles deviate from the streamlines of the fluid and, owing to this deviation; the particles may touch a fibre.

Electrostatic deposition: Both the particles and the fibres in the filter may carry electric charges. Deposition of particles on the fibres may take place because of the forces acting between charges or induced forces.

 25.1.2 Liquid filtration

 The term solid-liquid filtration covers all processes in which a liquid containing suspended solid is freed of some or the entire solid when the suspension is drawn through a porous medium.

Kozeny-Carman equation

 \[{{1.dv} \over {A.dt}} = {{\Delta P} \over {r\mu (l + L)}}\].....................................................................................(7.1)
where,

A = filter area

 v = total volume of filtrate delivered

t = filtration time

ΔP = pressure drop across cake and medium

r = specific cake resistance

μ = filtrate viscosity

l = cake thickness

L = thickness of cake equivalent to medium resistance

 Limitations of Kozeny-Carman equation: This equation does not take into account of the fact that depth of the granular bed is lesser than the actual path traversed by the fluid. The actual path is not straight throughout the bed, but it is sinuous or tortuous.

Poiseulle’s law: This Law considered that filtration is similar to the streamline flow of a liquid under pressure through capillaries.

\[{{1.A}\over{dv.dt}} ={{\Delta P}\over{\mu (R_M+R_C )}}\]................................................................................ (7.2)
Cake resistance

\[RM={{\alpha W}\over A}\]........................................................................................................................... (7.3)
Specific cake resistance

\[alpha=\alpha'\Delta P^S\].................................................................................................................................(7.4)
The filter resistance is much less than the cake resistance i.e. Rc < Rm

\[{{1.A}\over {dv.dt}}={{\Delta P}\over{\mu (\alpha'\Delta P^S WA)}}\]...................................................................(7.5)
where,

v = Filtrate volume

A = Filter area

t = Time

ΔP = Pressure driving force

μ = Broth viscosity

W = Mass of filter cake

R = Resistance

α = Specific cake resistance

s= Compressibility factor

Filter media: The filter medium acts as a mechanical support for the filter cake and it is responsible for the collection of solids. Minimum cake thickness of discharge for different types of filter is presented in Table 7.1.Table 7.1 Minimum cake thickness for discharge

Materials used as filter media: Different types of materials used as filter media are presented in Table 7. 2.

Woven materials such as felts or cloths: woven material is made of wool, cotton, silk & synthetic fibres etc. are used. Synthetic fibres have greater chemical resistance than wool or cotton. The choice of fibre also depends on the physical state & chemical constitution of the slurry. It includes mainly of two types.

Monofilament woven cloth (Fig.7.1): The yarns of a monofilament fabric are not only impermeable but also fairly smooth and cylindrical. Orifice analogy and drag theory approaches have been the most successful in predicting the resistance of these materials to fluid flow.

Multifilament woven cloth: The chief difficulty encountered when dealing with multifilament media is the highly complex geometry of the fibres and yarns that make up the cloth. Even in a fabric of apparently simple weave and construction, such as a plain-weave, continuous filament cloth, some of the flow takes place in the highly tortuous channels present in the yarns.

Perforated sheet metal: stainless steel plates have pores which act as channels as in case of Meta filter.

Bed of granular solid built up on a supporting medium: examples of granular solids are gravel, sand, asbestos, paper, pulp & kieselguhr.

Prefabricated porous solid unit: sintered glass, sintered metal, earthenware and porous plastics are material used for fabrication.

Membrane filter media: it includes surface & depth type of cartridges.

Criteria for choice of filter medium: There are three criteria for choice of filter medium.

1. Size of particle retained by the medium.

2. The permeability of the clean medium.

3. The solid holding capacity of the medium and the resistance to fluid flow of the used medium.

Measurement of pore size & particle retention: In some cases, the desirable component in the slurry is the liquid, which may be required in clarified form e.g., beverage filtration; here the choice of deep-bed elements of pre-coated candles of large solids-holding capacity may be indicated. While, where the solids are valuable, a sieve like mechanism is favoured, so that information about the pore size of the medium may be of more direct use in media selection. The pore structure of the medium will determine the feasibility of a separation.

 Fig. 7.1 Plain and Twill weave monofilament.

The pore size of a medium particularly for filters of the edge, simple wire or monofilament type is of use in deciding the upper limit of aperture size required by a particular process. In filters composed of random fibres, sintered or porous elements, staple or natural fibre cloths, the mean pore size will have less significance and use in predicting media behaviour. In certain cases, the geometry of septum allows direct measurement of aperture or pore size. In random situation, where complex weave pattern produce a distribution of pore sizes, such as a bubble point test or a permeability test are used.

 Table 7.2 Type of filter media, characteristics and their application