Rate of filtration

Eor vacuum filters, both the rate of filtration and the dryness of the cake may be important. The filter cake can be modeled as a porous soHd, and the best flocculants are the ones that can keep the pores open. The large, low density floes produced by high molecular weight polymers often coUapse and cause blinding of the filter. Low molecular weight synthetic polymers and natural products that give small but rigid floes are often found to be the best. 

Rotary-Siphon Peeler Centrifuges In this type of centrifuge, a partial vacuum is drawn on the outer diameter or tne filter such that the filtrate flows through the cake under both centrifugal force as well as a positive pressure difference of about I atm or less. Thus, a higher rate of filtration takes place due to the increased driving force. 

Filtration Rate When the centrifuge cake is submerged in a pool of liquid (Fig. 18-139Z ), as in the case of a fast-sedimenting, sohds-forming cake almost instantly, and the rate of filtration becomes limiting, the bulk filtration rate Q for a basket with axial length b is ... 

Because pore sizes in the cake and fiiter piate are smaii and the iiquid veiocity through the pores is iow, the flow of fiitrate may be considered iaminar and Poiseuilie s iaw is appiicabie. Fiitration rate is directiy proportional to the difference in pressure and inverseiy proportionai to the fluid viscosity, as weii as to the hydrauiic resistance of the cake and fiiter piate. Because the pressure and hydrauiic resistances of the cake and fiiter piate change with time, the variabie rate of filtration may be expressed as ... 

The following example helps to illustrate the use of the equations presented up to this point. An aqueous slurry was filtered in a small laboratory filter press with a pressure drop of 0.5 atm and at a temperature of 20 C. After 10 minutes, 4.7 liters of filtrate were obtained after 20 minutes, 7.0 liters were collected. From experiments at other pressures, it was determined that the cake compression coefficient was s = 0.4. We wish to determine the volume of filtrate expected after 30 minutes from a filter press having a filtering area 10 times greater than the laboratory press if the filtration is to be performed at 1.5 atm pressure. The liquid temperature will be 55 °C. We also wish to determine the rate of filtration at the end of the process. 

We now turn attention towards the ease of eonstant-rate filtration. When sludge is fed to a filter by means of a positive displaeement pump, the rate of filtration is nearly constant, i.e., dV/dx = constant. During constant-rate filtration, pressure increases with cake thickness. As sueh, the principal filtration variables are pressure ind filtrate volume, or pressure and filtration time. Integrating the filtration equation for a constant-rate process, we find that the derivative dV/dx ean simply be replaeed by V/x, and we obtain ... 

To apply these equations, let s consider the following example. Determine a constant rate of filtration and the time of operation corresponding to the maximum capacity of a batch filter having the following conditions maximum permissible pressure difference AP = 9x10 N/m sludge viscosity /r = 10 N-s/m filter plate resistance Rf = 56x 10 ° m specific cake resistance r = 3 X 10 m ° x = 0.333 auxiliary time = 600 s maximum permissible cake thickness h = 0.025 m. The solution is as follows ... 

Consider 1 m of very dilute suspension containing n number of suspended particles. Develop an expression describing the rate of filtration through the pores, taking into consideration the number of blocked pores. 

Filter aids are evaluated in terms of the rate of filtration and clarity of filtrate. Finely dispersed filter aids are capable of producing clear filtrate however, they contribute significantly to the specific resistance of the medium. As such, applications must be made in small doses. Filter aids comprised of coarse particles contribute considerably less specific resistance consequently, a high filtration rate can be achieved with their use. Their disadvantage is that a muddy filtrate is produced. 

When the space above the suspension is subjected to compressed gas or the space under the filter plate is under a vacuum, filtration proceeds under a constant pressure differential (the pressure in the receivers is constant). The rate of filtration decreases due to an increase in the cake thickness and, consequently, flow resistance. A similar filtration process results from a pressure difference due to the hydrostatic pressure of a suspension layer of constant thickness located over the filter medium. 

Consider 1 m of suspension eontaining n number of suspended partieles. If the suspension eoneentration is low, we may assume the volume of suspension and filtrate to be the same. Henee, after recovering a volume q of filtrate, the number of bloeked pores will be nq, and the number unbloeked will be (Np - nq). Then the rate of filtration is ... 

In the case of multiparticle blockage, as the suspension flows through the medium, the capillary walls of the pores are gradually covered by a uniform layer of particles. This particle layer continues to build up due to mechanical impaction, particle interception and physical adsorption of particles. As the process continues, the available flow area of the pores decreases. Denoting as the ratio of accumulated cake on the inside pore walls to the volume of filtrate recovered, and applying the Hagen-Poiseuille equation, the rate of filtration (per unit area of filter medium) at the start of the process is ... 

When the average pore radius decreases to r, the rate of filtration becomes ... 

Both particle size and the liquid viscosity affect the rate of particle settling. The rate of settling due to gravitational force decreases with decreasing particle size and increasing viscosity. The process mechanisms are sensitive to the relative rates of filtration and gravity sedimentation. 

For filter design and performance prediction it is necessary to predict the rate of filtration (velocity or volumetric flowrate) as a function of pressure drop, and the properties of the fluid and particulate bed. This can be achieved using the modified Darcy equation developed in Chapter 3. 

As a batch filtration proceeds, so the rate of filtrate collection decreases due to the increased cake thickness. While operation with thin filter cake results in a higher instantaneous filtration rate, however, it also requires more frequent dismantling of the filter and discharge of the filter cake. There is thus an optimum balance between filtration time and down time. 

The solubility of the precipitates encountered in quantitative analysis increases with rise of temperature. With some substances the influence of temperature is small, but with others it is quite appreciable. Thus the solubility of silver chloride at 10 and 100 °C is 1.72 and 21.1mgL 1 respectively, whilst that of barium sulphate at these two temperatures is 2.2 and 3.9 mg L 1 respectively. In many instances, the common ion effect reduces the solubility to so.small a value that the temperature effect, which is otherwise appreciable, becomes very small. Wherever possible it is advantageous to filter while the solution is hot the rate of filtration is increased, as is also the solubility of foreign substances, thus rendering their removal from the precipitate more complete. The double phosphates of ammonium with magnesium, manganese or zinc, as well as lead sulphate and silver chloride, are usually filtered at the laboratory temperature to avoid solubility losses. 

Assume laminar flow of filtrate of liquid through the filter cake. Rate of filtration is usually measured as the rate at which liquid filtrate is collected. The filtration rate depends on the area of the filter cloth, the viscosity of the liquid, the pressure drop across the filter and filter cake resistance. At any instant during filtration, the rate of filtration is given by the equation ... 

In several cases, a steady rate of filtration in never achieved. In such cases it is possible to describe the time dependence of filtration by introducing an efficiency factor fi representing the fraction of filtered particles remaining in the filter cake rather than being swept along by the bulk flow. Equation 16.7.4 then becomes... 

Upon what variables would you expect the rate of filtration of a suspension of fine solid particles to depend Consider the flow through unit area of filter medium and express the variables in the form of dimensionless groups. 

The most commonly used filter medium is woven cloth, but a great variety of other media is also used. The main types are listed in Table 10.2. A comprehensive discussion of the factors to be considered when selecting filter media is given by Purchas (1971) and Mais (1971) see also Purchas and Sutherland (2001). Filter aids are often used to increase the rate of filtration of difficult slurries. They are either applied as a precoat... 

Another method, which is even more successful in preventing binding of the septum, is the use of a precoat.53 Before filtration is begun a coating of 2-6 in (5-15 cm) of diatomaceous earth or perlite filter aid is deposited on the surface of the septum. During filtration operations the scraper is set so that it slowly removes the precoat and, of course, with it the materials that would have plugged the filter. Since the precoat causes a considerable pressure drop, the rate of filtration is slowed down. Flow rates may vary from 2 to 50 gal/hr/ft2 (0.025-0.60 m/hr). The precoat material costs around 3 or 40/lb and is used at the rate of 10- 15 lb/1,000 gal of feed (1,200 to 1,800 kg/m3). 

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