Liquid filtration permeation flux

Cross-flow filtration systems utilize high liquid axial velocities to generate shear at the liquid-membrane interface. Shear is necessary to maintain acceptable permeate fluxes, especially with concentrated catalyst slurries. The degree of catalyst deposition on the filter membrane or membrane fouling is a function of the shear stress at the surface and particle convection with the permeate flow.16 Membrane surface fouling also depends on many application-specific variables, such as particle size in the retentate, viscosity of the permeate, axial velocity, and the transmembrane pressure. All of these variables can influence the degree of deposition of particles within the filter membrane, and thus decrease the effective pore size of the membrane. 

Microfiltration and ultrafiltration are the two main filtration techniques for which ceramic membranes have been widely used to date. As described in Section 6.2.1.2, MF and UF ceramic membranes exhibit macro- and mesoporous structure, respectively, which result from packing and sintering of ceramic particles. Liquid flow in such porous media is convective in nature and the simplest description of permeation flux, J, is given by the Darcy s equation [20] ... 

Al-akoum et al. experimentally and theoretically reported the flux enhancement in three particular systems shear-enhanced filtration with a vibrating membrane module, gas/liquid two-phase flows, and Dean vortices for yeast suspension system. They reported that the permeate flux was found to obey the empirical law J -- Twm (where Twm is the mean wall shear stress. Pa) with 0.43 < n < S7 and K depending on the membrane type and the yeast concentration for a particular system. 

Screening Equipment Filtration Cake Filters Centrifugal Filters Principles of Cake Filtration Clarifying Filters Liquid Clarification Gas Cleaning Principles of Clarification Crossflow Filtration Types of Membranes Permeate Flux for Ultrafiltration Concentration Polarization Partial Rejection of Solutes Microfiltration... 

In a general way, most of ceramic membrane modules operate in a cross-flow filtration mode [37] as shown in Figure 9.18. However, as discussed hereafter, a dead-end filtration mode may be used in some specific applications. Membrane modules constitute basic units from which all sorts of filtration plants can be designed not only for current liquid applications but also for gas and vapor separation, membrane reactors, and contactors, which represent the future applications of ceramic membranes. In liquid filtration, hydrodynamics in each module can be described as one incoming flow on the feed side Qp which results in two outgoing flows related to retentate Q, and permeate gp sides, respectively. The permeation flux J per membrane surface unit is directly calculated from Q. Two important parameters account for hydrodynamic working conditions of a module, one is the flow velocity, v, in the module calculated as the ratio of the incoming flow <2/ (mVs) by the hydraulic section of the module Q (m ), the other is the transmembrane pressure, P. ... 

The high diflhisivity of colloidal particles has further implications for the processing of suspensions. That concerns, e.g., the purification of liquids by depth filtration or cross flow filtration—in particular for particles below 100 nm Diffusion enhances the efficiency of depth filters (Hinds 1999, pp. 196-200) and counteracts particle deposition on the membrane in cross flow filtration, it thus warrants stable permeate flux (Ripperger and Altmann 2002). In general, the diffusive mass transport of colloidal particles (e.g. to walls) cannot be ignored. 

In comparison to the above hydrodynamic factors, the micro-organisms also affect membrane filtration performance. The separation of liquid and solids using microflltration (MF) or ultrafiltration (UF) membranes is driven by trans-membrane pressure (TMP).The permeate flux, that is, the quantity of water passing through a unit area of membrane per unit time, is related to TMP by Darcy s equation ... 

Aimar et al. [19] noted that in the UF of complex liquids, such as cheese whey, which contains proteins, salts and casein fragments, concentration polarization, and adsorption and cake formation play a role in flux behavior during crossflow filtration. They may induce osmotic pressure in the retentate side since the chemical potential of the solute-rich polarized layer is lower than that of the permeate, and therefore at equilibrium, a positive osmotic pressure develops in the retentate to equal that of the permeate. The smaller the solute, the greater is its contribution to the osmotic pressure of the liquid, so that in milk, lactose and the minerals have the biggest contribution to osmotic pressure. In skim milk or whey, the osmotic pressure is around 7 bar (700 kPa) and this must be exceeded in RO to commence permeation in UF, only the proteins contribute to the osmotic pressure, which increases exponentially with protein concentration [56]. In any case, a TMP greater than the osmotic pressure is required for solvent to flow from the retentate side to the permeate side. This leads to the reduction in the effectiveness of applied TMP as driving force to permeation. 

Fortunately another transport resistance, which is extremely important in the filtration processes and in reverse osmosis, namely fouling, is of no concern in pervaporation or vapor permeation with polymeric membranes. In these membranes no pores exist that can be blocked by any precipitation out of the liquid or vapor phase. Even if precipitation, e.g. of salts in dehydration processes, does occur the growth of the salts crystals may attack and eventually destroy the separating layer of the membrane, but will usually not influence the flux of water to the membrane. 

Membrane filtration has many similarities to conventional filtration, and the mathematical description of the process uses many ccmcepts already introduced in Chapter 2. However, there are rignificant differences in the terminology enqiloyed the filtrate is referred to as the permeate , the residual slurry or suspension from the filtration is called the retentate and the permeate filtration rate is the flux rate , which in microfiltration is conventionally reported in the emits of litres per square metre of membrane area per hour (1 m h ). This rate is equivalent to the superficial liquid velocity through the menibrane. In nearly aU the instances of constant-pressure... 

Consider a membrane where the pores of uniform diameter 2r occupy a fraction of the membrane area. Let the membrane thickness be Sm and the pore tortuosity T . If a pressure AP is imposed across the membrane from the feed to the permeate (or the filtrate) side, the volume flux Vz through the pores (in units of cm /s-cm of pore area) of a liquid of viscosity p, and therefore the volume flux EmVz through the membrane (in units of cm /s-cm of membrane area), is given by the Poiseuille law ... 

Let us focus first on cake filtration and microfiltration for the case where the fluid is a liquid. In the configuration of Figure 6.3.21, the techrtique is called deadend filtration. The same configuration is routinely employed in lahoratories with a filter paper on, say, a Buchner funnel and a partial vacuum on the side of the permeate/filtrate a precipitate/ deposit builds up quickly on the filter paper as the slurry is filtered. As time passes, a particle based deposit continues to build up on the filter paper it is called a cake. This cake provides an additional resistance to the flow of the filtrate through the membrane/filter/cloth in deadend filtration. As time passes, deposition of the particles onto/in the cake continues. Therefore the resistance to the flow of the filtrate increases with time. If one wants to maintain a constant eflae of the filtrate flux, the applied pressure difference AP has to increase with time. Alternatively, for a constant applied pressure difference, the flux of the filtrate will decrease with time (Figure 6.3.22). 

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