Permeation flux defining

External fouling is caused by the formation of a cake layer of cells or other materials on the membrane surface, leading to a reduction in permeate flux (defined as the volume of permeate produced per time and membrane area). Internal fouling is caused mainly by proteins and particles smaller than membrane pores. Proteins and protein aggregates can adsorb or deposit at the pore entrance or inside the pores and cause pore blockage or narrowing, leading to increased hydraulic resistance (2). 

Using this simplified model, CP simulations can be performed easily as a function of solution and such operating variables as pressure, temperature, and flow rate, usiag software packages such as Mathcad. Solution of the CP equation (eq. 8) along with the solution—diffusion transport equations (eqs. 5 and 6) allow the prediction of CP, rejection, and permeate flux as a function of the Reynolds number, Ke. To faciUtate these calculations, the foUowiag data and correlations can be used (/) for mass-transfer correlation, the Sherwood number, Sb, is defined as Sh = 0.04 S c , where Sc is the Schmidt... 

The membrane resistance for CF-EF can be defined by specifying two permeate fluxes as... 

Results of such single-molecule permeation experiments, using the MV +/ Ru(bpy)3 pair (Fig. 16), and membranes with four different nanotubule i.d.s, are shown in Fig. 17. The slopes of these permeation curves define the fluxes of and Ru(bpy)3 across the membrane. A permeation selectivity coefficient (ai)t can be obtained by dividing the flux by the Ru(bpy)3 flux. 

A commercially available cellulose acetate film which we would now describe as homogeneous or isotropic, gave the results shown in Row 2 of Table I. The volumetric permeation rate of water per unit membrane area, called the water permeation flux Jl mVm day, and the water permeation constant. A, m m day atm were both very low, but a salt rejection of 94 percent was obtained. We define ... 

Besides some measures of separation efficiency such as the separation factor and extent of separation defined above, some quantity indicative of the throughput rate of a membrane system is needed to compliment the permselectivity of the membrane. It is quite common and practical in the membrane technology to use a phenomenological expression to relate the permeate flux (Ja in the unit of cm (STP)/s-cm7) of a given gas (A) through the membrane to the driving force, the transmembrane pressure difference (Ap) as follows ... 

In 1879, von Wroblewski showed that the solution of gases in rubber followed Henry s law, Eq. (1), and he defined an absorption coefficient as the lumber of cubic centimeten of gas measured at STP which dissdved in 1 cubic centimeter of rubber at one atmosphere pressure. Combining this with Pick s law, Eq. (2) he showed that the steady state permeation flux throu a membrane of thickness is given by Eq. (3) ... 

Permeate flux is defined as the permeation rate per unit of membrane area. Thus, maximizing the flux will reduce system size and cost. Permeate flux can be calculated as follows (15) ... 

A relative permeation flux cp or (p, y may be defined for the permeate phase as... 

Pulsate flows were applied to mineral microfiltrations membranes during apple juice filtration [36] illustrating the advantage of this method to enhance permeability compared to steady flow regime. With carefully chosen pulsations permeate flux increased up to 45% at 1 Hz pulsation frequency. Moreover well defined pulsations decreased the hydraulic power dissipated in the retentate per unit volume by up to 30%. In an other work on cross-flow filtration of plasma from blood [37] permeate flux increase was also observed when pressure and flow pulsations at 1 Hz are superimposed on the retentate. 

The electric field intensification in the surfactant-mediated separation processes is shown in Table In the feed, surfactant and metal ion concentrations are denoted by Csf and Cmf. respectively, while the corresponding concentrations in the permeate under steady-state conditions are denoted by C p and Cmp. Surfactant and metal ion rejections at a steady state are defined as Rs = (1-Csp/Csf) and Rm = (1-Cmp/Cmf)- The molar ratio of metal ion to surfactant is denoted by Fms- The separation of the electrodes is 3 mm. In Table 2, the initial current, pH, and solution conductivity are also given. It shows that both metal and surfactant are separated effectively under an electric field in which the permeate flux, surfactant, and metal ion rejections are enhanced. Economic analysis of the process indicates that some 20- to 50-fold efficiency increase is achieved compared with the no electric field case. For the process to be economical, low-solubility surfactants that can form multilamellar droplets should be used as carriers. 

In order to suppress fouling, a new concept called the critical flux concept was introduced by Howell and co-workers in the mid-1990s [24,25] and has been subject to a recently published review [26]. This concept describes a permeate flux below which no deposition of colloids and therefore no irreversible fouling occurs. In an early paper. Field et al. defined two types of critical flux the strong form, where the transmembrane pressure (TMP) deviates from a certain point on from the (linear) pure water line and the weak form, where already at the starting point fouling occurs and the TMP-flux relationship is stiU linear but below the pure water line (Fig. 5) [25]. At the critical flux /crit. the TMP-flux relationship becomes nonlinear. 

The instantaneous yield, r is defined as the proportion between the substrate flux and the permeate flux (protein basis). From the protein mass balance (33), r is immediately obtained ... 

Equations (7) to (13) constitute a system of 7 nonlinear algebraic equations, which allow the prediction of permeate flux and solute rejection, when the membrane permeability for a given component and the mass transfer characteristics of the equipment are known. Equations (7) and (8) describe the diffusion in the liquid film adjacent to the membrane, while Eqs. (9) to (12) describe membrane transport and Eq. (13) defines the rejection. 

Membrane performance is a trade-offbetween membrane selectivity and membrane productivity. Membrane selectivity, a (=A/B), is defined by the ratio of permeability of components through the membrane where A is the water permeability coefficient and B is the solute permeability coefficient. In the case of RO and NF membranes, water/NaCl selectivity for seawater RO membranes is about 10,000. The higher the selectivity, the lower the permeate flux or productivity. This relationship for various RO membranes used with dilute NaCl solution is shown in Figure 1.6. The shaded regions refer to different feed concentrations and to different types of membranes. The data is fairly independent of the feed concentration but is a function of the physical and chemical properties of the membrane. 

Flux J is defined as the volumetric flow rate of a permeating solvent or solute through a unit area of a membrane. The general form of solvent permeating flux, for forward osmosis, pressure-retarded osmosis, and reverse osmosis is given as... 

Fouling cannot be easily assessed by only interpreting the permeate flux data. Irreversible fouling is normally used as an indicator to estimate the membrane fouling index, named hereafter, irreversible fouling factor (FR, ). This is defined as the ratio of the water permeate flux difference measured before and after NF of a HA solution to the water permeate flux measured before NF of a HA solution. 

The permeate flux, when using an NaCl aqueous solution as the feed, was 25%-30% lower than the obtained permeate flux when distilled water was used as the feed, reflecting the lower vapor pressure of the salt solution. Another reason for the decrease in the DCMD flux is the concentration polarization due to the presence of the NaCl solute in the feed membrane side (Carman 1956 Khayet et al. 2005b Qtaishat et al. 2009a,b). Referring to the experiments with a salt solution, the solute separation factor (Equation 6.3) is defined as... 

Practically, membranes should have a high permeate flux, high contanunant rejection, great durability, good chemical resistance and low cost (Zhou Smith, 2002). The other property that is also important in the selection and/or classification of a membrane process is pore size or molecular weight cutoff (MWCO) (Zhou Smith, 2002). The MWCO expresses the retention characteristics of the membrane in terms of molecules of known sizes (Brock, 1983) and defines the maximum molecular weight of a solute to be rejected (Zhou Smith, 2002). 

The PV separation index (PSI) was also introduced to evaluate the overall performance of a membrane and is defined as the product of total permeation flux and selectivity ... 

The pol)mer concentration at which the permeate flux is zero, defined as gel point concentration, was found to be 655-665 mM (approximately 5.98-6.07 wt%). These values allow high water recoveries (higher than 99%) to be obtained. An advantage of the PEUF system in the... 

The permeation flux is defined as the rate of mass transport of a solute through the membrane. It is the parameter frequently used to evaluate SLM performance (Singh eta/., 2010). Calculation of fluxes can be done by using the following equation ... 

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