Constant flux operation

Flux and capacity improvements of up to 3.2-fold (constant TMP operation) and 3.9-fold (constant flux operation) with the helical module over the linear module... 

Membrane systems operate in either constant fltrx (variable feed pressure) or constant pressure (variable water flux) mode. During constant flux operation, trans-membrane pressure (TMP) is increased to maintain the desired or des u flux that otherwise... 

In order to measure the particulate fouling potential of feed water, Schippers and Verdouw [48] proposed a modified fouling index (MFI) by using a microfiltration membrane as a quick test of the feed water quality. They further improved the accuracy of the index and developed a new index of MFI-UF by using ultrafiltration membranes to increase the index sensitivity to the presence of colloidal particles for constant pressure operation [49, 50] and constant flux operation [51]. 

Constant Flux, Constant Pressure Membrane systems operate in one of two possible ways constant transmembrane water flux (flow rate per unit membrane area) with variable pressure or constant transmembrane pressure with variable water flux (Fig. 6.9). An increase in transmembrane pressure is required as the membrane fouls to maintain a particular water flux (constant-flux operation). In constant-pressure systems. 

Figure 6.9 (Leji) Constant-pressure and (right) constant-flux operation.

Figure 10.2 Tiansmembiane pressure (TMP) histories for constant-flux operation, typically applied to submerged membranes (a) cross flow filtration and (b) dead-end filtration.

Microfiltration cross-flow systems are often operated at a constant applied transmembrane pressure in the same way as the reverse osmosis and ultrafiltration systems described in Chapters 5 and 6. However, microfiltration membranes tend to foul and lose flux much more quickly than ultrafiltration and reverse osmosis membranes. The rapid decline in flux makes it difficult to control system operation. For this reason, microfiltration systems are often operated as constant flux systems, and the transmembrane pressure across the membrane is slowly increased to maintain the flow as the membrane fouls. Most commonly the feed pressure is fixed at some high value and the permeate pressure... 

An important recent theoretical development is the direct approaches for calculating rate constants. These approaches express the rate constant in terms of a so-called flux operator and bypass the necessity for calculating the complete state-to-state reaction probabilities or cross-sections prior to the evaluation of the rate constant [1-3]. This is the theme of this chapter. 

After having described the expression for the rate constant within the framework of classical mechanics, we turn now to the quantum mechanical version. We consider first the definition of a flux operator in quantum mechanics.2 To that end, the flux density operator (for a single particle of mass to) is defined by... 

In the following we present the axioms or basic postulates of quantum mechanics and accompany them by their classical counterparts in the Hamiltonian formalism. We begin the presentation with a brief summary of some of the mathematical background essential for the developments in the following. It is by no means a comprehensive presentation, and the reader is supposed to have some basic knowledge about quantum mechanics that may be obtained from any of the many introductory textbooks in quantum mechanics. The focus here is on results of particular relevance to the subjects of this book. We consider, for example, a derivation of a formal expression for the flux density operator in quantum mechanics and its coordinate representation. A systematic way of generating any representation of any combination of operators is set up, and is of immediate usage for the time autocorrelation function of the flux operator used to determine the rate constants of a chemical process. 

In Section 5.2, we have seen how the rate constant for a chemical reaction may be determined as a time integral of the auto-time-correlation function of the flux operator... 

In order to use this formal expression in a calculation of the rate constant we need to choose a representation. In the following we will determine the coordinate representation of the correlation function. We use the coordinate representation of the flux operator as derived above. It is introduced in the expression for the time-correlation function by introducing three unit operators like... 

Laplace transformation to the constant-flux boundary condition (4.50). Laplace transformation on the left-hand side of the boundary condition leads to (dc /dx), and the same operation performed on the right-hand side, to - l/Dp (Appendix 4.2). Thus, from the boundary condition (4.50) one gets... 

All units operated s steady state with constant flux rates. 

Figure 2.16 Xenon poison ratio during reactor operation at constant flux and after shutdown.

Membrane fouling may result in a significant increase in filtration resistance, leading to unstable filtration behavior. The pressure-driven membrane processes can be operated either with constant feed pressure or in constant flux mode. For constant pressure operation where the transmembrane pressure (TMP) is maintained at a constant value during the filtration, the flux will decline with time due to the... 

FIGURE 19.8 Conceptual stages of flux decline in UF at constant-pressure operation stage I, concentration polarization stage II, membrane fouling (usually due to protein deposition) stage III, further particle deposition or consolidation of the fouling layer. (From Marshall, A.D. et al.. Desalination, 91, 65, 1993. With permission.)... 

Cross-flow systems typically operate at constant pressure and not at constant flux. The design and mode of operation of UF and MF systems are defined by the process needs and application. There are three main process configurations (a) single-pass, (b) batch filtration, and (c) feed-and-bleed [34,48]. By contrast, aU RO and NF systems are of single-pass design. Batch and feed-and-bleed designs involve extensive recycling to... 

Feed pumps transfer water through 250 pm strainers to the membrane units at 1550 m /h and 5.5 bar g, as shown in Figure 4.14. The pumps maintain a constant feed water flow rate. The operation is in constant flux mode. The feed water enters the shell side of the hollow fibre and flows through the membrane pores into the fibre bore or lumen as filtrate. The membranes reject particles and colloids larger than the nominal pore size. The filtrate flows to filtered water storage tank. Both feed water and filtered water are monitored for turbidity. 

In the case of constantly fluxed synchronous motors, the stator cmrent will follow the motor torque more closely. After adding excitation losses, the synchronous motor efficiency is still shghtly better than the induction motor. The drive inverter for a synchronous motor supplies the armature or torque producing current, compared to the induction motor apph-cation where the inverter must supply torque producing current and magnetising current In the synchronous motor application, the motor operates at unity power factor, which reduces current demand in the inverter section. As a result, there are fewer losses in the inverter and motor, and to a lesser extent fewer losses in the converter. 

The key component of a membrane cell is the ion-exchange membrane, which determines the performance characteristics of the ceU, reckoned in terms of cell voltage, current efficiency, product purity, and the active life of the cell. The ion-exchange membrane operates best if it maintains its dimensional and structural integrity in the cell during startup, shutdown, and operation. It is essential that the membrane is fully stretched in the cell without any folds or wrinkles and is not subjected to physical wear or fluttering. Furthermore, the entire surface of the membrane should be exposed to a constant flux of sodium ions and water molecules during operation. 

The quantum flux operator F measures the probability current density. The latter satisfies the continuity equation resulting from the invariance of the norm of the wave packet in the coordinate basis. For a stationary wave function, the probability density is independent of time and the flux is constant across any fixed hypersurface. In reaction dynamics the flux operator is most generally defined in terms of a dividing surface 0 which... 

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