Hydrodynamics pressure drop

Decoupled Driving Force and Depolarization Needs for improved fractionation motivate designers to reduce autofiltration. Using fluid velocity for depolarization means that hydrodynamic pressure drop will be additive to the transmembrane pressure driving force. Schemes to hmit this effeci confront a harsh economic reahty. Two novel schemes decouple the driving from the depolarizing force. 

The main results of our first-order regular perturbation analysis are the expressions for the constant thin film thickness, hQ, and for the total hydrodynamic pressure drop across the entire... 

The other shaping techniques are used when specific requirements (hydrodynamics, pressure drop,. ..) have to be met on the the reactors used or to be constructed (12). Among those described in the literature, the following can be found described rather qualitatively ... 

Kashid and Agar (2007) investigated the effects of various operating conditions on pressure drop in a PTFE microchannel reactor with a Y-junction as mixing zone. They developed a theoretical prediction for pressure drop based on the capillary pressure and the hydrodynamic pressure drop without the presence of a continuous film and for a constant contact angle between the dispersed plug and the channel wall (Fig. 2.11a). 

Hydrodynamics, pressure drop, and mass transfer during liquid-liquid flows were investigated in two different systems, viz. in glass microchannels with circular cross section of 0.2 mm ID (Fig. 3.3a, b) using an ionic liquid and deionised water, and in Teflon channels of different sizes, i.e. 0.2-2 mm ID (Fig. 3.3c) using either different TBP/ionic liquid mixtures (30 %, v/v) (Table 3.2) and aqueous nitric acid solutions, relevant to spent nuclear fuel reprocessing, or ionic Uquid and deionised water. The internal diameter of the microchannels was measured using a microscope (Nikon Eclipse ME 600). 

In the case of withoutfilm, the pressure drop in liquid-liquid slug flow comes from two main contributions the hydrodynamic pressure drop of the individual phases and the pressure drop because of capillary phenomena,/). If we consider the single flow unit shown in Figure 7.16a, the overall pressure drop along its length can be written as ... 

The single-phase hydrodynamic pressure drop can be calculated using the Hagen-Poiseuille equation, while the capillary pressure is obtained from the Young-Laplace equation for a cylindrical tube as given by the following equations ... 

Van Buel, Van der Wielen, and Luyben have proposed a model to explain the considerable pressure drop arising in the column during CPC separation. The overall pressure drop is the sum of the hydrostatic pressure drop term and the hydrodynamic pressure drop terms over the individual parts of the system. The hydrostatic contribution is caused by the difference in density between the liquids in the ducts and in the channels (APstat = nlApu/R, where n is the number of channels, I the height of stationary phase in the channel, Ap the density difference between the phases. 

The area enclosed by the solvent circuit in the T, 5-diagram represents the thermodynamic work needed for the process of recycling the supercritical solvent. The lower the pressure drop needed for separating the dissolved components from the solvent, the lower the necessary work. From this point of view, a mass separating agent is advantageous, since only hydrodynamic pressure drop must be compensated (see chapter 7). 

Pressure drop over slug unit (a pair of tv o liquid slugs) and hydrodynamics pressure drop Total pressure drop, pressure drop due to phase 1, due to phase 2 respectively Frictional pressure gradient, gas and liquid... 

Carbonell and Guirardello (1997) performed simulations to establish the hydrodynamics (pressure drop, radial gas and slurry holdup distribution, effective eddy viscosity, and liquid-phase velocity profile). They also superimposed the thermal cracking reactions by accounting the radial variations in these transport properties so as to predict the heavy oil conversion. They found that the liquid recirculatory patterns (backmixing) strongly affect the product yields. However, the validation of the experimental was not carried out using these models. 

If, however, the reservoir pressure drops below the bubble point, then gas will be liberated in the reservoir. This liberated gas may flow either towards the producing wells under the hydrodynamic force imposed by the lower pressure at the well, or it may migrate... 

For a single fluid flowing through a section of reservoir rock, Darcy showed that the superficial velocity of the fluid (u) is proportional to the pressure drop applied (the hydrodynamic pressure gradient), and inversely proportional to the viscosity of the fluid. The constant of proportionality is called the absolute permeability which is a rock property, and is dependent upon the pore size distribution. The superficial velocity is the average flowrate... 

In Chap. 5 the available data related to flow and heat transfer of a gas-liquid mixture in single and parallel channels of different size and shape are presented. These data concern flow regimes, void fraction, pressure drop and heat transfer. The effects of different parameters on flow patterns and hydrodynamic and thermal characteristics of gas-liquid flow are discussed. 

Landau LD, Lifshitz EM (1959) Fluid mechanics, 2nd edn. Pergamon, London Landerman CS (1994) Micro-channel flow boiling mechanisms leading to Burnout. J Heat Transfer Electron Syst ASME HTD-292 124-136 Levich VG (1962) Physicochemical hydrodynamics. Prentice HaU, London Morijama K, Inoue A (1992) The thermohydraulic characteristics of two-phase flow in extremely narrow channels (the frictional pressure drop and heat transfer of boiling two-phase flow, analytical model). Heat Transfer Jpn Res 21 838-856... 

Equation (8.64) allows the shape of the velocity profile to be calculated (e.g., substitute ytr = constant and see what happens), but the magnitude of the velocity depends on the yet unknown value for dPjdz. As is often the case in hydrodynamic calculations, pressure drops are determined through the use of a continuity equation. Here, the continuity equation takes the form of a constant mass flow rate down the tube ... 

Catalytic reactors can roughly be classified as random and structured reactors. In random reactors, catalyst particles are located in a chaotic way in the reaction zone, no matter how carefully they are packed. It is not surprising that this results in a nonuniform fiow over the cross-section of the reaction zone, leading to a nonuniform access of reactants to the outer catalyst surface and, as a consequence, undesired concentration and temperature profiles. Not surprisingly, this leads, in general, to lower yield and selectivity. In structured reactors, the catalyst is of a well-defined spatial structure, which can be designed in more detail. The hydrodynamics can be simplified to essentially laminar, well-behaved uniform fiow, enabling full access of reactants to the catalytic surface at a low pressure drop. 

Recently, hydrodynamic aspects of multiphase applications have been studied in detail for the cocurrent and countercurrent flow regimes. Useful correlations were determined and it was found that foams combine high rates and low pressure drop, proving their high potential in multiphase applications [9, 107, 108]. 

Before putting a HEX in operation, it is necessary to characterize its properties in terms of heat and mass transfer, pressure drop, and hydrodynamics. A number of experimental methods have been presented and exemplified. These data are important to perform simulations and to define optimal operating conditions. 

The factors to consider in the selection of crossflow filtration include the flow configuration, tangential linear velocity, transmembrane pressure drop (driving force), separation characteristics of the membrane (permeability and pore size), size of particulates relative to the membrane pore dimensions, low protein-binding ability, and hydrodynamic conditions within the flow module. Again, since particle-particle and particle-membrane interactions are key, broth conditioning (ionic strength, pH, etc.) may be necessary to optimize performance. 

Two-phase flows are classified by the void (bubble) distributions. Basic modes of void distribution are bubbles suspended in the liquid stream liquid droplets suspended in the vapor stream and liquid and vapor existing intermittently. The typical combinations of these modes as they develop in flow channels are called flow patterns. The various flow patterns exert different effects on the hydrodynamic conditions near the heated wall thus they produce different frictional pressure drops and different modes of heat transfer and boiling crises. Significant progress has been made in determining flow-pattern transition and modeling. 

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