Flow-through, description

At very low densities It Is quite easy Co give a theoretical description of thermal transpiration, alnce the classical theory of Knudsen screaming 9] can be extended to account for Che Influence of temperature gradients. For Isothermal flow through a straight capillary of circular cross-section, a well known calculation [9] gives the molar flux per unit cross-sectional area, N, In the form... 

A thorough description of the internal flow stmcture inside a swid atomizer requires information on velocity and pressure distributions. Unfortunately, this information is still not completely available as of this writing (1996). Useful iasights on the boundary layer flow through the swid chamber are available (9—11). Because of the existence of an air core, the flow stmcture iaside a swid atomizer is difficult to analyze because it iavolves the solution of a free-surface problem. If the location and surface pressure of the Hquid boundary are known, however, the equations of motion of the Hquid phase can be appHed to reveal the detailed distributions of the pressure and velocity. 

Existing statistical methods permit prediction of macroscopic results of the processes without complete description of the microscopic phenomena. They are helpful in establishing the hydrodynamic relations of liquid flow through porous bodies, the evaluation of filtration quality with pore clogging, description of particle distributions and in obtaining geometrical parameters of random layers of solid particles. 

Glaser and Litt (G4) have proposed, in an extension of the above study, a model for gas-liquid flow through a b d of porous particles. The bed is assumed to consist of two basic structures which influence the fluid flow patterns (1) Void channels external to the packing, with which are associated dead-ended pockets that can hold stagnant pools of liquid and (2) pore channels and pockets, i.e., continuous and dead-ended pockets in the interior of the particles. On this basis, a theoretical model of liquid-phase dispersion in mixed-phase flow is developed. The model uses three bed parameters for the description of axial dispersion (1) Dispersion due to the mixing of streams from various channels of different residence times (2) dispersion from axial diffusion in the void channels and (3) dispersion from diffusion into the pores. The model is not applicable to turbulent flow nor to such low flow rates that molecular diffusion is comparable to Taylor diffusion. The latter region is unlikely to be of practical interest. The model predicts that the reciprocal Peclet number should be directly proportional to nominal liquid velocity, a prediction that has been confirmed by a few determinations of residence-time distribution for a wax desulfurization pilot reactor of 1-in. diameter packed with 10-14 mesh particles. 

Since the exact profile of the mobile phase flow through a packed bed is unknown, only an approximate description of the ] and broadening process can be attained. For packed column gas chronatography at low mobile phase velocities, equation (1.35) provides a reasonable description of the band broadening process [70,82,83]. 

Eikerling et al. ° used a similar approach except that they focus mainly on convective transport. As mentioned above, they use a pore-size distribution for Nafion and percolation phenomena to describe water flow through two different pore types in the membrane. Their model is also more microscopic and statistically rigorous than that of Weber and Newman. Overall, only through combination models can a physically based description of transport in membranes be accomplished that takes into account all of the experimental findings. 

While the description of viscosity is complex, the relative viscosity is directly related to the flow-through times using the same viscometer as shown in Equation 3.29, where t and are the flow times for the polymer solution and solvent, respectively, and the density of the solution (p) and solvent (p ) are related as in the following equation ... 

One other, very descriptive classification of flow-through sensors is based on the location of the active microzone and its relationship to the detector. Thus, the microzone can be connected (Figs 2.6. A and 2.6.B) or integrated (Fig. 2.6.C) with the measuring instrument. Sensors of the former type use optical or electric connections and are in fact probe sensors incorporated into flow-cells of continuous analytical systems they can be of two types depending on whether the active microzone is located at the probe end (e.g. see [17]) or is built into the flow-cell (e.g. see [18]) — in this latter case. 

The above four requirements vary somehow with the type of flowthrough sensor and detection system used. There are other, specific requisites, discussion of which is beyond the scope of this introductory chapter. A more detailed description of the optimal operational conditions for flow-through sensors is provided in subsequent chapters. 

There are two possible configurations for this type of flow-through sensor integrating gas diffusion, reaction and detection that differ in whether the reagent is dissolved in the acceptor solution or immobilized on a sensing microzone located near the diffusion membrane. The descriptions below are based on such a difference. 

Mass Meters Mass flowmeters measure the rate of mass flow through a conduit. Examples include Coriolis flowmeters and thermal mass flowmeters. Coriolis flowmeters can measure fluid density simultaneously with mass flow rate. This permits calculation of volumetric flow rate as well. Section 8 includes brief descriptions of Coriolis and thermal mass flowmeters. 

Flow through a slit head has been studied also in polymers using the power-function flow principle (Ostwald-de Villes model). Some of the first works in this field were carried out in 1967-1968 by N. V. Tyabin et al.21,22). Tests were arranged with molten polyethylene in an extrusion head having a rotary conic core. The divergence between theory and experiment was comparatively significant which, apparently, is accounted for, primarily, by the basence of a necessary similarity between the conducted experiment and the theoretical description of the flow in a flat slit. 

Figure 4.1 shows the concentration gradients that form on either side of a dialysis membrane. However, dialysis differs from most membrane processes in that the volume flow across the membrane is usually small. In processes such as reverse osmosis, ultrafiltration, and gas separation, the volume flow through the membrane from the feed to the permeate side is significant. As a result the permeate concentration is typically determined by the ratio of the fluxes of the components that permeate the membrane. In these processes concentration polarization gradients form only on the feed side of the membrane, as shown in Figure 4.3. This simplifies the description of the phenomenon. The few membrane processes in which a fluid is used to sweep the permeate side of the membrane,...

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