Liquid transport models

This result has been quoted in the latest paper by Swalin (30) as a support for a cooperative diffusion theory. The physical image is also in agreement with the liquid transport model recently derived by Rahman (27) from computer experiments. 

Weekman and Myers (W3) measured wall-to-bed heat-transfer coefficients for downward cocurrent flow of air and water in the column used in the experiments referred to in Section V,A,4. The transition from homogeneous to pulsing flow corresponds to an increase of several hundred percent of the radial heat-transfer rate. The heat-transfer coefficients are much higher than those observed for single-phase liquid flow. Correlations were developed on the basis of a radial-transport model, and the penetration theory could be applied for the pulsing-flow pattern. 

Alguacil, F. J. Coedo, A. G. Dorado, M. T. Padilla, I. Phosphine oxide mediate transport modelling of mass transfer in supported liquid membrane transport of gold(III) using Cyanex 923. Chem. Eng. Sci. 2001, 56, 3115-3122. 

In general, liquid-phase reactions (Sc > 1) and fast chemistry are beyond the range of DNS. The treatment of inhomogeneous flows (e.g., a chemical reactor) adds further restrictions. Thus, although DNS is a valuable tool for studying fundamentals,4 it is not a useful tool for chemical-reactor modeling. Nonetheless, much can be learned about scalar transport in turbulent flows from DNS. For example, valuable information about the effect of molecular diffusion on the joint scalar PDF can be easily extracted from a DNS simulation and used to validate the micromixing closures needed in other scalar transport models. 

The mass and heat transport model should be able to predict mass and energy fluxes through a gas/vapour-liquid interface in case a chemical reaction occurs in the liquid phase. In this study the film model will be adopted which postulates the existence of a well-mixed bulk and a stagnant transfer zone near the interface (see Fig. 1). The equations describing the mass and heat fluxes play an important role in our model and will be presented subsequently. 

Besides gas and liquid transport in the diffusion media, there is also electronic conduction. Most models neglect this due to the high conductivity of the carbon in the diffusion media, although it can become a limiting factor due to geometry or diffusion-media composition. For those that take it into account. Ohm s law is used... 

Transport Model. A general release equation is developed by considering diffusion in both the liquid and gaseous phases. Figure 1 is a sketch of a vessel containing liquid sodium, blanketed by a flowing inert gas and maintained at constant temperature. The assumed cesium concentration profiles for both phases are shown in the sketch. Fick s law of diffusion may be applied to the liquid phase ... 

Vergnaud J. M., 1991. Liquid Transport Processes in Polymeric Materials. Modeling and industrial applications. Prentice Hall, Englewood Cliffs, New Jersey. 

The current study is modeled after an NRC study that resulted in the 1990 report Fuels to Drive Our Future (NRC, 1990), which analyzed the status of technologies for producing liquid transportation fuels from domestic resources, such as biomass, coal, natural gas, oil shale, and tar sands. That study evaluated the cost of producing various liquid transportation fuels from these resources on a consistent basis, estimated opportunities for reducing costs, and identified R D needs to improve technologies and reduce costs. Fuels to Drive Our Future did not include the production and use of hydrogen, which is the subject of this committee s report. The statement of task for the committee was as follows ... 

When a chemical reaction takes place inside a porous catalyst, all reactants and products must find their way to and from the internal catalytically active surfaces. This transport can strongly influence the apparent reaction rates and selectivity, hence various mass transport models have been developed. Some of the best known and used models and the basic principles behind these models are described in this chapter. Since only little systematic information is available about transport in liquids, the discussion is mainly concerned gaseous mixtures. 

The objectives of this test pattern is to analytically resolve these problems into three manageable segments. The first task will be to define the viscoelastic kinetic properties of a material as a function of various reaction temperatures. These properties (viscosity, viscous modulus, elastic modulus, tan delta) define the rate of change in the polymers overall reaction "character" as it will relate to article flow consolidation, phase separation particle distribution, bond line thickness and gas-liquid transport mechanics. These are the properties primarily responsible for consistent production behavior and structural properties. This test is also utilized as a quality assurance technique for incoming materials. The reaction rates are an excellent screening criteria to ensure the polymer system is "behaviorally" identical to its predecessor. The second objective is to allow modeling for effects of process variables. This will allow the material to undergo environmental... 

Kimura and Sourirajan have offered a theory of preferential adsorption of materials at interfaces to describe liquid phase, selective transport processes in portms membranes. Lonsdale et al. have ofiered a simpler explanation of the transport behavior of asymmetric membranes which lack significant porosity in the dense surface layer. Their solution-diffusion model seems to adequately describe the cases for liquid transport considered to date. Similarly gas transport should be de-scribable in terms of a solution-diffusion model in cases where the thin dense membrane skin acts as the transport moderating element. 

The topic of this article is the study of transport properties of liquid crystal model systems by various molecular dynamics simulations techniques. It will be shown how GK relations and NEMD algorithms for isotropic liquids can be generalised to liquid crystals. It is intended as a complement to the texts on transport theory such as the monograph "Statistical Mechanics of Nonequilibrium liquids [8] by Evans and Morriss and "Recent Developments in Non-Newtonian Molecular Dynamics [9] by Sarman, Evans and Cummings and textbooks on liquid crystals such as "The physics of liquid crystals" [2] by de-Gennes and Frost and "Liquid Crystals" [3] by Chandrasehkar. 

A step-by-step simulation of the system can be carried out by numerical calculations when the initial values of capacitances and the values of parameters (constants) are assigned. The calculations have been performed using the model from Table 13.1 after assuming n = A. This value is sufficient [86] to achieve reliable simulation data of typical liquid transport processes under study. However, it should be noted that the increase in the number of layers, i.e., increasing in n will always result in more precise calculations and predictions comparable to those achieved by analytic calculation methods. The n-value equal to 4 should be treated as the lowest limit required for obtaining quantitative data sufficient for the interpretation of the separation effects. The problem of proper compartmentalization can be especially significant when reactions locally attain quasi-equUibrium conditions. 

Moreover, due to a net water flow toward the cathode and the production of water in it, oxygen diffusivity will be a function of the current density. At larger current densities larger amounts of water will accumulate within the cathode, thereby, hampering gaseous transport. Modeling approaches that incorporate the important issue of liquid water formation and partial saturation in CCLs have been developed only recently. They reveal a key role of the CCL in regulating the fuel cell water fluxes. 

Figure 5 t Schematic transport models of a bulk organic hybrid liquid membrane (BOHLM) system with (A, D) hydrophobic membranes and (B, E) hydrophilic or ion-exchange membranes. From Ref. [2] with permission. 

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