Model interconnected tubes

Primary outputs are produced essentially by sedimentation and (to a much lower extent) by emissions in the atmosphere. The steady state models proposed for seawater are essentially of two types box models and tube models. In box models, oceans are visualized as neighboring interconnected boxes. Mass transfer between these boxes depends on the mean residence time in each box. The difference between mean residence times in two neighboring boxes determines the rate of flux of matter from one to the other. The box model is particularly efficient when the time of residence is derived through the chronological properties of first-order decay reactions in radiogenic isotopes. For instance, figure 8.39 shows the box model of Broecker et al. (1961), based on The ratio, normal-... 

However, these two models assume either perfect mixing conditions (well-stirred model) or no mixing at all (parallel tube model) and cannot explain several experimental observations. Therefore, other approaches such as the distributed model [268], the dispersion model [269], and the interconnected tubes model [270,271] attempt to capture the heterogeneities in flow and an intermediate level of mixing or dispersion. Despite numerous comparisons [264,265,272-... 

Anissimov, Y., Bracken, A., and Roberts, M., Interconnected-tubes model of hepatic elimination Steady-state considerations, Journal of Theoretical Biology, Vol. 199, No. 4, 1999, pp. 435-447. 

Three-periodic hyperbolic surfaces of infinite genus carve space into two intertwined sub-volumes, both resembling three-dimensional arrays of interconnected tubes. They are simple candidates for the interfaces in bicontinuous structures, consisting of two continuous subvolumes [4, 5]. As such they have attracted great interest as models for microstructured complex fluid interfaces, biological membranes, and structures of condensed atomic and molecular systems, to be explored in subsequent Chapters. 

Bear (1969, 1972) developed a dispersive flow model based upon the idea of building a continuum at the mesoscopic scale by statistically averaging microscopic quantities over a representative elementary volume, defined with respect to porosity. Phis geometric model is an assemblage of randomly interconnected tubes... 

In a later article [59] the importance of hydrodynamic interactions in the formation of certain microphases was demonstrated by close comparison of simulations using DPD and Brownian dynamics (BD). Whilst both simulation methods describe the same conservative force field, and hence should return the same equilibrium structure, they differ in the evolution algorithms. As mentioned above, DPD correctly models hydrodynamic interactions, whereas these are effectively screened in BD. Distinctly different equilibrium structures were obtained using the two techniques in long simulations of a quenched 2400 A3B7 polymer system, as shown in Fig. 1. Whilst DPD ordered efficiently into the expected state of hexagonal tubes, BD remained trapped in a structure of interconnected tubes. By way of contrast, both DPD and BD reproduced the expected lamellar equilibrium structure of A5B5 on similar time scales, see Fig. 2. 

A field-scale simulator based on this approach would probably require simpler equations that captured the relevant phenomena without explicitly addressing many of them. Chapter 15, by Prieditis and Flumerfelt, models two-phase flow in a network of interconnected channels that consist of constricted tube segments. Work on the creation of a model that contains capillary snap-off in a network similar to that of Figure 6 has very recently been started at the University of Texas (R. Schechter, personal communication, October 26, 1987). 

This complex two phase flow is now modeled as a network of interconnected channels consisting of constricted tube segments which contain the flowing and non-flowing fractions of the gas and liquid phases. Although overly simplistic in many respects, this representation provides a basis for obtaining qualitative and semi-quantitative permeability results which are useful in... 

These network models are comprised of different-sized, interconnected elements of uniform shape (e.g., Fig 3-17B). The configuration of elements within the network can be either systematic or random. Marie and Defrenne (1960) were the first to use this type of model to predict solute dispersion. Their network was a modified capillary bundle model with regularly spaced interconnections between parallel tubes of radii r and r2. This model does not consider diffusion. Spreading of a solute in the model is given by ... 

The vector model has proven versatQe to this purpose. It employs the unit vectors of the graphene s two-dimensional unit ceU as a reference dimension. The vector C running in paraUel to the coiling direction is a Unear combination of integer multiples of the units vectors. It is an interconnection of two identical points on the graphene lattice (Figure 3.2). C describes a straight line that represents the uncoiled perimeter of the respective nanotube. It also defines the orientation of the nanotube as the tubular axis f is perpendicular to the tube s cross-section, which on its own part Ues in a plane defined by the perimeter (or the coUed C). 

For a tubular structure where distances between branching points are significantly greater than the tube diameter, we expect D/Do of the solvent in the tubes to be close to 1/3, because diffusion is allowed only along the axes of the tubules. The external solvent should have a D/Dq value not much below 1. (The obstruction effect of cylinders is small.) More plausible is an interconnected rod model for which the diffusion was theoretically analyzed by Anderson and Wennerstrom [33]. 

In this code, a 1-dimensional electrochemical element is defined, which represents a finite volume of active unit cell. This 1-D sub-model can be validated with appropriate single-cell data and established 1-D codes. This 1-D element is then used in FLUENT, a commercially available product, to carry out 3-D similations of realistic fuel cell geometries. One configuration studied was a single tubular solid oxide fuel cell (TSOFC) including a support tube on the cathode side of the cell. Six chemical species were tracked in the simulation H2, CO2, CO, O2, H2O, and N2. Fluid dynamics, heat transfer, electrochemistry, and the potential field in electrode and interconnect regions were all simulated. Voltage losses due to chemical kinetics, ohmic conduction, and diffusion were accounted for in the model. Because of a lack of accurate and detailed in situ characterization of the SOFC modeled, a direct validation of the model results was not possible. However, the results are consistent with input-output observations on experimental cells of this type. 

The crux of the problem of the relationship of form to function in sieve tubes relates to the disputed nature of the interconnections between the sieve tube units via the sieve plates and in a recent review it was concluded that at least four or five possible arrangements could not be excluded by the structural evidence (Fig. 7.7 a, b, c, d). These structure models can be considered in relation to hypotheses of the mechanism of solute transport in the sieve tubes. 

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