Two-dimensional porosity

Miralles-Mellado I, Canton Y, Sole-Benet A. Two-dimensional porosity of crusted silty soils indicators of soil quality in semiarid rangelands Soil Sci. Soc. Am. J. 2011 75 1330-1342. 

The developed methodology is now used to determine a two-dimensional porosity distribution on a Bentheimer sandstone sample (KBE) saturated with oil. The sample and reference used are the same as those for one-dimensional imaging in Section 2.4.1. A two-dimensional CPMG imaging sequence is applied with field of view of 10.00 cm x 3.50cm, which gives a voxel size of 0.078 cm x 0.11 cm x 0.58 cm. The porosity distribution of the two-dimensional... 

Figure 2.9.3 shows typical maps [31] recorded with proton spin density diffusometry in a model object fabricated based on a computer generated percolation cluster (for descriptions of the so-called percolation theory see Refs. [6, 32, 33]).The pore space model is a two-dimensional site percolation cluster sites on a square lattice were occupied with a probability p (also called porosity ). Neighboring occupied sites are thought to be connected by a pore. With increasing p, clusters of neighboring occupied sites, that is pore networks, begin to form. At a critical probability pc, the so-called percolation threshold, an infinite cluster appears. On a finite system, the infinite cluster connects opposite sides of the lattice, so that transport across the pore network becomes possible. For two-dimensional site percolation clusters on a square lattice, pc was numerically found to be 0.592746 [6]. 

Fig. 2.9.13 Qu asi two-dimensional random ofthe percolation model object, (bl) Simulated site percolation cluster with a nominal porosity map of the current density magnitude relative p = 0.65. The left-hand column refers to simu- to the maximum value, j/jmaK. (b2) Expedited data and the right-hand column shows mental current density map. (cl) Simulated NMR experiments in this sample-spanning map of the velocity magnitude relative to the cluster (6x6 cm2), (al) Computer model maximum value, v/vmax. (c2) Experimental (template) for the fabrication ofthe percolation velocity map. The potential and pressure object. (a2) Proton spin density map of an gradients are aligned along the y axis, electrolyte (water + salt) filling the pore space...

Similar neutron diffractogram modifications have been al-ready observed several time during our studies concerning the structural proper-ties of confined molecular species (D2, Ar, N2, Kr, CD4, C2D6) in Silicalite-I zeolite. But for such a MFI type of framework porosity, characterized by a two dimensional micropore network, the intensity of the diffraction peaks (101) and (020), observed at small wave vector Q (A1) values, vanishes completely when increasing the confined phase loading ( as shown on figure 6, for the Ar / Silicalite-I system Ld. = 68 % ). 

V. A. RusseU, C. C., Evans, W. Li, M. D. Ward, "Nanopor-ous molecular sandwiches pillared two-dimensional hydrogen bonded networks with adjustable porosity , Science 1997,276,575-579. 

The linear driving force model has much more physical significance. It has been derived from a two-dimensional model of intra-particle diffusion, solution of which is a series development. The particle size appears explicitly. The effective diffusion coefficient is related to the particle porosity and to the size of the adsorbate molecule. Thus it makes sense to search for correlation of with these properties. However such relations are complex and it is rather difficult to predict for a given carbon and a given molecule. 

Porosity may be generated, for instance, either by using awkwardly shaped molecules like 425 or by creating a net with large cages or channels (avoiding interpenetration)due to hydrogen bonds or coordination. In this way three-(3D) or two-dimensional (2D) nets are created which can host smaller molecules. Few... 

The controlled release of macromolecules from non-erodible, hydrophobic polymeric matrices is modelled as a discrete diffusion process with the release of solute occuring through distinct pores in the polymer which are formed as solid particles of molecule dissolve. In order to formulate predictive models of the release behavior of these devices, quantitative information on the microgeometry of the system is required. We present a computer-based system for obtaining estimates of the system porosity, isotropy, particle shape, and particle size distribution from observations on two-dimensional sections from the polymer matrix. 

These results clearly show that the intensity observed in the two-dimensional scattering patterns comes from the porosity of the samples, which can be filled partially or totally with dibromomethane. According to the CM results, the very narrow porosity existing in the original carbon fiber becomes wider during the activation process. It has been seen that the higher the burn off, the higher would be the CM effect, due to the existence of a wider mean pore size. 

A cylindrical container kept at a surface temperature of 40CC is buried in a bed of approximately spherical pebbles with a mean diameter of 5 mm with a porosity of 0.3. Water at a temperature of 15°C trickles through the bed at a mean velocity of 0.01 m/s, the axis of the cylinder being normal to the water flow. Find the distribution of the local heat transfer rate around the container assuming two-dimensional flow. 

Tsardaka and co-workers [102,141,142] presented the Heckel plot with dependence on time and analyzed deformation in combination with elastic recovery. Additional areas to describe plasticity were determined from two-dimensional (2D) plots [129], Finally, the three-dimensional (3D) model [143, 144] was developed by fitting a plane to a 3D data plot on the basis of normalized time, pressure, and porosity according to Heckel. 

In all the cellular models described, the cells throughout the medium were initially uniform. A microheterogeneous cell model has recently been developed, where the cells have varying initial properties (Hwang et ai, 1997). In such a model, the structure of the reaction medium is stochastic, and the heterogeneity of the reactant medium is considered explicitly. For example, the structure can be described as a regular two-dimensional matrix of circular cylinders (with nominally flat sides) in contact, with a number of cylinders randomly removed until the ratio of the voids to total volume equals the porosity (Fig. 23a). The cylinder diameter is assumed to be similar to the particle diameter. 

A very important form of such disturbances is caused by the presence of the wall of the tube containing the packed bed. Vortmeyer and Schuster (1983) have used a variational approach to evaluate the steady two-dimensional velocity profiles for isothermal incompressible flow in rectangular and circular packed beds. They used the continuity equation, Brinkman s equation (1947), and a semiempirical expression for the radial porosity profile in the packed bed to compute these profiles. They were able to show that significant preferential wall flow occurs when the ratio of the channel diameter to the particle diameter becomes sufficiently small. Although their study was done for an idealized situation it has laid the foundation for more detailed studies. Here CFD has definitely contributed to the improvements of theoretical prediction of reactor performance. 

Kuipers, J. A. M., Tammes, H., Prins, W., and van Swaaij, W. P M., Expermental and theoretical porosity profiles in a two-dimensional gas-fluidized bed with a central jet. Powder Technol. 71, 87 (1992b). 

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