Porous cross-section

Fig. 4.18 Phase behavior of P(F)S49-i>-PLA192 g jj at the fihn/substrate interface studied by SEM. a SEM of the free-surface of the used FTO-coated glass substrates revealing a rough surface topography, b Nonporous film/substrate interface of a PLA etched film prepared on super hydrophobic FTO. The inverse topography of the FTO and the porous cross-section are clearly visible. c Highly porous film/substrate interface of a PLA etched film prepared on a FTO substrate, the surface of which was modified according to Sect. 4.2.2. d Cross-sectional view of the film shown in (c) revealing that the DG phase starts directly at the interface with no other phase such as cylinders or HPL present...

So a smooth surface and uniform circular cross section is the only profile we need In order to improve some properties and even add some new properties or functions to chemical fiber, fibers with noncircular cross sections are prepared, and the changed profiles will vary the friction coefficient between fibers, appearance, bulk density, specific surface area, water retention, and dyeabihty. Namral fibers always have rough and irregular surfaces and cross sections, like vegetable fibers, which have a hollow and porous cross section and ribbon surface. With the development of bionics, a series of functional fibers have been designed since 1980, and a new filament with a triangle or trilobal cross section was prepared then. 

Slurry or slip casting provides a relatively inexpensive way to fabricate unifonn-thickness, thin-wall, or large cross section shapes [4o, 44, 45, 46, 42 aiid 48]. For slip casting, a slurry is first poured into a porous mould. Capillary suction then draws the liquid from the slurry to fonn a higher solids content, close-packed, leather-hard cast on the inner surface of the mould. In a fixed time, a given wall thickness is fonned, after which the excess slurry is drained. 

The framework for the solution of porous media flow problems was estabUshed by the experiments of Henri Darcy in the 1800s. The relationship between fluid volumetric flow rate, hydraulic gradient, and cross-sectional area, yi, of flow is given by the Darcy formula ... 

The cross-sectional area of the wick is deterrnined by the required Hquid flow rate and the specific properties of capillary pressure and viscous drag. The mass flow rate is equal to the desired heat-transfer rate divided by the latent heat of vaporization of the fluid. Thus the transfer of 2260 W requires a Hquid (H2O) flow of 1 cm /s at 100°C. Because of porous character, wicks are relatively poor thermal conductors. Radial heat flow through the wick is often the dominant source of temperature loss in a heat pipe therefore, the wick thickness tends to be constrained and rarely exceeds 3 mm. 

Fig. 8. (a) Cross section of cellulose acetate isotropic porous hoUow-fiber dry-jet wet spun at incipient gelation point of dope mixture (b) magnification at... 

Fig. 10. Composite hoUow-fiber membranes (a) polysulfone boUow fiber coated witb fiiran resin. A and B denote fiiran resin surface and porous support, respectively (b) cross section of composite boUow fiber (PEI/TDI coated on polysulfone matrix). C, D, and E denote tightly cross-linked surface, "gutter" gel layer, and porous support, respectively. Both fibers were developed for reverse osmosis appHcation (15).

Fig. 11. (a) Cross-sectional view of substrate with porous fibers and polyurethane sponge, (b) Cross-sectional view of substrate with bundle of microfibers... 

Fig. 3. Microporous membranes are characterized by tortuosity, T, porosity, S, and their average pore diameter, d. (a) Cross-sections of porous membranes containing cylindrical pores, (b) Surface views of porous membranes of equal S, but differing pore size.

The sol—gel technique has been used mosdy to prepare alumina membranes. Figure 18 shows a cross section of a composite alumina membrane made by sHp coating successive sols with different particle sizes onto a porous ceramic support. SiUca or titanium membranes could also be made by the same principles. Unsupported titanium dioxide membranes with pore sizes of 5 nm or less have been made by the sol—gel process (57). 

Diffusivity and tortuosity affect resistance to diffusion caused by collision with other molecules (bulk diffusion) or by collision with the walls of the pore (Knudsen diffusion). Actual diffusivity in common porous catalysts is intermediate between the two types. Measurements and correlations of diffusivities of both types are Known. Diffusion is expressed per unit cross section and unit thickness of the pellet. Diffusion rate through the pellet then depends on the porosity d and a tortuosity faclor 1 that accounts for increased resistance of crooked and varied-diameter pores. Effective diffusion coefficient is D ff = Empirical porosities range from 0.3 to 0.7, tortuosities from 2 to 7. In the absence of other information, Satterfield Heterogeneous Catalysis in Practice, McGraw-HiU, 1991) recommends taking d = 0.5 and T = 4. In this area, clearly, precision is not a feature. 

Porous media is typically characterized as an ensemble of channels of var ious cross sections of the same length. The Navier-Stokes equations for all chaimels passing a cross section normal to the flow can be solved to give ... 

Fig. 15.1 Diagrammatic cross-section of porous anodic oxide film...

Now let s take a more detailed look into the electrochemical cell. Figure 12-5 shows a cross-section of a cell that uses the same chemical reaction as that depicted in Figure 12-1. The only difference is that the two solutions are connected differently. In Figure 12-1 a tube containing a solution of an electrolyte (such as KNOa) provides a conducting path. In Figure 12-5 the silver nitrate is placed in a porous porcelain cup. Since the silver nitrate and copper sulfate solutions can seep through the porous cup, they provide their own connection to each other. 

The >eff across the porous medium for this example is linearly related to the porosity of the path, which is in turn simply the ratio of the open cross-sectional area to the total cross-sectional area. There are no constriction or tortuosity effects in this example i.e., t = 1 and... 

S is the total solution cross section in the porous solid). 

Streaming Potential When the solution is forced through the porous solid under the effect of an external pressure P, the character of liquid motion in the cylindrical pores will be different from that in electroosmotic transport. Since the external pressure acts uniformly on the full pore cross section, the velocity of the liquid will be highest in the center of the pore, and it will gradually decrease with decreasing distance from the pore walls (Fig. 31.5). The velocity distribution across the pore is quantitatively described by the Poiseuille equation. 

Molecular sieves (zeolites) are artificially prepared aluminosilicates of alXali metals. The most common types for gas chromatography are molecular sieve 5A, a calcium aluminosilicate with an effective pore diameter of 0.5 nm, and molecular sieve 13X, a sodium aluminosilicate with an effective pore diameter of 1 nm. The molecular sieves have a tunnel-liXe pore structure with the pore size being dependent on the geometrical structure of the zeolite and the size of the cation. The pores are essentially microporous as the cross-sectional diameter of the channels is of similar dimensions to those of small molecules. This also contrilsutes to the enormous surface area of these materials. Two features primarily govern retention on molecular sieves. The size of the analyte idiich determines whether it can enter the porous... 

Where u, is the mobile phase velocity at the column outlet, Fg the column volumetric flow rate, and Ag the column cross-sectional area available to the mobile phase. In a packed bed only a fraction of the column geometric cross-sectional area is available to the mobile phase, the rest is occupied by the solid (support) particles. The flow of mobile phase in a packed bed occurs predominantly through the interstitial spaces the mobile phase trapped within the porous particles is largely stagnant (37-40). 

Fig. 2.9.9 (a) Schematic cross section of a compartments at the top and bottom, respec-convection cell in Rayleigh-Benard configura- tively. (b) Velocity contour plot of typical tion. In the version examined in Refs. [8, 44], a convection rolls expected in the absence of any fluid filled porous model object of section flow obstacles (numerical simulation). 

If the pores of a catalyst pellet are randomly oriented, geometric considerations require that if one takes an arbitrary cross section of the porous mass, the fraction of the area occupied by the solid material will be a constant that will... 

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