Capillary parallel slit

Fig. 4.2. Some idealised pore structures (a) cylindrical pores (ai,a2 parallel non-intersecting capillaries ai t = 1 a2 t > 1 as non-parallel intersecting capillaries (b) slit-shaped pores (c) voids between packed spheres (d) closed pores (e) blind pores (f) open pores (g) funnel (h) ink bottle ...

Capillary flows occur (e.g., parallel slit or cylindrical) and are driven by surface tension. The flow regime is viscous-dominated (see above) with a possible exception at the very beginning of the flow [22]. The scaling length scale is associated with the channel width or radius. Capillary flows are very convenient for initial loading of micro- and nanofluidic devices. The fluid must wet the surface and then a curved air/solution interface is formed at the flow front (Figure 19.2). Then the pressure drop in a perfectly wetted circular capillary with radius R is [23]... 

At the point where capillary condensation commences in the finest mesopores, the walls of the whole mesopore system are already coated with an adsorbed film of area A, say. The quantity A comprises the area of the core walls and is less than the specific surface A (unless the pores happen to be parallel-sided slits). When capillary condensation takes place within a pore, the film-gas interface in that pore is destroyed, and when the pore system is completely filled with capillary condensate (e.g. at F in Fig. 3.1) the whole of the film-gas interface will have disappeared. It should therefore be possible to determine the area by suitable treatment of the adsorption data for the region of the isotherm where capillary condensation is occurring. 

The limits of pore size corresponding to each process will, of course, depend both on the pore geometry and the size of the adsorbate molecule. For slit-shaped pores the primary process will be expected to be limited to widths below la, and the secondary to widths between 2a and 5ff. For more complicated shapes such as interstices between small spheres, the equivalent diameter will be somewhat higher, because of the more effective overlap of adsorption fields from neighbouring parts of the pore walls. The tertiary process—the reversible capillary condensation—will not be able to occur at all in slits if the walls are exactly parallel in other pores, this condensation will take place in the region between 5hysteresis loop and in a pore system containing a variety of pore shapes, reversible capillary condensation occurs in such pores as have a suitable shape alongside the irreversible condensation in the main body of pores. 

In calculations of the mesopore size distribution from physisorption isotherms it is generally assumed (often tacitly) (a) that the pores are rigid and of a regular shape (e.g. cylindrical capillaries or parallel-sided slits), (b) that micropores are absent, and (c) that the size distribution does not extend continuously from the mesopore into the macropore range. Furthermore, to obtain the pore size distribution, which is usually expressed in the graphical form AV /Arp vs. rp, allowance must be made for the effect of multilayer adsorption in progressively reducing the dimensions of the free pore space available for capillary condensation. 

Viscometers can be divided into rotational instruments and axial flow instruments. Rotational instruments include concentric cylinder (cup and bob), cone and plate and parallel disc viscometers, while axial flow instruments include capillary, slit and extrusion rheometers. 

Flow between two parallel stationary walls as a result of an applied pressure gradient is known as slit flow. It can be considered as the two-dimensional analog of capillary flow. This technique is used when studying practical industrial processes such as injection molding of plastics, for example, for bottle-pack lines. The shear stress is here calculated from ... 

A typical example of eonstrained liquid is that present in pores or capillaries. The surface is of liquid/solid type, and the same remarks about interaction potentials and computational methods we have already offered may be applied here. More attention must be paid in computations of interactions among separate portions of the liquid interface. In the slit pore case (i.e., in a system eomposed of two parallel plane solid surfaces, with a thin amount of liquid between them), there maybe an interference between the two distinct surfaces, more evident when the fliiekness ofthe liquid is small, or when there is an electrical potential between the two faces. The slit pore model is extensively used to describe capillarity problems in the most usual cylindrical capillary types there is a radial interaction similar in some sense to the interaction with a single solid surface. 

The surface area of the kaolinite and the produced sample are obtained using nitrogen adsorption/desorption at 77 K (Fig.3). The lUPAC hysteresis analysis for both samples show types H4 and H3, respectively, as a result of capillary condensation in mesoporous structure. The hysteresis loop for kaolinite sample shows vertically inclined parallel branches at a pressure close to saturation. This is attributed to the existence of narrow slit-like pores. Those pores have opened more with hydroxide treatment and yielded a product with aggregates of plate-like pores (Fig. 4). The total pore volume of 0.0339 cmVg is obtained in comparison with the 0.016476 cmVg for the original kaolinite. The Single point surfaee area of the produced sample obtained at a relative pressure of 0.3 is 6.85 mVg. 

In additional to cylindrical capillary tubes, another type of capillary with a simple cross-sectional shape is the slit capillary, i.e., a channel formed between two parallel plates. For an electrolyte solution flowing through a slit capillary, it can be shown that, in analogy to Eq. 13,... 

Type B. The adsorption branch is steep at saturation pressure, the desorption branch at intennediate relative pressure (lUPAC Type H3). These include open slit-shaped capillaries with parallel walls capillaries with very wide bodies and narrow short necks. lUPAC state that this type is observed with aggregates of plate-like particles giving rise to slit-shaped pores... 

For parallel plates or open slit-shaped capillaries, a meniscus cannot be formed during adsorption, but during desorption a cylindrical meniscus is already present, hence adsoiption is delayed to produce hysteresis. During desorption (Figure 3.5) rj = r and r2 = hence ... 

Dubinin et al. evaluated the amount surface area from the benzene isotherm measured for the nonporous reference adsorbent /7/, we, however estimated the specific surface area Sme of the mesopores from the adsorption isotherm studied /8/, In calculations of the mesopore size distribution and the specific surface area Sme it has been assumed that the parallel - sided slits are rigid and the size distribution does not extend continuously from the mesopore into both the macropore and micropore range. We have used the desorption branch of the hysteresis loop of the isotherm for the computation. The procedure of B.F. Roberts /9/ has been applied. In this computation, which is a rigorous application of the concept of simultaneous capillary condensation and multilayer adsorption, the adsorbed volume is first expressed as a function of pore size then it is converted to pore volume. A standard t - curve /lO/, which represents the benzene adsorption onto nonporous carbon blacks, has been used for correction for multilayer thickness. 

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