Pore, capillary

The principle underlying surface area measurements is simple physisorb an inert gas such as argon or nitrogen and determine how many molecules are needed to form a complete monolayer. As, for example, the N2 molecule occupies 0.162 nm at 77 K, the total surface area follows directly. Although this sounds straightforward, in practice molecules may adsorb beyond the monolayer to form multilayers. In addition, the molecules may condense in small pores. In fact, the narrower the pores, the easier N2 will condense in them. This phenomenon of capillary pore condensation, as described by the Kelvin equation, can be used to determine the types of pores and their size distribution inside a system. But first we need to know more about adsorption isotherms of physisorbed species. Thus, we will derive the isotherm of Brunauer Emmett and Teller, usually called BET isotherm. 

Here the phenomenon of capillary pore condensation comes into play. The adsorption on an infinitely extended, microporous material is described by the Type I isotherm of Fig. 5.20. Here the plateau measures the internal volume of the micropores. For mesoporous materials, one will first observe the filling of a monolayer at relatively low pressures, as in a Type II isotherm, followed by build up of multilayers until capillary condensation sets in and puts a limit to the amount of gas that can be accommodated in the material. Removal of the gas from the pores will show a hysteresis effect the gas leaves the pores at lower equilibrium pressures than at which it entered, because capillary forces have to be overcome. This Type IV isotherm. 

Concrete is a composite material composed of cement paste with interspersed coarse and fine aggregates. Cement paste is a porous material with pore sizes ranging from nanometers to micrometers in size. The large pores are known as capillary pores and the smaller pores are gel pores (i.e., pores within the hydrated cement gel). These pores contain water and within the water are a wide variety of dissolved ions. The most common pore solution ions are OH", K+ and Na+ with minor amounts of S042" and Ca2+. The microstructure of the cement paste is a controlling factor for durable concrete under set environmental exposure conditions. 

Precipitation and accumulation of clay. Precipitation of clay particles takes place at some depth in the soil as a result of 1. flocculation of clay particles, or 2. (mechanical) filtration of clay in suspension by fine capillary pores. 

For practical purposes, if the contact angle is greater than 90° the liquid is said not to wet the solid (if the liquid is water one speaks of a hydrophobic surface) in such a case drops of liquids tend to move about easily and not to enter capillary pores. If 8 = 0, (ideal perfect wettability) Eq. (A.4.3) no longer holds and a spreading coefficient, Sls(V). reflects the imbalance of surface free energies. 

The adsorption of organics from the liquid to a solid phase is generally assumed to occur in three stages [50]. The brst is the movement of the contaminant (adsorbate or solute) through a blm surface surrounding the solid phase (adsorbant). The second is the diffusion of the adsorbate within the pores of the activated carbon. The bnal stage is the sorption of the material onto the surface of the sorbing medium. The overall rate of adsorption is controlled by the rate of diffusion of the solute molecules within the capillary pores of the carbon particles [27]. 

It should be pointed out that deterioration under freeze-thaw conditions can also be caused by a mechanism other than the direct freezing of the non-evaporable water. The capillaries contain dissolved salts, such as hydroxides, sulfates and carbonates. As part of the water is frozen, the concentration of salts in the remaining water increases and water will flow by osmotic pressure from the gel pores to the capillary pores, setting up an additional disruptive pressure. 

Although reverse osmosis, ultrafiltration and microfiltration are conceptually similar processes, the difference in pore diameter (or apparent pore diameter) produces dramatic differences in the way the membranes are used. A simple model of liquid flow through these membranes is to describe the membranes as a series of cylindrical capillary pores of diameter d. The liquid flow through a pore (q) is given by Poiseuille s law as ... 

We have now demonstrated that both the FDSP and FDE responses are dependent on the capillary/pore dimension. Once the pore dimension is known this can applied to an appropriate permeability model to obtain more information about the porous media. Using an appropriate permeability model along with formation factor measurements we can estimate the permeability of porous samples. Alternatively, if we measure the permeability of a sample we can then use the permeability model to determine the formation factor and tortuosity of the sample using measurements that are base on the hydraulic properties and not the electrical properties. This is currently a work in progress to compare formation factor measurements made using the two methods. 

The pore radius determined from infiltration kinetics can be reconciled to the experimentally determined radii from SEM and porosimetry, by assuming a two-pore-size model (pore neck and pore bulge), instead of a single capillary pore-size [Dullien etal., 1977 Einset, 1996]. The schematic diagram for this two-pore-size model is shown in Fig. 5.2(b). 

The drawbacks of SC and IM injections include potentially decreased bioavailability that is secondary to variables such as local blood flow, injection trauma, protein degradation at the site of injection, and limitations of uptake into the systemic circulation related to effective capillary pore size and diffusion. The bioavailability of numerous peptides and proteins is, for example, markedly reduced after SC or IM administration compared to their IV administration. The pharmacokine-tically derived apparent absorption rate constant is thus the combination of absorption into the systemic circulation and presystemic degradation at the absorption site. The true absorption rate constant ka can then be calculated as ... 

Therefore, steps 2 and 3 can be combined into a single step, and the overall kinetics can then be described in three compositional fractions the permanent (formed from insolubles), the resistant (in capillary pores and sorbed within aggregates), and the labile (in gravitational pores). The contribution of the permanent fraction (the insoluble portion) to the soluble portion in the leachate is proportional to its concentration. The release of the resistant fraction is represented by mass transfer, and the translocation of the labile fraction relates to convection flow and dispersion. 

Good quality RO membranes can reject >95-99% of the NaCl from aqueous feed streams (Baker, Cussler, Eykamp et al., 1991 Scott, 1981). The morphologies of these membranes are typically asymmetric with a thin highly selective polymer layer on top of an open support structure. Two rather different approaches have been used to describe the transport processes in such membranes the solution-diffusion (Merten, 1966) and surface force capillary flow model (Matsuura and Sourirajan, 1981). In the solution-diffusion model, the solute moves within the essentially homogeneously solvent swollen polymer matrix. The solute has a mobility that is dependent upon the free volume of the solvent, solute, and polymer. In the capillary pore diffusion model, it is assumed that separation occurs due to surface and fluid transport phenomena within an actual nanopore. The pore surface is seen as promoting preferential sorption of the solvent and repulsion of the solutes. The model envisions a more or less pure solvent layer on the pore walls that is forced through the membrane capillary pores under pressure. 

Matsuura, T., and Sourirajan, S. (1981). Reverse osmosis transport through capillary pores under the influence of surface forces, lnd. Engr. Chem., Proc. Des. Dev. 20, 273. 

As more liquid is added, the capillary pores (00 in Figure 26) eventually fill with liquid, and this condition continues at the expense of the funicular stage. The suction gradually diminishes as the menisci and other pores disappear. This is called the capillary stage, and the cycle repeats in each successive layer of spheres. 

In this model, the biocatalyst is entrapped in a thin layer of solution between a working electrode and a membrane with capillary pores [64]. The electrode is poised at a potential sufficiently positive to ensure that the surface concentration of reduced mediator is negligible. In addition, it is assumed that (i) the microbial activity is constant in the absence of external perturbations (ii) the concentration of reduced mediator in the external medium is negligibly different from zero (iii) the microbial cells are point sources of reduced mediator homogeneously distributed throughout the biological layer and (iv) the concentration gradients are linear. 

It may again be noted that in the case of adsorption isotherm of type IV and V there is formation of multimolecular adsorbed layer of the gas molecules within the narrow capillary pores of... 

One innovative technique that has been developed to limit the mobility of a liquid plasma-facing surface is the capillary pore system [27]. This system has been successfully deployed in a tokamak environment [28]. Although this system addresses many of the mobility and erosion issues of a liquid plasmafacing surface, as will be discussed later in this chapter in order to achieve the full benefits from a low-recycling boundary a larger scaled-up version of this system will need to be developed. 

The theory of effective viscosity has been developed by Betherton [172], Hirasaki and Lawson [173], Falls et al. [171] and Kovscek and Radke [153]. It was shown that the effective viscosity is a sum of three terms the first accounts for the contribution of the slugs of liquid between bubbles, the second is the resistance against surface deformation in the advancement of bubbles through the capillaries (pores) and the third is the gradient of surface tension caused by the withdrawal of the surfactant (from the bubble front to the bubble back). The experimental data of Falls et al. [171], Hirasaki and Lawson [173], Ettinger and Radke [166] for bead packs and Berea core agree with the calculations from Hirasaki and Lawson s models [173],... 

---