Penetrant diameter, physical

Important physical properties of catalysts include the particle size and shape, surface area, pore volume, pore size distribution, and strength to resist cmshing and abrasion. Measurements of catalyst physical properties (43) are routine and often automated. Pores with diameters <2.0 nm are called micropores those with diameters between 2.0 and 5.0 nm are called mesopores and those with diameters >5.0 nm are called macropores. Pore volumes and pore size distributions are measured by mercury penetration and by N2 adsorption. Mercury is forced into the pores under pressure entry into a pore is opposed by surface tension. For example, a pressure of about 71 MPa (700 atm) is required to fill a pore with a diameter of 10 nm. The amount of uptake as a function of pressure determines the pore size distribution of the larger pores (44). In complementary experiments, the sizes of the smallest pores (those 1 to 20 nm in diameter) are deterrnined by measurements characterizing desorption of N2 from the catalyst. The basis for the measurement is the capillary condensation that occurs in small pores at pressures less than the vapor pressure of the adsorbed nitrogen. The smaller the diameter of the pore, the greater the lowering of the vapor pressure of the Hquid in it. 

FIGURE 16.2 Three possible modes through which inertial cavitation may enhance SC permeability, (a) Spherical collapse near the SC surface emits shock waves, which can potentially disrupt the SC lipid bilayers, (b) Impact of an acoustic microjet on the SC surface. The microjet possessing a radius about one tenth of the maximum bubble diameter impacts the SC surface without penetrating into it. The impact pressure of the microjet may enhance SC permeability by disrupting SC lipid bilayers, (c) Microjets may physically penetrate into the SC and enhance the SC permeability. (From Mitragotri, S., and Kost J., Adv. Drug Deliv. Rev., 56, 589, 2004. With permission.)... 

Consider the impingement between two opposed particles-gas suspension streams from accelerating tubes of the same diameter. The assumptions made in the establishment of the model are (1) The streams are symmetrical with respect to both the jet axis and the impingement plane (2) The gas flow velocity and all the physical properties of gas and solid are kept constant and (3) The particles beyond collision penetrate into the opposing stream up to. rlllas, while any particle will be drawn out of the system immediately once it collides with another particle. 

Measurements of kinetic parameters of liquid-phase reactions can be performed in apparata without phase transition (rapid-mixing method [66], stopped-flow method [67], etc.) or in apparata with phase transition of the gaseous components (laminar jet absorber [68], stirred cell reactor [69], etc.). In experiments without phase transition, the studied gas is dissolved physically in a liquid and subsequently mixed with the liquid absorbent to be examined, in a way that ensures a perfect mixing. Afterwards, the reaction conversion is determined via the temperature evolution in the reactor (rapid mixing) or with an indicator (stopped flow). The reaction kinetics can then be deduced from the conversion. In experiments with phase transition, additionally, the phase equilibrium and mass transport must be taken into account as the gaseous component must penetrate into the liquid phase before it reacts. In the laminar jet absorber, a liquid jet of a very small diameter passes continuously through a chamber filled with the gas to be examined. In order to determine the reaction rate constant at a certain temperature, the jet length and diameter as well as the amount of gas absorbed per time unit must be known. 

One of the most important parameters in the S-E theory is the rate coefficient for radical entry. When a water-soluble initiator such as potassium persulfate (KPS) is used in emulsion polymerization, the initiating free radicals are generated entirely in the aqueous phase. Since the polymerization proceeds exclusively inside the polymer particles, the free radical activity must be transferred from the aqueous phase into the interiors of the polymer particles, which are the major loci of polymerization. Radical entry is defined as the transfer of free radical activity from the aqueous phase into the interiors of the polymer particles, whatever the mechanism is. It is beheved that the radical entry event consists of several chemical and physical steps. In order for an initiator-derived radical to enter a particle, it must first become hydrophobic by the addition of several monomer units in the aqueous phase. The hydrophobic ohgomer radical produced in this way arrives at the surface of a polymer particle by molecular diffusion. It can then diffuse (enter) into the polymer particle, or its radical activity can be transferred into the polymer particle via a propagation reaction at its penetrated active site with monomer in the particle surface layer, while it stays adsorbed on the particle surface. A number of entry models have been proposed (1) the surfactant displacement model (2) the colhsional model (3) the diffusion-controlled model (4) the colloidal entry model, and (5) the propagation-controlled model. The dependence of each entry model on particle diameter is shown in Table 1 [12]. 

We note that Higbie s penetration theory (HI5), with contact time assumed as that required by the drop to traverse a distance of one diameter (W6), gives an expression identical with Eq. (18). Although potential-flow theory, unlike the penetration theory, takes interfacial acceleration into account, the two are actually physically identical, both being based on diffusion into an element of fluid sliding over the constant-temperature interface. 

The collectors are 11-liter plastic buckets approximately 30 cm in diameter with a 6 mm O.D. plastic tube that is 1 -2 m long for sampling the accumulated gas. The buckets float on the surface of the water (Zimmerman, 1979) or positioned over small plants or in open water areas and also directly adjacent to plants that were too large (over 30 cm in diameter or height) to fit under the collector. At each site, four buckets were carefully positioned (with floats) on the water surface in order that the underlying sediment is not disturbed. Our portable static chamber method contrasts with the often used method of a permanently placed (i.e. one location) collar that penetrates the sediments and is left in place, but requires physical connection and seaUng of the above-water collector to the base before measurement. 

Here, w r) is the attractive (or repulsive) tail of the potential, a is the diameter of spheres, and we have assumed that the fluid is uniform, therefore translational invariance is implied. The first equality in the above equation embodies the physical requirement that the center of a sphere can not penetrate the excluded volume of other spheres. The second equality is just obtained from (1.25) by linearizing the entire exponential factor. Actually, it is the asymptote of the direct correlation function at the infinite separation. The approximation is known to be superior for describing the critical phenomena. The radial distribution function, however, shows an ill-behavior for a Coulombic system, similar to those from the PY closure. 

---