Pore tortuosity

Assay conditions Porosity and pore tortuosity Composition Sink conditions Disappearance, appearance, or both Reservoir volume... 

The sole purpose of the filter support and any applied extracellular matrix is simply to provide a surface for cell attachment and thus to provide mechanical support to the monolayer. However, the filter and matrix also can act as serial barriers to solute movement after diffusion through the cell monolayer. The important variables are the chemical composition of the filter, porosity, pore size, and overall thickness. In some cases, pore tortuosity also can be important. It is desired that the filter, with or without an added matrix, provide a favorable surface to which the cells can attach. However, in some cases these properties can also result in an attractive surface for nonspecific adsorption of the transported solute. In these instances, the appearance of the solute in the receiver compartment of the diffusion cell will not be a true reflection of its movement across the mono-layer. Such problems must be examined on a case-by-case basis. 

Drug release profiles from the tablets in various dissolution media are shown in Fig. 2. In all cases the release rates decreased initially from the control (distilled water) as electrolyte concentration increased, until a minimum release rate was obtained. As the electrolyte concentration further increased the release rates similarly increased until a burst release occurred. These initial decreases in release rates were probably coincident with a decrease in polymer solubility, in that as the ionic strength of the dissolution medium is increased the cloud point is lowered towards 37°C. It may be seen from Table 5 that minimum release rates occurred when the cloud point was 37°C. At this point the pore tortuosity within the matrix structure should also be at a maximum. It is unlikely to be an increase in viscosity that retards release rates since Ford et al. [1] showed that viscosity has little effect on release rates. Any reduction in hydration, such as that by increasing the concentration of solute in the dissolution media or increasing the temperature of the dissolution media, will start to prevent gelation and therefore the tablet will cease to act as a sustained release matrix. 

Porous Membrane DS Devices. The applicability of a simple tubular DS based on a porous hydrophobic PTFE membrane tube was demonstrated for the collection of S02 (dilute H202 was used as the scrubber liquid, and conductometric detection was used) (46). The parameters of available tubular membranes that are important in determining the overall behavior of such a device include the following First, the fractional surface porosity, which is typically between 0.4 and 0.7 and represents the probability of an analyte gas molecule entering a pore in the event of a collision with the wall. Second, wall thickness, which is typically between 25 and 1000 xm and determines, together with the pore tortuosity (a measure of how convoluted the path is from one side of the membrane to the other), the overall diffusion distance from one side of the wall to the other. If uptake probability at the air-liquid interface in the pore is not the controlling factor, then items 1 and 2 together determine the collection efficiency. The transport of the analyte gas molecule takes place within the pores, in the gas phase. This process is far faster than the situation with a hydrophilic membrane the relaxation time is well below 100 ms, and the overall response time may in fact be determined by liquid-phase diffusion in the boundary layer within the lumen of the membrane tube, by liquid-phase dispersion within the... 

Coppens and Froment (1995a, b) employed a fractal pore model of supported catalyst and derived expressions for the pore tortuosity and accessible pore surface area. In the domain of mass transport limitation, the fractal catalyst is more active than a catalyst of smooth uniform pores having similar average properties. Because the Knudsen diffusivity increases with molecular size and decreases with molecular mass, the gas diffusivities of individual species in... 

Here, is the experimental mean rate of reaction per unit volume of catalyst, L is a characteristic length of the porous photocatalyst (i.e., the film thickness), t is the pore tortuosity (taken as three), D is the diffusion coefficient of the pollutant in air, Cg is the mean concentration at the external surface, and e is the catalyst grain porosity (0.5 for Degussa s P25). Such a treatment was performed by Doucet et al. (2006) while taking D of the pollutants to be approximately 10 m s. The estimated Weisz modulus ranged between 10 and 10, depending on the type of pollutant, that is, some three to five orders of magnitude smaller than the value of unity, which is often taken as a criterion for internal mass transport limitation. 

Analyzing this equation with reference to hydrogen flow in hydride beds, it is possible to note a number of constructive measures which promote reduction of resistance of hydrogen flow P-m-Poud reduction of thickness of a bed of hydride (characteristic size 8Ch), passing hydrogen reduction of pores tortuosity (asjn) and increase in their diameter (dp) increase in porosity of covering s. Presentation of these requirements speaks about necessity of use for porous beds of structures with the open, organized porosity of small relative size (l/dp <100, at 8ch=5 mmdp <50 microns). 

Applications of ultrasonic techniques to solid-gas systems rely on the fact that velocity and attenuation of US-waves in porous materials is closely related to pore size, porosity, tortuosity, permeability and flux resistivity. Thus, the flux resistivity of acoustic absorbents oan be related to US attenuation [118,119], while the velocity of slow longitudinal US is related to pore tortuosity and diffusion, and transport properties, of other porous materials [120]. Ultrasound attenuation is very sensitive to the presence of an external agent suoh as moisture in the pore space [121] and has been used to monitor wetting and drying prooesses [122] on the other hand, US velocity has been used to measure the elastic coefficients of different types of paper and correlate them with properties such as tensile breaking strength, compressive strength, etc. [123]. 

Pore tortuosity—Ratio of actual pore length to membrane thickness. 

In Eq. 6.25 the transport in the pore fluid is modeled as free diffusion in the macro-and mesopores, but the diffusion coefficient Dpolej is usually lower than in the liquid mobile phase because of the random orientation and variations in the diameter of the pores (tortuosity) (Section 6.5.8). 

Adsorption of molecules proceeds by successive steps (1) penetration inside a particle (2) diffusion inside the particle (3) adsorption (4) desorption and (5) diffusion out of the particle. In general, the rates of adsorption and desorption in porous adsorbents are controlled by the rate of transport within the pore network rather than by the intrinsic kinetics of sorption at the surface of the adsorbent. Pore diffusion may take place through several different mechanisms that usually coexist. The rates of these mechanisms depend on the pore size, the pore tortuosity and constriction, the cormectivity of the pore network, the solute concentration, and other conditions. Four main, distinct mechanisms have been identified molecular diffusion, Knudsen diffusion, Poiseiulle flow, and surface diffusion. The effective pore diffusivity measured experimentally often includes contributions for more than one mechanism. It is often difficult to predict accurately the effective diffusivity since it depends so strongly on the details of the pore structure. 

Three mechanisms have been invoked to describe the transfer of water vapor from the feed-membrane interface to the strip-membrane interface, namely Poiseuille flow, Knudsen diffusion, and Fickian (molecular) diffusion. The operative mechanism in a particular system depends on the pore diameter and on whether or not the pores are filled with stationary air. The membrane mass transfer co-efficient (as kgm h Pa ) applicable to each of these mechanisms can be estimated using Eqs. (4), (5), and (6), respectively. Here, r is the pore radius, e is the membrane porosity, is the molar mass of water, is the mean water vapor pressure in the pores, is the membrane thickness, x is the pore tortuosity, is the viscosity of water vapor, R is the gas constant, T is the absolute temperature, is the diffusion co-efficient of water vapor in air,... 

Pore tortuosity Membrane porosity Membrane thickness (m)... 

MCM-48. It is well known that the effective diffusion coefficient (Dg) of a compo-nenf A in a porous pellet is proportional to the pellet porosity (c), and is inversely proportional to pore tortuosity (t) [18]. That is. 

Catalyst particles size -35 -i-48 Tyler mesh were used in all tests. Porosity was measured using a mercury porosimeter. A 0.1356 pm pore mean diameter was determined. The Satterfield and Sherwood (7) methodology was used to verify that reaction occurs without any diSusional limitation (internal or external). The effective diffusivity was estimated from the porosity measurements and binary diffusion coefficient and pore tortuosity pubhshed in the hterature, leading to an estimated value of 10 for the generahzed Thiele Modvdus based on the reaction rate. The efi ectiveness factor was then considered as 1.0. 

The diffusion equations just used are simplifications of more complex processes. The F factor was empirically derived and must take into account those matrix pore geometric factors contributing to decreases in diffusion rates. Such factors may include pore tortuosity, dead-end pores, and pore constrictions. Initial modeling studies suggest that constrictions, in particular, have large effects in retarding release (8,9). 

Equation 71 is the basic equation that relates permeability of a porous medium to its other properties. However, equation 71 contains the hydraulic diameter of the passage (pore), tortuosity, and areal porosity of the medium, which may not be easily accessible. For example, sandstones or rock formations have irregular pore structure and often have inconsistent pore size measurement values (see previous section). It is rather difficult to measure the average hydraulic pore diameter. On the other... 

As described in Sec. 35a, there are still many puzzling aspects of conf nra-tional diffusion that remain to be explained. About the only theoretical infcmna-tion available concerns the motion of spherical particles in liquids through cylindrical pores. Anderson and Quinn [71] have shown that the fective difiiirivity in straight, round pores (tortuosity t = 1.0) is given by ... 

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