Hydrodynamic pore size

Instead of considering the largest particle diameter that can pass through a given void space, the hydrodynamic pore size may be used for predicting the hydromechanics of non-woven geotextiles. If the void is assumed to be equivalent to a circular flow channel, then the hydrodynamic pore size may be defined by its hydraulic radius, Rh, where ... 

For a single fluid flowing through a section of reservoir rock, Darcy showed that the superficial velocity of the fluid (u) is proportional to the pressure drop applied (the hydrodynamic pressure gradient), and inversely proportional to the viscosity of the fluid. The constant of proportionality is called the absolute permeability which is a rock property, and is dependent upon the pore size distribution. The superficial velocity is the average flowrate... 

The factors to consider in the selection of cross-flow filtration include the cross-flow velocity, the driving pressure, the separation characteristics of the membrane (permeability and pore size), size of particulates relative to the membrane pore dimensions, and the hydrodynamic conditions within the flow module. Again, since particle-particle and particle-membrane interactions are key, broth conditioning (ionic strength, pH, etc.) may be necessary to optimize performance. 

The effects of the concentration of divinylbenzene on pore-size distribution and surface areas of micropores, mesopores, and macropores in monosized PS-DVB beads prepared in the presence of linear polymeric porogens have been studied (65). While the total surface area is clearly determined by the content of divinylbenzene, the sum of pore volumes for mesoforms and macropores, as well as their pore-size distribution, do not change within a broad range of DVB concentrations. However, the more cross-linked the beads, the better the mechanical and hydrodynamic properties. 

The elution volume of a molecule in HPSEC is determined by its hydrodynamic size and the pore size of the column packing. In setting up an HPSEC experiment, the chromatographer must match the pore size of the column to the molecular size range of the sample. 

Shifts in the SEC fractionation range are not new. It has been known for decades that adding chaotropes to mobile phases causes proteins to elute as if they were much larger molecules. Sodium dodecyl sulfate (SDS) (9) and guanidinium hydrochloride (Gd.HCl) (9-12) have been used for this purpose. It has not been clearly determined in every case if these shifts reflect effects of the chaotropes on the solutes or on the stationary phase. Proteins are denatured by chaotropes the loss of tertiary structure increases their hydrodynamic radius. However, a similar shift in elution times has been observed with SEC of peptides in 0.1% trifluoroacetic acid (TEA) (13-15) or 0.1 M formic acid (16), even if they were too small to have significant tertiary structure. Speculation as to the cause involved solvation effects that decreased the effective pore size of the... 

Hydrodynamic volume refers to the combined physical properties of size and shape. Molecules of larger volume have a limited ability to enter the pores and elute the fastest. A molecule larger than the stationary phase pore volume elutes first and defines the column s void volume (Vo). In contrast, intermediate and smaller volume molecules may enter the pores and therefore elute later. As a measure of hydrodynamic volume (size and shape), SE-HPLC provides an approximation of a molecule s apparent molecular weight. For further descriptions of theoretical models and mathematical equations relating to SE-HPLC, the reader is referred to Refs. 2-5. 

Although most PCHdC studies are conducted using columns packed with nonporous gels, the hydrodynamic separation also occur in SEC columns. This can be easily observed using small pore-size SEC columns (29) as shown in... 

The HdC calibration curves of different particle sizes, as shown in Fig. 22.12 (30), are similar to the calibration curves of different pore size columns the separation ranges of MW due to hydrodynamic chromatography depend on particle size. The larger the particle size, the higher the MW ranges. Stegeman et al. (30) proposed that a smooth calibration curve may be achieved by proper ratio of the particle diameter to the pore diameter. 

In this process good hydrodynamics on the membrane surface are required to scour away the accumulated solids and prevent the membrane being blinded. This cannot be totally effective, and in practice the nominal membrane cut-off is often masked by the tendency of particulates to form a thin layer on the membrane surface whose effective pore size may be smaller. 

Porous packed systems represent in addition to the hydrodynamic effect, the possibility for separation due to size-related exclusion of particles from the pores, essentially LEG. In this section a brief overview of some of o ir more recent results pertaining to the question of pore size distribution effects will be given, fore detailed discussions are presented elsewhere (23>2U). 

A (3 fibril formation an identifiable nucleating species has yet be isolated. Direct observation has been made difficult by the small size of the (3 peptide, which has an effective hydrodynamic radius of 4 nm [98-100], and by the apparent low abundance of nucleating species due to the low probability of their formation. Such species would be formally akin to an enzyme transition state that is usually kinetically inferred or sometimes trapped with certain kinds of inhibitor. In disaggregated, ultrafiltered (20 nm pore size) preparations, less than 1% of the molar peptide concentration is inferred to be present as seeds or nuclei determined by the kinetics of fibril formation [101]. 

Synthetic peptides have relatively large Stokes radii and hydrodynamic volumes, and smaller diffusion coefficients, compared to low-molecular-weight organic pharmaceutical molecules. As a consequence, the mean pore size and the pore size distribution of the... 

Ksec = 0 when the molecule hydrodynamic radius is higher than the mean pore diameter. KSEC is 1 with small molecules, which can easily penetrate into the pores. The most important parameters influencing resolution are the pore volume, pore size distribution, and particle size. The separation domain is between the exclusion volume Va and the inclusion volume ( V0 + Vp). 

In summary, the effect of porosity on electrical conductivity and ion diffusivity in agarose gels is studied. Both electrical conductivity and ion diffusivity increase with porosity. The model obtained from the electrical conductivity data, i.e., Equation (7), can predict the diffusivity of macromolecules in 2% agarose gel for solutes with hydrodynamic radius less than the pore size of the gel. This study suggests that electrical conductivity method used in this study can be applied to investigating diffusion behavior of macromolecules in uncharged porous media. 

The permeability Ps is a measure of the transport of a molecule by diffusion. The reflection coefficient a of a given component is the maximal possible rejection for that component (at infinite solvent flux). Various models have been proposed for the reflection coefficient [75-77]. In the lognormal model [78], a lognormal distribution is assumed for the pore size. No steric hindrance in the pores or hydrodynamic lag is taken into account, but it is assumed that a molecule permeates through every pore that is larger than the diameter of the molecule. Moreover, the diffusion contribution to the transport through the membrane is considered to be negligible. Therefore, the reflection curve can be expressed as ... 

Surprisingly, intuition fails to predict the behavior of the same solute and solvent in a membrane with a uniform pore size larger than both the solvent and solute. The expectation that such a membrane will provide no rejection of the solute has been refuted repeatedly. Indeed, careful experiments indicate that partial rejection of the solute occurs even when the solute is considerably smaller (say 1/1 Oth as large as the pore size) (Miller, 1992 Deen, 1987 Ho and Sirkar, 1992 Happel and Brenner, 1965). The extent of rejection increases monotonically to the total rejection limit as the solute size approaches the pore size. These effects arise both from entropic suppression of partitioning and from augmented hydrodynamic resistance to transport through the fine pores. Thus, in this case, for a porous membrane, thermodynamic partitioning can play a role in the physical chemical processes of transport. 

Hindered transport of a solute moving within a continuum of solvent in a small pore can be analyzed in terms of classical hydrodynamics (Deen, 1987). The penetrant-to-pore size ratio (k) and the position of the penetrant within a... 

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