Capillaries description

At first we tried to explain the phenomenon on the base of the existence of the difference between the saturated vapor pressures above two menisci in dead-end capillary [12]. It results in the evaporation of a liquid from the meniscus of smaller curvature ( classical capillary imbibition) and the condensation of its vapor upon the meniscus of larger curvature originally existed due to capillary condensation. We worked out the mathematical description of both gas-vapor diffusion and evaporation-condensation processes in cone s channel. Solving the system of differential equations for evaporation-condensation processes, we ve derived the formula for the dependence of top s (or inner) liquid column growth on time. But the calculated curves for the kinetics of inner column s length are 1-2 orders of magnitude smaller than the experimental ones [12]. 

Usually one varies the head of mercury or applied gas pressure so as to bring the meniscus to a fixed reference point [118], Grahame and co-workers [119], Hansen and co-workers [120] (see also Ref. 121), and Hills and Payne [122] have given more or less elaborate descriptions of the capillary electrometer apparatus. Nowadays, the capillary electrometer is customarily used in conjunction with capacitance measurements (see below). Vos and Vos [111] describe the use of sessile drop profiles (Section II-7B) for interfacial tension measurements, thus avoiding an assumption as to the solution-Hg-glass contact angle. 

At very low densities It Is quite easy Co give a theoretical description of thermal transpiration, alnce the classical theory of Knudsen screaming 9] can be extended to account for Che Influence of temperature gradients. For Isothermal flow through a straight capillary of circular cross-section, a well known calculation [9] gives the molar flux per unit cross-sectional area, N, In the form... 

Although each capillary electrophoretic method has its own unique considerations, the following description of the determination of a vitamin B complex provides an instructive example of a typical procedure. 

A microscopic description characterizes the structure of the pores. The objective of a pore-structure analysis is to provide a description that relates to the macroscopic or bulk flow properties. The major bulk properties that need to be correlated with pore description or characterization are the four basic parameters porosity, permeability, tortuosity and connectivity. In studying different samples of the same medium, it becomes apparent that the number of pore sizes, shapes, orientations and interconnections are enormous. Due to this complexity, pore-structure description is most often a statistical distribution of apparent pore sizes. This distribution is apparent because to convert measurements to pore sizes one must resort to models that provide average or model pore sizes. A common approach to defining a characteristic pore size distribution is to model the porous medium as a bundle of straight cylindrical or rectangular capillaries (refer to Figure 2). The diameters of the model capillaries are defined on the basis of a convenient distribution function. 

Sec. Ill is concerned with the description of models with directional associative forces, introduced by Wertheim. Singlet and pair theories for these models are presented. However, the main part of this section describes the density functional methodology and shows its application in the studies of adsorption of associating fluids on partially permeable walls. In addition, the application of the density functional method in investigations of wettability of associating fluids on solid surfaces and of capillary condensation in slit-like pores is presented. 

The present model takes into account how capillary, friction and gravity forces affect the flow development. The parameters which influence the flow mechanism are evaluated. In the frame of the quasi-one-dimensional model the theoretical description of the phenomena is based on the assumption of uniform parameter distribution over the cross-section of the liquid and vapor flows. With this approximation, the mass, thermal and momentum equations for the average parameters are used. These equations allow one to determine the velocity, pressure and temperature distributions along the capillary axis, the shape of the interface surface for various geometrical and regime parameters, as well as the influence of physical properties of the liquid and vapor, micro-channel size, initial temperature of the cooling liquid, wall heat flux and gravity on the flow and heat transfer characteristics. 

In this section we present the system of quasi-one-dimensional equations, describing the unsteady flow in the heated capillary tube. They are valid for flows with weakly curved meniscus when the ratio of its depth to curvature radius is sufficiently small. The detailed description of a quasi-one-dimensional model of capillary flow with distinct meniscus, as well as the estimation conditions of its application for calculation of thermohydrodynamic characteristics of two-phase flow in a heated capillary are presented in the works by Peles et al. (2000,2001) and Yarin et al. (2002). In this model the set of equations including the mass, momentum and energy balances is ... 

OS 79] ]R 17] ]no protocol] 4-Methoxybenzaldehyde and methyl diethoxyphos-phonoacetate were reacted by means of the Wittig-Horner-Emmons reaction [85] (see a more detailed description in [42]). A modified micro reaction system consisting of two mixers, for deprotonation of the phosphonates and introduction of the aldehyde, connected to an HPLC capillary of 0.8 m length and 0.25 mm diameter was employed. The micro reactor showed higher yields than laboratory batch synthesis. 

Cross-flow is the usual case where cake compressibility is a problem. Cross-flow microfiltration is much the same as cross-flow ultrafiltration in principle. In practice, the devices are often different. As with UF, spiral-wound membranes provide the most economical configuration for many large-scale installations. However, capillary devices and cassettes are widely employed, especially at smaller scale. A detailed description of cross-flow microfiltration had been given by Murkes and Carlsson [Crossflow Filtration, Wiley, New York (1988)]. 

Before discussing column preparation procedures a few comments on nomenclature are in order. Open tubular columns are also widely known as capillary columns. The characteristic feature of these columns is their openness, which provides an unrestricted gas path through the column. Thus open tubular colximn rather than capillary column is a more apt description. However, both descriptions appear frequently in the literature and can be emsidered interchangeable. The type of columns discussed so far are also known as wall-coated open tubular columns (WCOT). Here the liquid phase is deposited directly onto the column wall without the inclusion of any additive that might be considered as... 

Peng, X., Bowser, M.T., Britz-McKibbin, P., Bebault, G.M., Morris, J.R., and Chen, D.D.Y., Quantitative description of analyte migration behavior based on dyamic complexation in capillary electrophoresis with one or more additives, Electrophoresis, 18, 706, 1997. 

Currently used equations for water flow in unsaturated soil are based on the assumption that soils are similar to a bundle of capillary tubes and that water flow can be approximated by the Hagen-Poiseuille equation.58 While it is obvious that the pore space in soil is not the same as a bundle of capillary tubes, the concept has proven highly useful and is currently used in mathematical descriptions of water flow in soil. 

Kapur and Fuerstenau (K5) have presented a unified description of the agglomeration process in which the phenomena of the compaction of the agglomerates and their passage through the various capillary regimes have... 

FIGURE 15.2 The concept of capillary viscosity measurement. See text for full description. 

Since a comprehensive description of all monolithic materials would exceed the scope of this chapter and a number of other monolithic materials are also described elsewhere in this volume, this contribution will be restricted mainly to monoliths for chromatographic purposes and prepared by polymerization of monomer mixtures in non-aqueous solvents. Monolithic capillary columns for CEC are treated in another chapter and will not be presented in detail here. 

Novel general expressions were developed for the description of the behaviour of the height equivalent of a theoretical plate in various chromatographic columns such as unpacked (open capillary), packed with spherical nonporous particles and packed with spherical porous adsorbent particles. Particles may have unimodal or bimodal pore size distribution. The expression describing the mass balance in open capillaries is... 

One of the major advantages of CE as a separation technique is the wide variety of separation modes available. Analytes can be separated on the basis of charge, molecular size or shape, pi, or hydrophobicity. The same CE instrument can be used for zone electrophoresis, IEF, sieving separations, isotachophoresis, and chromatographic techniques such as MEKC and capillary electrokinetic chromatography. This section provides a brief description of each separation mode. Zone electrophoresis, IEF, and sieving are the primary modes used for protein separations, and these will be discussed in detail in the following sections. 

Cryostats have been much used in small-molecule crystallography because they allow rapid cooling to very low temperatures with minimal cold gas consumption and offer great advantages in the area of frost prevention. Unfortunately, most designs employ beryllium shrouds or other nontransparent material, and are of a size which does not lend itself to crystals mounted in capillary tubes and flow cells. A recent advance is the description of a Mylar cryostat specifically designed for... 

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