Carman equation

The specific resistance coefficient for the dust layer Ko was originally denned by Williams et al. [Heat. Piping Air Cond., 12, 259 (1940)], who proposed estimating values of the coefficient by use of the Kozeny-Carman equation [Carman, Trans. Inst. Chem. Fng. (London), 15, 150 (1937)]. In practice, K and Ko are measured directly in filtration experiments. The K and Ko values can be corrected for temperature by multiplying by the ratio of the gas viscosity at the desired condition to the gas viscosity at the original experimental conditions. Values of Ko determined for certain dfists by Williams et al. (op. cit.) are presented in Table 17-5. 

Carman equation is not vahd at void fractions greater than 0.7 to 0.8 (Billings and Wilder, op. cit.). In addition, in situ measurement of the void fraction of a dust layer on a filter fabric is extremely difficult and... 

Clearly, the factors determining Ko are far more complex than is indicated by a simple application of the Kozeny-Carman equation, and when possible, filter design should be based on experimental determinations made under conditions approximating those expected in the planned installation. 

Estimation of the pressure-drop The system is designed to work within a given pressure limit thus, one needs a relation giving the pressure-drop in the column (per unit length). Darcy s law gives the relation of AP/L versus the mobile phase velocity u. However, the Kozeny-Carman equation is best adapted for laminar flows as described ... 

Kovats RI scale 176 Kozeny-Carman equation 11 Kubelka-Hunk equation (TLC) 705 Kuderna-Danish concentrator 763... 

The determination of the specific surface area of a powder by air permeability methods essentially involves the measurement of the pressure drop across a bed of the powder under carefully controlled flow conditions. The data obtained are substituted in the Kozeny-Carman equation to estimate the specific surface area. Permeability methods have certain advantages, one of them being that the equipment used for carrying out the measurements is cheap and robust. Another advantage is that sample problems are minimized because a large sample of powder is required to be used for analysis. 

Because of the assumptions underlying its derivation, the Kozeny-Carman equation is not valid at void fractions greater than 0.7 to 0.8 (Billings and Wilder, op. cit.). In addition, in situ measurement of the void fraction of a dust layer on a filter fabric is extremely difficult and has seldom even been attempted. The structure of the layer is dependent on the character of the fabric surface as well as on tfie characteristics of the dust, whereas the application of Eq. (17-12) implicitly assumes that K2 is dependent only on the properties of the dust. A smooth fabric surface permits the dust to become closely packed, leading to a relatively high value of K2. If the surface is napped or has numerous extended fibrils, the dust cake formed will be more porous and have a lower value of K2 [Billings and Wilder, op. cit. Snyder and Pring, Ind. Eng. Chem., 47, 960 (1955) and K. T. Semrau, unpublished data, SRI International, Menlo Park, Calif., 1952-1953]. 

Re Modified Reynolds number based on pore size as used by Carman (equation 4.13) — —... 

Kinetics, of secondary equilibria, 159 Kovats index, 280 Kozeny-Carman equation, 6... 

Continuous strand mats are approximately isotropic and have almost the same permeability in all directions (in the plane of the fabric). Many other fabrics, however, are strongly anisotropic and have different permeability in different directions. Gebart [18] proposed a model for this class of fabrics derived theoretically from a simplified fiber architecture. The model, which is valid for medium to high fiber volume fractions, was developed for unidirectional fabrics, but it can also be used for other strongly anisotropic fabrics. In this model the permeability in the high permeability direction (which is usually, but not always, in the direction of the majority of fibers) follows the Kozeny-Carman equation (Eq. 12.2). In the perpendicular direction, however, it is ... 

Liquid infiltration into dry porous materials occurs due to capillary action. The mechanism of infiltrating liquids into porous bodies has been studied by many researches in the fields of soil physics, chemistry, powder technology and powder metallurgy [Carman, 1956 Semlak Rhines, 1958]. However, the processes and kinetics of liquid infiltration into a powdered preform are rather complex and have not been completely understood. Based on Darcy s fundamental principle and the Kozeny-Carman equation, Semlak Rhines (1958) and Yokota et al. (1980) have developed infiltration rate equations for porous glass and metal bodies. These rate equations can be used to describe the kinetics of liquid infiltration in porous ceramics preforms, but... 

Here p is the density of the infiltrant,, > is the acceleration due to gravity (9.8 m/s2) and Patm is the pressure of the surrounding space above the liquid infiltrant. This model is useful for predicting the influence of pressure on the rate of infiltration. Another formula is the Kozeny-Carman equation [Carman, 1956] ... 

The Kozeny-Carman equation is suitable for the laminar flows met in chromatography ... 

All of the permeability methods are based on the Kozeny-Carman equation, which is used to calculate a surface area of a packed powder bed from its permeability. The Kozeny-Carman equation is expressed as [16]... 

At low selectivity to achieve the same resolution, one has to use a longer column to increase efficiency and consequently operate under higher-pressure conditions. The relationship between the column length, mobile-phase viscosity, and the backpressure is given by equation (2-17), which is the variation of the Kozeny-Carman equation. Expression (2-17) predicts a linear increase of the backpressure with the increase of the flow rate, column length, and mobile phase viscosity. The decrease of the particle diameter, on the other hand, leads to the quadratic increase of the column backpressure. 

The permeability of the reaction medium is a function of porosity, given by the Kozeny-Carman equation. 

The constant Bo characterises the permeability of the column, which depends on the interstitial porosity of the column, c, (with regularly packed columns, e, is usually close to 0.40) and increases with the second power of the mean particle diameter, dp. From the Koz.eny-Carman equation [16.171 it follows ... 

For particles under viscous conditions and Re < 1 a more simplified form, known as the Kozeny-Carman equation, can be used to calculate the pressure drop within the chromatographic column. 

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