Kozeny-Carman relationship

The surface porosity is equal to the ratio of the pore area to membrane area multiplied by the number of pores. In most cases volume flux through ceramic membranes can be best described by the Kozeny-Carman relationship, which corresponds to a system of close packed spheres (see Figure 6.8a) ... 

Equation (30) gives a good description of transport through membranes consisting of a number of parallel pores. However, very few membranes possess such a structure in reality. Membranes consists a system of closed spheres, which can be found in organic and inorganic sintered membranes or in phase-inversion membranes with a nodular top layer structure. Such membranes can best be described by the Kozeny-Carman relationship ... 

As opposed to this, in ullrafiltration, membranes are porous in nature and the pore diameter varies between 2nm and 10 pm. The simplest representation of the membrane would be a set of parallel eylindrieal pores, and based on Kozeny-Carman relationship, the flux eould be written as... 

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 dimensionless separation impedance E depends on u (or F) and has a minimum like a van Deemter curve (middle right). With the Kozeny-Carman factor of ffi = 1000 we come to the relationship ... 

A relationship between porosity and permeability based on the Kozeny-Carman equation... 

As we know from experience, the backpressure of a column packed with small particles is larger than the backpressure of a column packed with larger particles. The specific permeability depends on the particle size d, and the interstitial porosity e, of the packed M. The relationship is known as the Kozeny-Carman equation (16,17) ... 

Perturbation theory cannot be applied to describe the effect of the strong roughness. An approach based on Brinkman s equation has been used instead to describe the hydrodynamics in the interfacial region [82]. The flow of a liquid through a nonuniform surface layer has been treated as the flow of a liquid through a porous medium [83-85]. The morphology of the interfacial layer of thickness, L, has been characterized by a local permeability, that depends on the effective porosity of the layer, (j). A number of equations for the permeability have been suggested. For instance, the empirical Kozeny-Carman equation [83] yields a relationship... 

Thus, from the Kozeny-Carman theory, the relationship between porosity and permeability is given by the relation... 

Obtain a relationship for the ratio of the terminal falling velocity of a particle to the minimum fluidising velocity for a bed of similar particles. It may be assumed that Stokes Law and the Carman-Kozeny equation are applicable. What is the value of the ratio if the bed voidage at the minimum fluidising velocity is 0.4 ... 

To calculate the reduction in the concentration of surfactant in the fluid by adsorption it is necessary to have an estimation of the inner surface area of the reservoir. This parameter is related to the porosity of the medium and to its permeability. Attempts have been made to correlate these two quantities but the results have been unsuccessful, because there are parameters characteristic of each particular porous medium involved in the description of the problem (14). For our analysis we adopted the approach of Kozeny and Carman (15). These authors defined a parameter called the "equivalent hydraulic radius of the porous medium" which represents the surface area exposed to the fluid per unit volume of rock. They obtained the following relationship between the permeability, k, and the porosity, 0 ... 

If the first set of measurements is given subscript 1 and the second subscript 2, and if s stands for the gradient of pressure drop with gas velocity, pb is bulk density and pp is the particle effective density, it can be shown (using the well-known Carman-Kozeny equation) that the basic relationship is as follows ... 

In the literature, there exists a relationship which relates the permeability K with the relative density p, and the mean pore size d of porous object [13]. This relation is called the Carman-Kozeni equation... 

When a fluid passes vertically through a bed of particles the pressure drop APg will initially increase as the velocity u is increased, as shown in Figure 7.2. The relation between pressure drop and velocity will be that applicable to a fixed bed. For fine particles, the increasing straight line in Figure 7.2 has been properly described by a relationship known as the Carman-Kozeny equation ... 

For fine particles the pressure drop-velocity relationship will be given by the Carman-Kozeny equation, which will take the following form for incipient fluidization ... 

Carman Equation. A relationship, derived from kozeny s equation (q.v.), permitting determination of the specific surface, S, of a powder from permeability measurements ... 

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