Hagen-Poiseuille-Kozeny equation

It is indicated that these transport parameters are functions of A. The hydraulic permeability (D Arcy coefficient), /Cp (A), exhibits strong dependence on A because larger water contents result in an increased number of pores used for water transport and better connectivity in the porous network, as well as in larger mean radii of these pores. A modification of the Hagen-Poiseuille-Kozeny equation was considered by Eikerling et aU- to account for these structural effects ... 

For K w) a percolation-type modification of the Hagen-Poiseuille-Kozeny equation is considered... 

Liquid permeability Hagen- Poiseuille Kozeny- Carman Cylindrical Voids between spheres 0.1-10 p Pore hydraulic radius Experimental simplicity. Assumptions laminar flow in HP equation, zero wetting angle, no pre-existing agent on the surface. Great influence of pore geometry and tortuosity on the interpretation of results. Network effects. 

For the description of this flow, the Carman-Kozeny expression [16] can be applied, since the Hagen-Poiseuille equation is not valid, given that usually inorganic macroporous and mesoporous membranes are prepared by the sinterization of packed quasispherical particles, which develop a random pore structure [19]. In this case, the Carman-Kozeny factor for a membrane formulated with pressed spherical particles is [74]... 

Generally, the pure solvent transporting through porous UF membranes is directly proportional to the applied transmembrane pressure (AP). The Kozeny-Carman and Hagen-Poiseuille equations describe the convection flow (J ) as follows (49) ... 

For membranes with straight capillaries as pores the Hagen-Poiseuille equation (2) applies, while the Karman-Kozeny equation (3) various forms of this equation have been applied) is valid for transport through membranes with a more nodular structure. 

When the pressure is increased further the flux increases linearly with pressure, see figure IV - 13). The Hagen-PoLscuillc relationship assumes that the pores in the membrane are cylindrical but generally this is not the case. Therefore, these limitations should be considered carefully in applying this equation.The Kozeny-Cannan equation can be used instead of the Hagen-Poiseuille equation. It is assumed in this equation that the pores are interstices between close-packed spheres as can be found in sinter structures. Tlie flux is given by cq. IV - 6. 

This is a typical equation for porous membranes where the volume flux is proportional to the pressure difference (see, for example, the Kozeny-Carman and Hagen-Poiseuille equations for porous membranes). 

In spite of this, there are today computer programmes [1—3], which are gaining in significance for operational practice, based on the Hagen—Poiseuille Law which has been known for decades, and the experimental equations of Darcy, Kozeny-Carman [4]. 

All these methods lead to a set of parameters (membrane thickness, pore volmne, hydraulic radius) which are related to the working (macroscopic) permselective membrane properties. In the case of liquid permeation in a porous membrane, macro- and mesoporous structures are more concerned with viscous flow described by the Hagen-Poiseuille and Carman-Kozeny equations whereas the extended Nernst-Plank equation must be considered for microporous membranes in which diffusion and electrical charge phenomena can occur (Mulder, 1991). For gas and vapor transport, different permeation mechanisms have been described depending on pore sizes ranging from viscous flow for macropores to different diffusion regimes as the pore size is decreased to micro and ultra-micropores (Burggraaf, 1996). 

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