The Capillary Model of a Low-permeable Porous Medium

The flow of solution through a layer of gel that was considered in the previous section is an example of flow through a porous environment. At small Reynolds 

The velocity U is defined as the ratio of the liquid s volume flow rate to the net cross section of all spacings between particles in the given layer of porous medium. It is obvious that U Ug, since also includes the volume flow rate of liquid through the pores of particles. The constant k is known as permeability (its dimensionality is m ). In order to determine k, we must choose a certain model of porous medium. A low-permeable porous medium can be conceptualized as a medium consisting of a set of microchannels of diameter de (it is called hydraulic, or equivalent, diameter). This diameter is usually defined as 

Porosity is defined as the fraction of empty space in the gel layer  

Introduce the parameter s - specific area which is equal to the ratio of the cross - sectional area of the reservoir to the volume fraction of gel particles in the reservoir  

Comparing (6.267) with (6.260), we get the following expression for permeability of a porous medium  

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