Straight capillaric model

The simplest capillaric model is the one representing a porous medium by a bundle of straight parallel capillaries of average diameter 5, as shown in Fig. 5.14. The equivalent voidage a can be related to the averaged diameter by 

Let us first consider the case when a flow passes through a single circular tube. The flow is assumed to be steady, incompressible, highly viscous, and fully developed. Thus, the radial velocity distribution can be obtained as (Problem 5.6) 

By comparing the preceding equation with Darcy s law, the specific permeability k can be given as 

It is noted that straight capillary tubes may not portray the complex structure of the porous medium. Thus, in practice, the factor 32 in Eq. (5.321) is commonly replaced by an empirical parameter known as tortuosity. The tortuosity accounts for the tortuous paths of the porous medium. 

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With the aid of the straight capillaric model and according to the Hagen-Poiseuille equation and Darcy s law, a is proportional to the viscosity of the fluid. Thus, Eq. (5.322) becomes... 

The porous medium may be assumed to consist of a bundle of straight capillaries of equal size (capillaric model). A particle follows a certain trajectory and is captured when it hits the wall. 

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