Quantitative measurement of pore flux

Because the theory is relatively simple and well developed, the tip collection mode has been employed extensively for quantitative measurements of pore flux and radius. 

These techniques involving the measurement of membrane permeability to a fluid (liquid or gas) lead to a mean pore radius (usually the effective hydraulic radius Th) whose quantitative value is often highly ambiguous. The flux of a fluid through a porous material is sensitive to all structural aspects of the material [129]. Thus, in spite of the simplicity of the method, the interpretation of flux data, even for the simplest case of steady state, is subject to uncertainties and depends on the models and approximations used. 

There is also the effect of the structure of the porous material. For a nonequilibrium measurement of diffusion, one can consider that there is no straight path for solutes to travel in the direction of the flux. In an equilibrium measurement of intradiffusion, this represents the fact that solutes are not longer subject to a purely random walk. When a solute is near a pore surface, the probabilities for moving in each direction are no longer uniform certain directions are prohibited by the pore wall. For technical precision, then, one should differentiate between a structure factor and a tortuosity. A tortuosity, t, quantitatively describes experimental results in which multiple interactions affect the diffusion. A structure factor, q, quantitatively describes only the effect of pore space geometry and topology on diffusion. Note that for limited conditions—when studying diffusion of small molecules and a passive pore surface—this allows for x cj. 

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