GNGTS 2014 - Atti del 33° Convegno Nazionale

capillary increases while at the opposite side it decreases. Decreasing of concentration cannot continue infinitely: it will reach zero causing a rupture of the electrical circuit. No electrical current flows through the capillaries any more, since the current pass is blocked. Calling t 0 the time of blockage, i.e. the time when rupture of the electrical circuit occurred, it has been shown (for more details we address the reader to the above-cited papers by Zadorozhnaya) that, for cations and anions respectively the following equation apply: (3) t 0 is controlled by current I and it depends on transfer numbers n a and n k , i.e. on pore radii of the connected pores and on the conductivity of pore fluid σ k and σ a . In Eq. (3) S 1 : is the surface area of the central pore, S 2 : and S 3 : are surface areas of left and right pores/channels respectively, F : the Faraday number, z : valence, u 0 : ion’s salinity of free solution. Subscripts k and a indicate captions and anions, respectively. The amplitude of the potential difference (voltage) also depends on the mobility’s of both anions M a and cationes M k and on the diffusion coefficient D too. The process of polarization continues up to time t 0 , after which the rupture of the electrical circuit occurs and the potential difference between the ends of the pore becomes constant. During the polarization process all contacts between pores of different transfer numbers will be blocked and the electrical current will flow through the remaining pore channels. This brings us to define the phenomenon of membrane polarization as the successive blockage of inter-pore connections due to the excess/loss distribution of ions during current flow. Under these premises, it can be shown that both resistivity and chargeability of a model built by many capillaries of different diameters depend on current intensity, which means that the electrical behavior is not linear. Moreover, since the response of the model depends on the pore-size parameterization, i.e. the amount of non-linearity can be predicted, the inverse path is also possible, i.e. it becomes possible to estimate the pore-size distribution using measurements made in the non-linear range of the supplied electrical current. Another consequence of the mechanism, which produces the excess of ions concentration at the boundary between pores, is that it depends on time of the applied current: �� ��� ����� if the pulse length is short, then the excess of the ions is small and time of levelling (discharging) is also short. However, increasing current pulse length the membrane effect increases. The direction of accumulation of ions along the boundaries is the same as the current flow; therefore the direction of discharge is also the same as the direction of transient emf. That is why the resistivity of bodies, where this membrane IP effect occurs, can considerably decrease. To account for the time-dependence of the phenomenon, the solution of the constitutive diffusion equation: (4) which led to Eq. (3), consists of numerous exponentials. For a preliminary interpretation we assumed that the membrane IP effect could be modelled using Cole-Cole model [Eq. (2)] with Tab. 3 - 1D models of sounding 3 using the Cole-Cole formula and eq. (4) at 4 Hz repetition rate. # of layer ρ Ohmm h m η 1 τ 1 s η 2 τ 2 s a 2 1 50 28 4.0e-3 0.032 2.0e-2 0.5 0.17 2 1.5 25 - - - - - 3 1.1 25 - - - - - 4 2.0 29 - - - - - 164 GNGTS 2014 S essione 3.2