## 1 Introduction
In view of better understanding the extent of surface modification of stones after the application of a protective product or formulation, a potentially useful contribution may come from electrokinetic analysis based on streaming potential/streaming current measurements. As far as macroscopic and non-conductive solid materials are concerned, these measurements have established themselves as valuable tools for investigating the chemical properties of solid/liquid interfaces [11] and, in particular, for pinpointing the contribution of the surface chemical composition to the electrostatic component of the overall interaction with an electrolyte-carrying aqueous medium. Moreover, it must be considered that, in the case of a porous substrate, an aqueous medium is also likely to interact with the outermost layer of the pore network, and since the latter may be significantly modified upon application of a protective treatment, electrokinetic analysis may allow a more complete and far-reaching characterization of treatment-induced changes of surface properties. The theoretical foundations of electrokinetic techniques were laid more than one century ago by [PERSON] [12], who introduced the fundamental concept of zeta potential and described its measurement by drawing on [PERSON]'s theory of the electrical double layer (EDL). Zeta potential is defined as the electric potential at the slip plane of a solid/electrolyte interface, the slip plane being a virtual surface separating the layer of molecules and ions immobilized by adsorption onto the solid surface (roughly the Stern layer) from the rest of the EDL where they are free to move. Its magnitude reflects the net charge density at the solid surface and the charge distribution in the EDL and is an indicator of the ability of the solid material to establish electrostatic interactions with charged species (ions of the electrolyte, colloidal particles) coming close to its surface. In a streaming current or a streaming potential measurement, a macroscopic laminar flow of the electrolyte fluid tangential to the solid surface is induced by a hydrostatic pressure gradient, resulting in a net charge flow if the EDL presents an unbalanced ionic composition, as is the case when the zeta potential is not zero. This convective transport of mobile ions in the direction of the liquid flow, which is called streaming current, can be detected directly by measuring the electric current between two non-polarizable electrodes positioned up- and down-stream, respectively, with an electrometer of sufficiently low internal resistance. Alternatively, the electric potential generated by the convective charge transport, or streaming potential, can be measured between the same two electrodes with a high-input impedance voltmeter. According to the Smoluchowski model, if the EDL is sufficiently thin and the flow is laminar, the zeta potential is directly proportional to the derivative of streaming current (I\({}_{8}\)) with respect to the applied pressure difference (\(\Delta\)p), according to Equation (1):  
\[\zeta=\frac{\mathrm{d}I_{8}}{\mathrm{d}\Delta\mathrm{p}}.\frac{\eta\cdot \kappa}{\varepsilon_{0}\cdot\varepsilon}\cdot\mathrm{R}, \tag{1}\]  
where \(\kappa\), \(\varepsilon\) and \(\eta\) are the electrical conductivity, dielectric constant and viscosity of the bulk electrolyte solution, respectively, \(\varepsilon_{0}\) is the vacuum permittivity and \(\mathrm{R}\) is the electrical resistance of the streaming channel. Currently, the electrokinetic characterization via streaming current/streaming potential measurements is the most straightforward technique for measuring the zeta potential of macroscopic solid surfaces, and it has been used for a broad range of materials, including paper, textiles, membranes, biomaterials, soil and minerals [13; 14; 15; 16; 17; 18; 19].