**2. Zeta potential approach**

Zeta potential is defined as the difference in potential between the particle and its ionic atmosphere surrounding medium, measured in the plane of shear, as depicted in **Figure 2** [10]. In the ideal case, the potential at the Stern layer, *Ψd*, is desired potential. However, due to the non-conductive nature of most minerals, it becomes challenging to measure it [11]. Thus, zeta potential measurements are

#### **Figure 2.**

*Diagram illustrating the surface potential, stern potential, and zeta potential as a function of distance of a negatively charged particle in a dispersion medium.* 

considered that are slightly greater than the Stern potential [10]. Mechanistically speaking, when a solid particle is dissolved in water, the charge on its surface leads to the formation of counterions [12]. For example, in the case of a limestone slurry, the co- and counterions, Ca2+ and OH<sup>−</sup>, are formed. The charged particles then attract a layer of counterions from the aqueous phase, known as the Stern layer.

 Due to ionic radius considerations, the strongly adsorbed anions do not fully offset the surface charge, and hence, a second layer of more loosely held counterions forms, known as the diffuse layer. This diffuse layer is made of free ions which are mobile under the influence of electric attraction and thermal motion. The two layers combined are known as the electric double layer (EDL). At a certain distance away from the charged particle, the surface charge will be fully balanced by the counterions, and beyond this point, a bulk suspension with a balance of positive and negative electrolyte exists [9, 12]. Particles, with a high surface charge, form a large double layer, which prevents particles from getting close to each other because of the electrostatic repulsion between them due to identical charges. However, this behavior aids in stabilizing suspensions [13].

Due to the presence of electric charges in an applied electric field, different phenomena occur in the system, which are collectively known as electrokinetic effects. The zeta potential can be measured based on different phenomena classified as electrokinetic or electroacoustic. Electroacoustic differs from electrokinetic as the former uses ultrasound waves to induce movement of particles in one direction. Unlike the latter, it does not utilize an electric field. However, they are both used to measure the surface charges of stable suspensions composed of small particles of sizes less than 10 μm.

#### **2.1 Electrokinetic measurement**

The electrokinetic phenomena are differentiated based on the induced motion of particles [14]. These techniques include:


#### *2.1.1 Electrophoresis*

Electrophoresis is considered to be the most widely used technique in electrokinetics to measure the zeta potential. It considers the movement of a charged particle relative to its liquid medium under the influence of the electric field [14]. It occurs when an electric field is applied across the sample electrolyte and causes the suspended particles to move [14]. However, with an opposing viscous force, equilibrium is achieved. As a result, the particles move with constant velocity. This velocity, or electrophoretic mobility, depends on [14]:


The electrophoretic mobility is measured in a microelectrophoresis system. This system consists of a cell with electrodes at both ends applying a potential across the sample. The suspended particles will move toward the opposite-charged electrode during which the velocity is measured.
