Calculation of re-defined electrical double layer thickness in symmetrical-electrolyte solutions

An electrical double layer (EDL) has crucial roles to play in diverse chemical/physical/biological phenomena and technological processes. The thickness of an EDL is one of the most important characteristics significantly affecting the value of zeta and streaming potentials, physicochemical properties of solutions, concentration polarization, the extent of stability of colloidal systems, coagulation and flocculation of colloids, etc. Although such thickness seems to be a straightforward characteristic of charged particles in contact with electrolyte solutions, there is no universal consensus among specialists on its definition and quantification. In spite of being incorporated in interface and colloid science for a century, the EDL thickness still has remained a dubious concept as there exist a variety of perceptions between scientists, researchers, and engineers. Unfortunately, the quantification of EDL thickness in current practices is founded primarily on rules of thumb with poor scientific justifications. Our comprehensive review of the literature shows that the EDL thickness is taken to be the Debye-Huckel length (i.e., kappa(-1)) in a lot of applications, but sometimes the thickness is assumed to be equal to a few times kappa(-1). Such an assumption ignores the fact that the distribution of electric potential, and consequently EDL thickness, around a charged particle is affected by surface properties such as surface charge density and particle size. In other words, the common practice of kappa(-1)-EDL-thickness suffers from not taking into account several other key factors contributing to the spatial extension of an EDL. This study is directed at development of theoretical physics-based formulas for accurate quantification of EDL thickness in symmetrical electrolyte solutions in different coordinate systems. The new analytical expressions are founded on the basis of exact or approximate solutions of the Poisson-Boltzmann (PB) equation for plate-like, cylindrical, and spherical charged particles. In fact, one of the targets of the present research work is to analytically address factors other than kappa(-1) affecting EDL thickness. Eventually, the degree of deviation of the commonly-used rule-of-thumb kappa(-1)-thickness from the corresponding exact value is investigated by conducting sensitivity analyses over wide ranges of influential parameters.