“…Despite the fact that these equations have been well known and studied for over a century, they remain of current interest because of applications ranging from batteries (Torabi & Aliakbar, 2012;Venkatraman & Van Zee, 2007), bioelectric dressings used in wound healing (Banerjee et al, 2014), diffusion of charged species through ion channels in cell membranes and ion selective membranes (Coalson & Kurnikova, 2005;Fíla & Bouzek, 2003), electro-osmosis in micro and nano-channel systems (Hrdlička, Červenka, Přibyl, & Šnita, 2010), transport of charge carriers in semiconductors (Markowich, 1986), ionic current rectification through charged micro and nano channels (Chein & Chung, 2013) to as diverse a field as deterioration of reinforced concrete structures due to diffusion and attack by the chloride ion (K. Krabbenhøft, & J. Krabbenhøft, 2008). In their most general form (unsteady, 3-D), the PNP equations are usually solved numerically.…”