Department of Mathematics
National Taiwan University
To describe ionic liquids with finite size effects involving different ion radii and valences, we derive new PNP (Poisson-Nernst-Planck) type systems and develop mathematical theorems for these systems. Symmetry and non-symmetry breaking conditions are represented by their coupling coefficients. When non-symmetry breaking condition holds true, we prove the existence theorems of solutions of new PNP type systems. On the other hand, when symmetry breaking condition holds true, two steady state solutions can be found and the excess currents (due to steric effects) associated with these two steady state solutions are derived and expressed as two distinct formulas. Our results indicate that new PNP type systems may become a useful model to study ionic liquids and related topics of liquid crystals.