Electrical structures of interfaces: a Painleve II model

Bass, L., Nimmo, J. J. C., Rogers, C. and Schief, W. K. (2010) Electrical structures of interfaces: a Painleve II model. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 466(2119), pp. 2117-2136. (doi: 10.1098/rspa.2009.0620)

Abstract

A Painleve II model derived out of the classical Nernst-Planck system is applied in the context of boundary value problems that describe the electric field distribution in a region x > 0 occupied by an electrolyte. For privileged flux ratios of the ion concentrations, the auto-Backlund transformation admitted by the Painleve II equation may be applied iteratively to construct exact solutions to classes of physically relevant boundary value problems. These representations involve, in turn, either Yablonskii-Vorob'ev polynomials or classical Airy functions. The requirement that the electric field distribution and ion concentrations in these representations be non-singular imposes constraints on the physical parameters. These are investigated in detail along with asymptotic properties.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Nimmo, Dr Jonathan
• Authors: Bass, L., Nimmo, J. J. C., Rogers, C., and Schief, W. K.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences
• ISSN: 1364-5021
• ISSN (Online): 1471-2946