Doubly conjugate asymptotic analysis for the temperature and electric fields in a combined gel and stratum corneum system

In the present work, we study with the aid of regular perturbation techniques under what physical conditions, the thermal and electrical simultaneous interactions that occur between a gel and a stratum corneum of the skin, can operate in direct contact to avoid possible damage to the human skin. This doubly conjugate asymptotic analysis was formulated in terms of a pair of dimensionless conservation equations for the energy and electrical charge in each medium and it was solved by using asymptotic perturbation techniques, identifying a dimensionless parameter, denoted as β, that measures the competition of electrical conductivities in the two medium affected by the electrical pulse. Because the electrical conductivity of the stratum corneum is very small, this parameter assumes usually very large values compared with unity and the theoretical predictions show the relevance that this parameter has on the increment of the temperature in both media. Therefore, we consider that this parameter can guide a positive performance of this class of medical treatments based on electric signals because delimits, under transient conditions, up to where the simultaneous presence of thermal and electrical effects control the reversible skin electroporation. The asymptotic analysis was validated with experimental data of other authors and a numerical solution of the full governing equations. [Display omitted] •Asymptotic methods used to solve a double conjugate problem for the skin electroporation.•Moderate voltages and very short pulse times are required to obtain the better operation conditions.•The Joule effect dominates on the gel and it is a weak effect for the stratum corneum.