Study of Existence, Uniqueness, Regularity and Asymptotic Behaviour of Solutions to The Poisson-Boltzmann Equation

Electrokinetic phenomena have an important connection to microfluidics because electrolytes can be used to manipulate small masses of fluids by means of suitably applied electric fields. Fluids at such small scales appear both in various natural systems and in microdevices intended for applications ranging from gene sequencing and gene expression to micropixels in electronic paper. Perhaps one of the most interesting applications of electrokinetic effects is electrowetting. Electrowetting has become one of the most widely used tools for manipulating tiny amounts of liquids on surfaces. Applications range from “lab-on-a-chip” devices [14] to adjustable lenses and new kinds of electronic displays [9], [10]. The presence of free charges creates or modifies an imposed electric field in an electrolyte. This is expressed by means of Poisson’s equation