Inhomogeneous electric field generated by two long electrodes placed along parallel infinite walls separating different dielectric media

摘要

Analytical solutions for the electric potential in different mixed-boundary-value problems are found by use of the Wiener-Hopf method. The problem arises in the investigation of the influence of a non-uniform electric Held on an electrorheological fluid flowing through a plane channel. The solution is given in terms of infinite series involving Gamma functions. The electric field in the vicinity of the electrode edges is evaluated asymptotically. Some parametric studies are made with respect to the ratio between the permittivity of the electrorheological fluid and the permittivity of the isolating material outside the channel. Numerical solutions are also given.