The Entrance Effect on the Electric Potential and Field in the Microchannel With Two Reservoirs

In this paper we consider the effect of the entrance into the microchannel having two reservoirs on the electric potential and the electric field. For the case when the channel width is much smaller than the reservoir size, as usual, we designed a method to patch the numerical solutions obtained for the reservoir domain and the asymptotic solutions valid for the region near the entrance to the channel which is attached to the reservoir. Based on the assumption of small channel size, we also derived two asymptotic solutions for the potential and the electric field applicable to the reservoir region and to the channel region. Then the working formula has been established which can predict the effect of the electrode and channel size relative to the reservoir on the electric field built inside the channel. It was shown that the working formula is robust and applicable to the wide range of the parameters.