Mathematical simulation of electrophoresis of live cells by multielectrode device

A mathematical model of the microchip that concentrates live cells in a small volume of liquid by electrophoresis is created. Space distributions of electric field are calculated for a cylindrical conductor with axially symmetrical electrodes. Equipotentials, field lines and lines of constant electric field strength squared are plotted. Cells are simulated as good conducted balls bounded with a low conducting membrane. The membrane has no influence on electric current if the frequency of the electric field is high enough. Then a cell behaves as a good conducting ball. It is polarized and a force appears which pulls the cell into the regions with the strong electric field. Trajectories of the cells are defined for the cell movement that is the result of this force and viscosity of the liquid. Singularities of the electric field distributions are found near the lines which separate boundary isolators and electrodes. The factors which limit effectiveness of the microchip are analyzed.