Direct calculation of Maxwell stress tensor for accurate trajectory prediction during DEP for 2D and 3D structures

It is known that careful engineering of dielectrophoresis (DEP) forces can be strong enough to move microparticles towards regions of higher or lower field strength. While many of the microdevices exploit differing electrical properties between cells to enact separation, the use of DEP as a generic electrical technique to position and move cells is still under investigation. Our work focuses on developing a robust numerical tool based on calculation of the Maxwell stress tensor (MST) both in a 2D and in a 3D formulation that aims towards providing a deeper understanding of cells interaction using DEP as a handle to position and manipulate cells for fundamental cell biology. The complex Laplace equation is first solved to obtain a value for the potential everywhere on the structure under investigation. The electric field is then obtained by a simple finite difference approach and the time-averaged DEP force exerted on a cell immersed in a medium with complex permittivity and subject to a sinusoidal electric field is calculated using the MST technique. MST is compared with a more approximate method and the ability of the approach to model a cell trajectory from a random initial point within the vicinity of an electrode system, in addition to cell–cell interaction, is also demonstrated.