Figure 4: DEP forces.
From: Formation of printable granular and colloidal chains through capillary effects and dielectrophoresis
(a) Electric field generated by a spherical electrode at U=100 V and a polarized metal sphere right beneath it. The two spheres (solid circles) have radius a=30 μm and are separated by s=3 μm. Other details are provided in the Methods section. The induced surface charge density σ (on the lower sphere) and the electric potential φ (throughout space) are shown as colour maps. Electric field E and resultant surface forces f=σE are presented as black and white arrows, respectively. (b) Dependence of DEP force on particle surface separation s. Two different voltages are considered, U=100 V (red) and U=600 V (blue), respectively. For each voltage, we compare the result from the finite-element analysis (FEA, dots) and that from the conventional DEP model (solid curves), that is, Fe=2πɛoilɛoa3κ∇(E2)=8πɛoilɛoa5κU2/(2a+s)5. The functional form of the asymptotic solution Fe∝1/[s(ln s)2] as s→0 is plotted as the black curve. The capillary force Fsp≈5.6 μN is also shown (dashed line).
