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For the electrostatic approximation to apply, the characteristic time scale for electric phenomena, τ=ϵ=σ must be small. Note that τ is the ratio of dielectric permeability to conductivity of the medium. For the microfluidic applications considered here, this condition will usually be valid. For example, pure water has a electrical relaxation time of ≈10−4 and a hydrodynamic time scale of ≈0.045. See (
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If the droplet is initially charged or if it is short cut to the electrodes on one side of the channel while isolated from the electrodes on the other side, there will be another source of force on the droplet represented locally by ρfE. Our approach here can be easily extended to this case as well.
Unless the droplet is isolated only from the electrodes on one side of the channel. In this case the droplet stays at the voltage of the electrodes on the other side of the channel.
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