The author theoretically demonstrates a gel-free electrophoretic ratchet under a nearly unidirectional traveling electric field whose wavelength is much longer than the transverse dimension. Because of length scale separation, a charged particle can migrate synchronously or asynchronously with the field as if it was surfing on the wave. The author shows, with a dynamical phase portrait, that if the wave speed is slower than the characteristic electrophoretic velocity, a suspension of charged particles can be trapped into distinct particle bands synchronizing with the field. A tunable sieving capability of this ratchet provides the potential for continuous fractionation and characterization of colloidal suspensions.
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Electrostatic interactions could become important when the separation between particles is comparable to the Debye layer, which is obviously beyond the validity of our point-particle ansatz.
