“…Electrophoresis is the movement of a charged particle with respect to a liquid electrolyte under an applied electric field. , It has found many applications, ranging from DNA sequencing by capillary electrophoresis to cell manipulation in electrokinetic microfluidic devices. − The electrophoretic velocity of a moderately charged particle with σ* = σ a /εϕ ∼ 1, where σ is the particle’s surface charge density, a is the particle radius, ε is the liquid permittivity, and ϕ is the thermal voltage, is a linear function of the imposed electric field strength, E , when β = Ea /ϕ ≪ 1. , This velocity follows Henry’s formula and exhibits an explicit dependence on the particle size through δ = 1/κ a , with 1/κ being the Debye length. , It reduces to Smoluchowski’s formula under the thin-Debye-layer limit with δ ≪ 1, which becomes independent of the particle size and shape . This regime of linear electrophoresis, however, breaks down for a highly charged particle with σ* ≫ 1 and/or under a large electric field with β ≫ 1 because of the surface conduction effect in the Debye layer. − The resulting nonlinear contribution to the electrophoretic velocity has been demonstrated to depend on the size, charge, and shape of the particle. − Particle size-dependent electrophoretic velocity (more accurately, electrokinetic velocity because of the contribution of fluid electroosmosis) also occurs in a confined microchannel because of the boundary effect. , This dependence, however, remains insignificant unless the particle size-to-channel width ratio reaches the order of unity. , …”