(425g) Phoretic Particle Motion in Asymmetric Rectified Electric Fields

We use singular perturbation methods to analyze the steady "asymmetric rectified electric field" (AREF) generated when an oscillating voltage is applied across a parallel plate electrochemical cell containing an asymmetric electrolyte, as discovered numerically by Amrei et. al. [Amrei, S. H., Bukosky, S. C., Rader, S. P., Ristenpart, W. D., & Miller, G. H. (2018), Physical review letters, 121(18), 185504.]. We adopt the classical Poisson-Nernst-Planck framework for ion transport in dilute electrolytes, taking into account unequal ionic diffusivities. We consider the mathematically singular, and practically relevant limit of thin Debye layers, λ_D << L, where λ_D is the Debye length, and L is the length of the half-cell. The dynamics of the electric potential and ionic strength in the "bulk" electrolyte (i.e., outside the Debye layers) are obtained using a weakly nonlinear expansion for applied voltages on the order of the thermal voltage V_T = k_BT/e, where k_B is the Boltzmann constant, T is temperature, and e is the charge on a proton. We find that the AREF varies on a characteristic length scale proportional to (D_A /ω)^0.5, where D_A = 2D₊D_-/(D₊ + D_-) is the ambipolar diffusity, D_± are the ionic diffusivities, and ω is the frequency of the applied voltage. The AREF varies non-monotonically in the bulk and switches signs more than once. The existence of an AREF implies that a charged colloidal particle in the bulk solution undergoes net electrophoretic motion under macro-scale oscillatory voltage. Additionally, the AREF is non-uniform in space; therefore, an uncharged particle would also under go motion via dielectrophoresis. Finally, the non-uniform ionic strength in the bulk due to unequal ionic diffusivities gives rise to diffusiophoretic particle motion. Here, we use our theory for the AREF to predict the electrophoretic, dielectrophoretic, and diffusiophoretic velocities for a hard, spherical, colloidal particle.