Bipolar model for traveling-wave induced nonequilibrium double-layer streaming in insulating liquids

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Abstract
A model is proposed for the time evolution of ion concentrations in a thin charge layer near an interface between an insulating solid and a semi‐insulating bipolar liquid, subjected to an applied electric field. Given the specific case of a traveling‐wave applied field of peak magnitude E0 and planar geometry, solutions for the charge density and electric field in the layer are used to calculate the time‐average stress moment and, hence, the pumping velocity of the liquid. Analytic solutions, valid in the regimes of small applied field magnitude (E0LD/Vt≪1, where L0 and Vt are the Debye length and thermal voltage, respectively) or frequency (ωε/σ≪1, ω the angular frequency and ε and σ the permittivity and equilibrium conductivity, respectively), predict charge layers with a characteristic dimension of the Debye length and fluid pumping in the direction of propagation of the traveling wave (forward). Numerical solutions, in the regime of large magnitude fields with ωε/σ∼1, predict either forward or backward pumping, as well as a charge layer with thickness on the order of a migration length (L = 2πbE0/ω, where b is the ion mobility). Parameters such as ion mobility, thermal generation rate, and level of ionization in the liquid are important in determining the rate (and even direction) of the pumping.

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