Revisiting the Electroacoustic Phenomenon in the Presence of Surface Acoustic Waves

Abstract

Recently, one has been observing abundant studies on the application of surface acoustic waves (SAWs) in solid substrates for manipulating liquids and particulates in micron-to-nanometer thick films and channels and in porous media. At these length scales, contributions of SAWs to the electrical double layer (EDL) of ions and of the latter to particulates and flow may become appreciable. However, the nature of the interplay between SAWs and EDLs is unknown. We demonstrate the contribution of a SAW to the near-equilibrium electrical and ion-concentration fields in an EDL near inert and piezoelectric substrates. In particular, we concentrate on the leakage of transient and steady components of electrical potential through the excited EDL. Far from the solid, the leakage may be interpreted by different models of the EDL to give information about the EDL characteristic relaxation time, ζ-potential, and the Stern layer therein. In addition, the analysis given here may explain observed SAW-induced electrochemical effects on piezoelectric substrates.

Measurements of Ion Dynamics and Electro-Mechanical Resonance in an Electrical Double Layer near a Surface Acoustic Wave

“…20 Recent evidence suggests that SAWs interfere with EDLs, thus generating electrokinetic effects in applications of catalysis, 21,22 liquid film dynamics, 23−25 the leakage should disclose encoded information about static and dynamic EDL properties. 28 We report measurements of the previously theorized electrical leakage of SAW-excited EDLs and show that reality exceeds previous expectations. In the followings, we expand the previous theoretical analysis for the SAW excitation of an EDL so as to account for practical features of the EDL, SAW, and our measurement in Theory; present our experimental procedure in Methods; give results and analysis of the measured electrical leakage off the SAW excited EDL and discuss our findings in Results and Discussion; and summarize our findings in Summary.…”

“…We place the working electrode, designed for measuring the electrical leakage, ψ 1 , at a separation of 40 μm away from the solid surface to avoid the anticipated dispersion of the leakage at separations from the solid surface that are greater than the 200 μm SAW wavelength. 28 The reference electrode, which accounts for the electrical potential at the bulk of the drop, is placed at a separation of approximately 1 mm away from the solid. The electrodes are connected through an active differential voltage probe (RT-ZD02, Rohde & Schwarz, Germany) to an oscilloscope (HMO3004, Rohde & Schwarz, Germany) for obtaining the frequency variation and to an RF lock-in amplifier (SR844, Stanford Research Systems, CA) for measuring the 20 MHz frequency component of the electrical leakage, i.e., the linear (same frequency) response of the EDL to the exciting SAW.…”

“…The leading order contribution to the electrical field leakage off the EDL is dependent on the leading order flow field in the electrolyte solution. This is a product of the Navier–Stokes and continuity equations and is powered by the normal deformation of the solid surface by the SAW . The leading order flow field is given by ϕ 0 = ( κ δ ) − 1 ( 1 + α 2 ) − 1 ( sin false( t − x false) + α ⁡ cos false( t − x false) ) italice − α x , where we neglect terms far from the solid surface, assuming that y ≪ 1/κσ, and where we account for the exponential attenuation of the SAW under the electrolyte solution with an attenuation length α –1 under the drop at x > 0.…”

“…The physical insights that δ k ≫ St –1 and δ k ≫ Ol in the 1 MHz to 1 GHz SAW frequency range, regardless of ionic strength and electrical potential, motivate the following equation expansion methodology: We assume the small parameter ϵ ≡ St –1 ≈ Ol ≈ (κδ) 2 ≪ 1 and represent the different variables using the asymptotic series ϕ = ϵ − 1 / 2 ϕ 0 + ... , ψ = ψ 0 + ϵ 1 / 2 ψ̃ 1 + ... , c + = c 0 + + ϵ 1 / 2 c 1 + + ... , c − = c 0 − − ϵ 1 / 2 c 1 − + ... . The gauge functions (powers of ϵ) in the series alongside assuming that ψ s = scriptO ( 1 ) and ψ i = scriptO ( ϵ 1 / 2 ) render the leading order electrical potential independent of SAW.…”

“…Should the acoustic length (δ) and time (ω –1 ) scales overlap with the EDL Debye length (σ) and ion relaxation time (σ 2 / D ( m i )), respectively, one expects that the EDL and SAW become dynamically entangled. A recent theory suggests that such an electrokinetic entanglement should leak an electrical field off the EDL; the leakage should disclose encoded information about static and dynamic EDL properties …”