Linear response functions of an electrolyte solution in a uniform flow

Abstract

We study the steady state response of a dilute monovalent electrolyte solution to an external source with a constant relative velocity with respect to the fluid. The source is taken as a combination of three perturbations: an external force acting on the fluid, an externally imposed ionic chemical potential, and an external charge density. The linear response functions are obtained analytically and can be decoupled into three independent terms, corresponding to (i) fluid flow and pressure, (ii) total ionic number density and current, and (iii) charge density, electrostatic potential and electric current. It is shown how the uniform flow breaks the equilibrium radial symmetry of the response functions, leading to a distortion of the ionic cloud and electrostatic potential, which deviate from the standard Debye-Hückel result. The potential of a moving charge is under-screened in its direction of motion and over-screened in the opposite direction and normal plane. As a result, an unscreened dipolar electric field and electric currents are induced far from the charged source. We relate our general formalism to several experimental setups, such as colloidal sedimentation .

Electrification of water interface

“…where 1/κ 0 is the Debye length without flow, v is the flow rate, and C is the fitted parameter. The agreement between theory [229], and experiments [231] reveals that the distortion of the electric double layer due to the external flow plays a crucial role in the reduction of the Debye length. Further discussion of the fit parameters is described in Appendix C. These studies demonstrated that ion reaction dynamics and external flows substantially affect the surface charge density under non-equilibrium conditions [27,237].…”

“…The equilibrium Debye length, 1/κ 0 , was extracted from the experimental data without flow rate, and it was fixed during the fit. Assuming the flow rate Q = L 2 u, where L is the characteristic length of the channel and u is the flow velocity, the analytical theory predicts C = (4D ion κ 0 L 2 ) −2 ∼ (1/κ 0 ) 2 , where D ion is the diffusion constant of the ion [229]. However, the fitted C exhibits C ∼ const for different Debye lengths.…”

“…The electrification of clay and clay minerals is caused by isomorphic substitution for Si 4+ by Al 3+ and Al 3+ by Mg 2+ , respectively, [224,225]. In this section, we discuss two novel effects on surface electrification: flow effect [27,160,[226][227][228][229][230][231][232][233] and contact electrification [30,120,130,[234][235][236].…”

“…The solid black lines in Fig. 13 are theoretical predictions for a decrease in Debye length in a direction normal to the flow [229], which is described by the following equation:…”

“…The ionic strength was varied as (a,b) 0.1 mM, (c,d) 1 mM, and (e,f) 10 mM. The solid lines in (a,c,e) are the theoretical fits κ = κ0 √ 1 + Cv 2[229], where v is the flow rate. All the fit parameters are described in Appendix C. The lines in (bdf) are guide for the eyes.…”