Direct measurement of the viscoelectric effect in water

The viscoelectric effect concerns the increase in viscosity of a polar liquid in an electric field due to its interaction with the dipolar molecules and was first determined for polar organic liquids more than 80 y ago. For the case of water, however, the most common polar liquid, direct measurement of the viscoelectric effect is challenging and has not to date been carried out, despite its importance in a wide range of electrokinetic and flow effects. In consequence, estimates of its magnitude for water vary by more than three orders of magnitude. Here, we measure the viscoelectric effect in water directly using a surface force balance by measuring the dynamic approach of two molecularly smooth surfaces with a controlled, uniform electric field between them across highly purified water. As the water is squeezed out of the gap between the approaching surfaces, viscous damping dominates the approach dynamics; this is modulated by the viscoelectric effect under the uniform transverse electric field across the water, enabling its magnitude to be directly determined as a function of the field. We measured a value for this magnitude, which differs by one and by two orders of magnitude, respectively, from its highest and lowest previously estimated values.

The viscoelectric effect concerns the change in the viscosity of polar liquids in the presence of an electric field (1–3). It arises from the interaction of the field with the dipolar molecules, and while its molecular origins are still not well understood (4–6), it has considerable relevance in areas ranging from surface potential measurements (7–9) and boundary lubrication (10) to nanofluidics and its applications (11–13). Knowing the magnitude of the viscoelectric effect is thus of clear importance. It was first measured by Andrade and Dodd (1–3) for a range of polar organic liquids, by monitoring their flow in a narrow channel between metal electrodes across which a known electric field E was applied, and quantified via a viscoelectric coefficient f using an empirical relation based on their results:η(E)= η0(1 + f∣E∣2),1]a simplified analysis leading to such a relation is given in Ref. (8). Here, η₀ is the unperturbed bulk liquid viscosity (i.e., in the absence of any field). For the case of water, however, the most ubiquitous and important polar liquid, measurement of its viscosity in the presence of a strong, uniform field presents a strong challenge (as discussed later in this section), and to our knowledge no such direct measurements have been reported. Over the past six decades, therefore, the magnitude of the viscoelectric effect in water has been only indirectly estimated by extrapolation from its values for organic liquids (8), from estimates of its effect on electrokinetic phenomena (11, 14–19), or by other approaches (7, 12, 20, 21). These estimated values, as expressed in the viscoelectric coefficient f, vary over more than three orders of magnitude, ranging from f ∼10⁻¹⁷–2.5 × 10⁻¹⁴ (V/m)² (SI Appendix, Section 7). For completeness, we note that results contradictory to the viscoelectric model have also been reported (22) (i.e., suggesting a decreased water viscosity in an electric field). The reasons for the large span of these estimated f values were attributed to various factors such as solid/liquid coupling, varying ionic sizes, and varying water permittivity (12, 19); however, while these factors may play some role, there is no evidence that they could lead to such large discrepancies.We believe, rather, that the origin of the large variance in the estimated magnitude of the viscoelectric effect arises because none of the experimental studies on water to date in which the f values were estimated was direct, in the sense of probing how the water viscosity varied with field in a uniform electric field. In all cases, viscosity changes were assumed to occur only in the nonuniform, rapidly decaying electrostatic potential near charged surfaces immersed in water. Changes in electrophoretic mobility, electro-osmosis, or hydrodynamic dissipation or water mobility between similarly charged solid surfaces were then attributed to some mean viscosity increase in these thin surface-adjacent layers (7, 11, 12, 14–21). In practice, however, the effect on these electrokinetic phenomena of viscosity or water mobility changes in the thin layers where such nonuniform, rapidly decaying fields are present is not easy to quantify reliably, especially in the presence of salt ions (12). At the same time, measuring the viscosity of water in a uniform electric field between two surfaces at different potentials, as was done for the polar organic solvents (2, 3) and which would provide a direct determination of its viscoelectric effect, presents a considerable difficulty. This is due to two main factors and arises because, in contrast to organic solvents, water may self-dissociate. Firstly, the potential difference that may be applied between the surfaces across water is limited, if electrolysis is to be avoided (23, 24), and secondly, electrostatic screening implies that the field decays strongly (within a Debye screening length) away from the surfaces (25–27). Even in purified water with no added salt (as in the present study), the potential decays rapidly away from a charged surface (see, e.g., Fig. 1C), so that to measure viscosity in a uniform field between two surfaces, one would require flow channels of width of order some tens of nanometers or less, presenting a major challenge.Open in a separate windowFig. 1.Numerical solution to the nonlinearized PB equation with σ_mica = −8.1 mC/m², ψ_gold = 0.07 V, and ion concentration c_b = 8 × 10⁻⁵ M, corresponding to the conditions of Fig. 4A. (A) Surface potential on the mica surface and surface charge on the gold surface as a function of separation D. (B) Average electric field approximated as (|ψ_gold − ψ_mica|/D). (C) Local potential ψ as a function of distance d from the mica surface for different separations D. Dashed line in larger-scale inset is an eye guide of a linear approximation.In the present study, we overcome this by directly probing the viscosity of purified water across which a uniform electric field acts while it is confined between two surfaces in a surface force balance (SFB). In our experiments, a molecularly smooth gold surface at a controlled (positive) surface potential approaches an atomically smooth mica surface at constant surface (negative) charge density, so that a known electric field acts across the water-filled gap of width D between them; moreover, this field is very close to uniform at the most relevant surface separations (D ≲ 30 nm, Fig. 1C). The dynamics of approach is strongly modulated by the viscous damping due to squeeze-out of the water as D decreases, and hence by its viscosity in the uniform electric field; by monitoring the approach rate of the surfaces at high temporal (millisecond) and spatial (approximately angstrom) resolutions, we are able therefore to directly evaluate the magnitude of the viscoelectric effect (the value of f).