Electric-double-layer structure close to the three-phase contact line in an electrolyte wetting a solid substrate

Abstract

The electric-double-layer structure in an electrolyte close to a solid substrate near the three-phase contact line is approximated by considering the linearized Poisson-Boltzmann equation in a wedge geometry. The mathematical approach complements the semianalytical solutions reported in the literature by providing easily available characteristic information on the double-layer structure. In particular, the model contains a length scale that quantifies the distance from the fluid-fluid interface over which this boundary influences the electric double layer. The analysis is based on an approximation for the equipotential lines. Excellent agreement between the model predictions and numerical results is achieved for a significant range of contact angles. The length scale quantifying the influence of the fluid-fluid interface is proportional to the Debye length and depends on the wall contact angle. It is shown that for contact angles approaching 90° there is a finite range of boundary influence.

Filling of charged cylindrical capillaries

“…As shown in Ref. [79], the EDL in the vicinity of such a wedge-shaped TPCL would be nontrivially different from the one-dimensional EDL distribution, and would substantially alter the present calculations. More importantly, the electroosmotic flow field in such a geometry remains unknown, particularly given the large singularity associated with the stress for r → 0 at the TPCL.…”

“…This is the charge contained in the liquid volume (at the air-liquid interface) resulting from consideration of the wedge geometry at the three-phase contact line, especially relevant for thick EDLs and 0 < θ < π/2. This charge, therefore, is the charge of the EDL in a wedgelike volume [79,92], and is different from the charge that accumulates at the meniscus on account of the axial separation of charges (responsible for triggering the streaming potential). We have neglected this charge in the present analysis.…”

“…First, we consider that the wall charge and the induced EDL electrostatics do not affect the dynamic contact angle that governs the capillary drive-the role of such a charge-affected dynamic contact angle has been discussed elsewhere [53]. Second, we consider that the EDL and the resulting electrostatic potential and the ion number density distribution are strictly one dimensional (i.e., varying only in the radial direction), and neglect the EDL in the wedge formed at the three-phase contact line [74][75][76][77][78][79]. Third, we neglect the charge accumulation at the air-liquid meniscus of the filling column.…”

Line tension and reduction of apparent contact angle associated with electric double layers

“…The zeroth-order problem is thus identical to the one treated by Dörr & Hardt [30], allowing to use the model equation φ (0) (r, θ) = π/(2θ) exp(−cη) which contains the function c = c(θ). Improving upon the empirical expression for c provided by Dörr & Hardt [30], we present an analytical formula below. By means of the known potential φ (0) , the exponential first-order shape can be found from Eq.…”

Ion size effects on the osmotic pressure and electrocapillarity in a nanoslit: Symmetric and asymmetric ion sizes

“…The interface in electrocapillarity is not perfectly flat since the electric field on the interface is not uniform along the interface, which will be discussed later in this section. A couple of studies showed that the interface deformation can be significant and might induce capillary filling in a nanochannel [57][58][59]. However, we limit our attention only to the flat interface in order to treat the problem analytically as we did in our previous work [11].…”