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

Abstract

The line tension of an electrolyte wetting a non-polar substrate is computed analytically and numerically. The results show that, depending on the value of the apparent contact angle, positive or negative line tension values may be obtained. Furthermore, a significant difference between Young's contact angle and the apparent contact angle measured several Debye lengths remote from the three-phase contact line occurs. When applying the results to water wetting highly charged surfaces, line tension values of the same order of magnitude as found in recent experiments can be achieved. Therefore, the theory presented may contribute to the understanding of line tension measurements and points to the importance of the electrostatic line tension. Being strongly dependent on the interfacial charge density, electrostatic line tension is found to be tunable via the pH value of the involved electrolyte. As a practical consequence, the stability of nanoparticles adsorbed at fluid-fluid interfaces is predicted to be dependent on the pH value. The theory is suited for future incorporation of effects due to surfactants where even larger line tension values can be expected.

Three-phase contact line and line tension of electrolyte solutions in contact with charged substrates

“…( 17) (dashed lines) derived in Refs. [46,48] for temperature T * = 0.8T * c , surface charge density 0 ≤ σ ≤ 0.01 (0 ≤ σ ≤ 1 µC/cm 2 ), and ionic strength I ∈ {3.9×10 −5 , 3.9×10 −4 } ( Ĩ ∈ {1 mM, 10 mM}). The asymptotic expressions apply up to surface charges σ for which the dimensionless parameter χ = |σ| 2πlB/(ǫI) attains unity, which is marked by the vertical arrows.…”

“…has been derived in Refs. [46,48] for the case of the dimensionless quantity χ := |σ| 2πl B ǫI being small (χ ≪ 1). Figure 7 compares the curves cos(ϑ(σ)) for the systems discussed in Fig.…”

“…( 17) applies to small surface charge densities not only in the case of the electric field being confined to a wedge-shaped liquid phase, as in Refs. [46,48], but also in the case of a non-vanishing electric field in the gas phase.…”

“…There are only few studies concerned with the influence of electrostatic interactions on the line tension [43][44][45][46][47][48]. In Ref.…”

“…[50], Das and Mitra calculated the Maxwell stress and the contact angle of drops or bubbles on a charged substrate, again without taking into account line effects [51]. More recently, Dörr and Hardt [48] computed the line tension of an electrolyte in contact with a charged substrate by considering a wedge geometry similar to Refs. [46,47,50,51].…”