Geometry-dependent electrostatics near contact lines

Pickering Emulsion Transitions in 2,6-Lutidine Plus Water Critical Liquid Mixtures

Silica particle (S) stabilized oil-in-water Pickering emulsions are observed in the two-phase region of the critical liquid mixture 2,6-lutidine (L) plus water (W). De-emulsification is found at temperatures below a particle wetting transition temperature T_w(R) where T_w(R) decreases toward the lower critical temperature T_c for smaller particle radii R. The presence of a Pickering emulsion transition and its dependence upon particle radius can be explained by a competition between destabilizing gravitational forces and stabilizing forces originating from the critical interfacial tension. As a corollary to these observations, the line tension τ at the three-phase SLW contact line is determined as a function of temperature.

Resolving the Apparent Line Tension of Sessile Droplets and Understanding its Sign Change at a Critical Wetting Angle

Despite strenuous research efforts for more than one century, identifying the magnitude and sign of the apparent line tension for a liquid-solid-gas system remains an elusive goal. Herein we accurately determine the apparent line tension from the size-dependent contact angle of sessile nanodrops on surfaces with different wetting properties via atomic force microscopy measurements and molecular dynamics simulations. We show that the apparent line tension has a magnitude of 10^{-11}-10^{-10}  J/m, in good agreement with theoretical predictions. Furthermore, while it is positive and favors shorter contact lines for droplets on very lyophilic surfaces, the apparent line tension changes its sign and favors longer contact lines on surfaces with an apparent contact angle higher than a critical value. By analyzing the density and the potential energy of liquid molecules within the sessile droplet, we demonstrate that the sign of the apparent line tension is a thermodynamic property of the liquid-solid-gas system rather than the local effect of intermolecular interactions in the three-phase confluence region.

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

The three-phase contact line formed by the intersection of a liquid-vapor interface of an electrolyte solution with a charged planar substrate is studied in terms of classical density functional theory applied to a lattice model. The influence of the substrate charge density and of the ionic strength of the solution on the intrinsic structure of the three-phase contact line and on the corresponding line tension is analyzed. We find a negative line tension for all values of the surface charge density and of the ionic strength considered. The strength of the line tension decreases upon decreasing the contact angle via varying either the temperature or the substrate charge density.

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

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.

Conceptual aspects of line tensions

We analyze two representative systems containing a three-phase-contact line: a liquid lens at a fluid-fluid interface and a liquid drop in contact with a gas phase residing on a solid substrate. In addition we study a system containing a planar liquid-gas interface in contact with a solid substrate. We discuss to which extent the decomposition of the grand canonical free energy of such systems into volume, surface, and line contributions is unique in spite of the freedom one has in positioning the Gibbs dividing interfaces. Curvatures of interfaces are taken into account. In the case of a lens it is found that the line tension is independent of arbitrary choices of the Gibbs dividing interfaces. In the case of a drop, however, one arrives at two different possible definitions of the line tension. One of them corresponds seamlessly to that applicable to the lens. The line tension defined this way turns out to be independent of choices of the Gibbs dividing interfaces. In the case of the second definition, however, the line tension does depend on the choice of the Gibbs dividing interfaces. We also provide form invariant equations for the equilibrium contact angles which properly transform under notional shifts of dividing interfaces which change the description of the system but leave the density configurations unchanged. It is shown that in order to accomplish this form invariance, additional stiffness coefficients attributed to the contact line must be introduced. The choice of the dividing interfaces influences the actual values of the stiffness coefficients. We show how these coefficients transform as a function of the relative displacements of the dividing interfaces. Our formulation provides a clearly defined scheme to determine line properties from measured dependences of the contact angles on lens or drop volumes. This scheme implies relations different from the modified Neumann or Young equations, which currently are the basis for extracting line tensions from experimental data. These relations show that the experiments do not render the line tension alone but a combination of the line tension, the Tolman length, and the stiffness coefficients of the line. In contrast to previous approaches our scheme works consistently for any choice of the dividing interfaces. It further allows us to compare results obtained by different experimental or theoretical methods, based on different conventions of choosing the dividing interfaces.

Electrowetting with electrolytes

A theory of electrowetting is developed for systems containing an interface between two immiscible electrolytic solutions. Laws for the dependence of contact angle on electrode potential are presented. Ionic impermeability of the liquid-liquid interface and nonlinear double-layer responses rationalize observed phenomena such as contact-angle saturation and droplet contraction or detachment. The theoretical results can be applied to design new, precisely controllable microfluidic devices.

Coupling hydrophobicity, dispersion, and electrostatics in continuum solvent models

An implicit solvent model is presented that couples hydrophobic, dispersion, and electrostatic solvation energies by minimizing the system Gibbs free energy with respect to the solvent volume exclusion function. The solvent accessible surface is the output of the theory. The method is illustrated with the solvation of simple solutes on different length scales and captures the sensitivity of hydration to the particular form of the solute-solvent interactions in agreement with recent computer simulations.

Coupling nonpolar and polar solvation free energies in implicit solvent models

Recent studies on the solvation of atomistic and nanoscale solutes indicate that a strong coupling exists between the hydrophobic, dispersion, and electrostatic contributions to the solvation free energy, a facet not considered in current implicit solvent models. We suggest a theoretical formalism which accounts for coupling by minimizing the Gibbs free energy of the solvent with respect to a solvent volume exclusion function. The resulting differential equation is similar to the Laplace-Young equation for the geometrical description of capillary interfaces but is extended to microscopic scales by explicitly considering curvature corrections as well as dispersion and electrostatic contributions. Unlike existing implicit solvent approaches, the solvent accessible surface is an output of our model. The presented formalism is illustrated on spherically or cylindrically symmetrical systems of neutral or charged solutes on different length scales. The results are in agreement with computer simulations and, most importantly, demonstrate that our method captures the strong sensitivity of solvent expulsion and dewetting to the particular form of the solvent-solute interactions.

Electrowetting films on parallel line electrodes

A lubrication analysis is presented for the spreading dynamics of a high permittivity polar dielectric liquid drop due to an electric field sustained by parallel line electrode pairs separated by a distance R(e). The normal Maxwell stress, concentrated at the tip region near the apparent three-phase contact line, produces a negative capillary pressure that is responsible for pulling out a thin finger of liquid film ahead of the macroscopic drop, analogous to that obtained in self-similar gravity spreading. This front-running electrowetting film maintains a constant contact angle and volume as its front position advances in time t by the universal law 0.43R(e)(t/T(cap))1/3, independent of the drop dimension, surface tension, and wettability. T(cap)=pi(2)mu(l)R(e)/8(epsilon0epsilonl)V2 is the electrocapillary time scale where mu(l) is the liquid viscosity, epsilon0epsilonl the liquid permittivity, and V the applied voltage. This spreading dynamics for the electrowetting film is much faster than the rest of the drop; after a short transient, the latter spreads over the electrowetting film by draining into it. By employing matched asymptotics, we are able to elucidate this unique mechanism, justified by the reasonable agreement with numerical and experimental results. Unlike the usual electrowetting-on-dielectric configuration where the field singularity at the contact line produces a static change in the contact angle consistent with the Lippmann equation, we show that the parallel electrode configuration produces a bulk negative Maxwell pressure within the drop. This Maxwell pressure increases in magnitude toward the contact line due to field confinement and is responsible for a bulk pressure gradient that gives rise to a front-running spontaneous electrowetting film.

Ion redistribution and meniscus stability at Langmuir monolayer deposition

Considering the deposition of charged Langmuir monolayers, it is necessary to take into account electrostatic interactions between the monolayer and the substrate surface. These interactions depend on the nature of ionizable surface groups and on the ionic composition of the subphase (e.g. pH, multivalent counterions, indifferent electrolytes). The non-uniformity of electric, concentration and hydrodynamic velocity fields leads to the formation of ion concentration profiles near the three-phase contact line during the deposition. This effect is similar to the effect of concentration polarization in membranes and electrode systems. The ions redistribution results in change of the monolayer ionization, adhesion work, dynamic contact angle, and, therefore, in the change of morphology, composition and structure of the deposited monolayer. With increasing withdrawal velocity the meniscus can become unstable because of concentration polarization in the solution.

Dynamic mechanisms for apparent slip on hydrophobic surfaces

Recent experiments [Y. Zhu and S. Granick, Phys. Rev. Lett. 87, 096105 (2001)] have measured a large, shear-dependent fluid slip at partially wetting fluid-solid surfaces. We present a simple model for such a slip, motivated by the recent observations of nanobubbles on hydrophobic surfaces. The model considers the dynamic response of bubbles to change in hydrodynamic pressure, due to the oscillation of a solid surface. Both the compression and diffusion of gas in the bubbles decrease the force on the oscillating surface by a "leaking mattress" effect, thereby creating an apparent shear-dependent slip. With bubbles similar to those observed by recent atomic force microscopy, the model predicts a force decrease consistent with the experimental measurements of Zhu and Granick.

Interface profiles near three-phase contact lines in electric fields

Long-range electrostatic fields deform the surface profile of a conductive liquid in the vicinity of the contact line. We have investigated the equilibrium profiles by balancing electrostatic and capillary forces locally at the liquid vapor interface. Numerical results show that the contact angle at the contact line approaches Young's angle. Simultaneously, the local curvature displays a weak algebraic divergence. Furthermore, we present an asymptotic analytical model, which confirms these results and elucidates the scaling behavior of the profile close to the contact line.