Lippmann Equation Research Articles

Effect of electric field on the wetting behavior of GaInSnBiZn high-entropy alloy in NaOH aqueous solution

The GaInSnBiZn low-melting-point high-entropy alloy exhibits promising prospects for utilization in the realm of flexible electronic devices, offering a promising alternative to common binary or ternary room-temperature liquid metals. By utilizing the sessile drop method, the wetting behavior of GaInSnBiZn/SiO2 was investigated, focusing on the effects of applied voltage and NaOH solution concentration. It was revealed that the alloy's electro-wetting is primarily influenced by the generation and dissolution of the surface oxide layer, as well as the interaction of the electric double-layer effect. The optimal response voltages for achieving the fastest wetting rate were found to be 16 V, 10 V, 18 V, and 8 V in 0.5 mol/L, 1.0 mol/L, 1.5 mol/L, and 2.0 mol/L concentrations, respectively, with 18 V at 1.5 mol/L concentration identified as the optimal process selection. The spreading behavior of the alloy in low-concentration NaOH solutions followed Tanner's Law, while in the 2.0 mol/L concentration, significant repellence and wetting angle saturation were observed. The wetting process of the alloy at various stages was described using the power-law equation R = atc, while the wetting mechanism of the alloy was elucidated through the application of the Lippmann equation and the electric double-layer effect equation.

On the electrode charge at the metal/solution interface with specific adsorption

The electrode charge is one of the most fundamental concepts in electrochemistry. However, ambiguousness often comes to its definition as specific adsorption occurs. In this review, three types of electrode charges, the metallic excess charge, the free charge, and the total charge, are discriminated via a modelistic description at the metal/solution interface, and the relationships between them are formulated. The total charge is proved to be the thermodynamic charge in a general Lippmann equation. Based on this equation, thermodynamic analysis can be performed to estimate the adsorbate coverage, then the free charge can be derived. As an example, manipulation has been made on a previous work in the (bi)sulfate adsorption system, the surface charging relations are obtained, displaying nonmonotonic relationships. In addition, a modeling study for specific adsorption is introduced and exemplarily performed in the (bi)sulfate adsorption system.

Colorimetric Sensing with Gold Nanoparticles on Electrowetting-Based Digital Microfluidics.

Digital microfluidic (DMF) has been a unique tool for manipulating micro-droplets with high flexibility and accuracy. To extend the application of DMF for automatic and in-site detection, it is promising to introduce colorimetric sensing based on gold nanoparticles (AuNPs), which have advantages including high sensitivity, label-free, biocompatibility, and easy surface modification. However, there is still a lack of studies for investigating the movement and stability of AuNPs for in-site detection on the electrowetting-based digital microfluidics. Herein, to demonstrate the ability of DMF for colorimetric sensing with AuNPs, we investigated the electrowetting property of the AuNPs droplets on the hydrophobic interface of the DMF chip and examined the stability of the AuNPs on DMF as well as the influence of evaporation to the colorimetric sensing. As a result, we found that the electrowetting of AuNPs fits to a modified Young–Lippmann equation, which suggests that a higher voltage is required to actuate AuNPs droplets compared with actuating water droplets. Moreover, the stability of AuNPs was maintained during the processing of electrowetting. We also proved that the evaporation of droplets has a limited influence on the detections that last several minutes. Finally, a model experiment for the detection of Hg2+ was carried out with similar results to the detections in bulk solution. The proposed method can be further extended to a wide range of AuNPs-based detection for label-free, automatic, and low-cost detection of small molecules, biomarkers, and metal ions.

Liquid metal enabled continuous flow reactor: A proof-of-concept

Liquid metal enabled continuous flow reactor: A proof-of-concept

Experimental study and predicted model analysis of nanofluid wetting behavior under high voltage

To explore the wetting behavior of nanofluid under high voltage, a contact angle measurement system under electric field is designed and set up. The effects of mass concentration, the type of nanoparticles and the temperature of dielectric layer are considered. The experimental results manifest that the contact angle reduction rate of SiO2-water nanofluid is gradually increased with the increase of nanofluid concentrations from 0 to 0.05 wt%. While, it is decreased when the concentration is varied from 0.05 to 0.25 wt%. On the other hand, the contact angle reduction rate of Al2O3-water nanofluid is generally greater than SiO2-water nanofluid with the same volume concentration. In addition, the reduction rate of the contact angle of the SiO2-water nanofluid would be gradually increased with the increase of the surface temperature of the dielectric layer. Moreover, the experimental values are greatly deviated from the results calculated by Young–Lippmann equation and its modified form of nanofluid. Hence, the present study proposes a dimensionless surface tension correct factor to obtain the modified equation which is based on the Young–Lippmann equation. The influence of electric charge, electric field force, drag force and Brownian force on nanoparticles under high voltage are considered in the modified equation. The results show that the modified equation can predict the trend of the nanofluid contact angle under higher voltage.

A molecular dynamics study on the interfacial properties of millerite

The present study aims at developing force field parameters for describing the millerite structure and subsequently for investigation of its interfacial properties under varying conditions within the framework of molecular dynamics simulations. The first set of calculations were performed to obtain the required force field parameters, validated through reproduction of the bulk properties. This was followed by estimation of the surface energy and evaluation of the collector physisorption onto the non-polar (100) and (110) surfaces. Collector molecules exhibited higher affinity towards the former, with the branched alkyl chain favoring the interactions with either of the surfaces. Further simulations were conducted to examine the changes in the contact angle of the intrinsically hydrophilic (110) surface upon oxidization. Observations through transition from the neutral surface fully covered by elemental sulfur to a charge-bearing surface containing sulfur and polysulfides were compared against the theoretical predictions made by the Lippmann equation, and the discrepancies were attributed to the significance of line tension at the atomic scale. Finally, propensity of collector molecules towards the positively and negatively charged (110) surface was examined in the absence and presence of excess calcium hydroxide. In both cases, the collector-surface interactions were impeded in the strong alkaline solution.

Mathematical model of neuronal membrane mechanical deformations under the influence of an electric pulse

Mechanical deformations of neuronal membrane occur when exposed to an electrical pulse. A one-dimensional mathematical model of such deformations of a cylindrical cell is proposed, based on the fluid dynamics equations and the Lippmann equation connecting electric effects with the membrane strength. The model qualitatively reproduces experimentally observed effects of cell membrane mechanical deformations evoked by both an action potential moving along axon and an electric pulse injected through electrode.

Some remarks to the derivation of the \u201cgeneralized Lippmann equation\u201d

In the present communication, an attempt is made to demonstrate (once again) some of the problems with the derivation of the “generalized Lippmann equation” considered to be valid by many researchers for solid electrodes and to address the problems in the framework of the Gibbs model of the interface by using only the basic principles of thermodynamics. By surveying the relevant literature, it has been shown that during the derivation of the equation, it was completely ignored that the Gibbs-Duhem equation (i.e., the electrocapillary equation) is a mathematical consequence which follows directly from the homogeneous degree one property of the corresponding thermodynamic potential function; consequently, the resulting expression cannot be correct. Some alternative approaches have also been considered. The adequacy of the open system and the partly closed system approach has been critically discussed, together with the possibility of introducing new thermodynamic potential functions.

Vertical manipulation of fluids through electrostatic formation: model development and experimental validation

A novel actuation method, called electrostatic formation (ESF), for MEMS and other applications, is introduced. The ESF mechanism uses a droplet of liquid material that is electrostatically deformed. ESF differs from Electrowetting and Electrowetting on Dielectric as the electrode used to apply the voltage is of a smaller diameter than the droplet being manipulated, and the electrode is located above the manipulated fluid. Modeling this movement requires adherence to the Lippmann and Young–Laplace equations simultaneously. In order to understand how the surface tension is specifically manipulated, as is required for the development of a model of representation of the phenomenon, a force-based interpretation of the Lippmann equation is outlined, with focus on how it compares to the force response provided by hydrostatic pressure under the influence of gravitational field forces. Additionally, it is demonstrated that a differential surface charge must be present of which the formulation is complex in nature, likely stemming from the combination of the internal pressure and a localized skin effect caused by an electric double layer that is present at the surface of the transformed liquid. In this study, a target liquid of gallium is manipulated under electrostatic charge in a physical experiment and compared against the geometry suggested by the developed model. By utilizing the assumptions highlighted in this article, a coefficient of variance (R2) of 0.907 was calculated between the measurements and model. This coefficient of variance was improved to 0.915 through the introduction of varied electrostatic and internal pressure terms.

Динамика зажатой капли в неоднородном электрическом поле

The forced oscillations of an incompressible liquid drop under the influence of an alternating electric field are considered. The drop is sandwiched between two homogeneous plates and surrounded by an incompressible fluid of a different density. In equilibrium, the drop has the shape of a circular cylinder which is bounded axially by parallel solid plates. These plates have different surface properties. An external electric field acts as an external force which is a reason of the motion of the contact line. A modified Hocking boundary condition is used to describe the motion of the contact line: the velocity of the contact line is proportional to the deviation of the contact angle and the rate of fast relaxation processes, the frequency of which is proportional to the doubled frequency of the electric field. Using this equation allows one to qualitatively describe the experimental dependence of the contact angle as a function of stress, in contrast to the Young – Lippmann equation. The solution to the problem is presented as a Fourier series expansion in eigen functions of the Laplace operator. Graphs of the amplitude-frequency characteristics and evolution of the drop shape are constructed for various values of the problem parameters. In the case of identical surfaces, only odd modes of droplet oscillations are excited, while for different surfaces, even harmonics additionally appear. It was found that in a wide range of parameters the shape of the side surface of the drop is close to the description by an odd function. The oscillation amplitude of even modes is significant only near resonances at the frequencies of these modes. In the case of an inhomogeneous field, azimuthal oscillations are excited, which leads to the appearance of additional resonance peaks. Travel waves propagate along the lateral surface of the drop, which are caused by vibrations of the contact line and the contact angle. The dependences of the values of the contact angle on the upper and lower surfaces on the square root of the amplitude for different values of the frequency of the electric field, which qualitatively coincide with similar graphs of experimental data, are constructed. It is possible to determine the parameters of the Hocking.

Electric-Field-Controlled Motion of Liquid Droplets on the Surface of Dielectric Films

Kinetics of water droplets on the surface of shielded metal electrodes is studied in the presence of external electric field. It is shown that the difference of contact angles of droplet fragments on the control electrodes plays the key role in motion. It is also shown that a droplet always moves toward the negative electrode regardless of the polarity of control electrodes and grounding for the dielectric system under study. The theoretical analysis of the results is based on the Lippmann equation written for a polarized droplet that is localized on control electrodes shielded with a multilayer insulator.

Electrodewetting and Wetting of an Extended Meniscus.

Here, we report the intriguing movements of an extended liquid meniscus on a silicon substrate under the influence of sinusoidal alternating current (AC) voltages at different operating frequencies. As opposed to droplet electrowetting, wherein the droplet spreads and experiences oscillations at the free surface, the application of AC voltage to a thin liquid film results in distinct and uniform dewetting, in conjunction with augmented wetting. Image analyzing interferometry is used for the precise measurement of the film thickness profile and other associated parameters. We postulate that the classic Young-Lippmann equation fails to explain the dynamics of an extended meniscus and evince that the dynamics of film displacement could be successfully explained by considering the product of the applied electric field and its gradient, as opposed to the existing consideration of a square dependence on the applied voltage. The physics of the hitherto unreported phenomena is elucidated by developing a mathematical model, taking into consideration all of the germane forces governing the dynamics of the thin liquid film. We affirm that the present study would serve as a fundamental background for a fascinating mode of liquid actuation, with inherent application potential in several existing and novel microfluidic systems.

(Invited) Mechano-Chemical Coupling at Interfaces in Novel Hybrid Materials

The strong coupling between chemistry or electrochemistry and mechanics at interfaces may be exploited for designing materials with unexpected functional behavior. One example is provided by nanoporous-metal based hybrid materials that behave similar to piezoelectric ceramics: Bodies of nanoporous gold impregnated with electrolyte emit exceptionally robust electric signals when subjected to external load. The metal-based material may thus be considered as piezoelectric, in a literal interpretation of the term. Another example is a class of novel phenomena in which the mechanical response to load – which may be elastic or plastic – can be tuned by an electric potential. The relevant capillary parameters can be either, surface stress or surface tension. In each case, a coupling between the capillarity and electricity is crucial, and the coupling strengths can be quite different. While the energy-charge coupling at a surface is described by the Lippmann equation, a predictive understanding of the interfacial stress-charge coupling, which governs the apparent piezoelectricity, remains elusive. The talk will discuss relevant issues from the perspectives of experiment, phenomenological thermodynamics, and atomistics.

Numerical and theoretical analyses of the dynamics of droplets driven by electrowetting on dielectric in a Hele-Shaw cell

Droplet movement by electrowetting on dielectric (EWOD) in a Hele-Shaw cell is analysed theoretically and numerically. We propose a simple theoretical model for the motion, which describes well the voltage dependency of droplet speed below the saturation voltage as measured experimentally. The simulation method for numerical analyses is constructed by using the Young–Lippmann equation to represent EWOD and the generalised Navier boundary condition to represent the moving contact line in the context of the front-tracking method. With an adjusted slip parameter, the present full three-dimensional numerical simulation reproduces well the shape evolution and movement speed of droplets as observed experimentally. We verify the proposed theoretical model in numerical experiments with various shapes and voltages. Furthermore, we analyse theoretically the behaviour of the contact line at the onset of droplet motion as observed in the simulation and experiment, and we are able to estimate very well the time scale on which the contact angle changes.

New insights on the interfacial tension of electrochemical interfaces and the Lippmann equation

The Lippmann equation is considered as universal relationship between interfacial tension, double layer charge, and cell potential. Based on the framework of continuum thermo-electrodynamics, we provide some crucial new insights to this relation. For general interfaces such that the local curvature radius is large compared to the Debye length, we apply asymptotic analysis methods to obtain the Lippmann equation. We give precise definitions of the involved quantities and show that the interfacial tension of the Lippmann equation is composed of the surface tension of our general model, and contributions arising from the adjacent space charge layers that can only lower the interfacial tension. Moreover, it turns out that surface reactions can be consistently incorporated into the Lippmann equation, provided that there is no charge transfer from one side of the interface to the other. We apply the model to curved liquid metal electrodes and compare our model to experimental data of several mercury–electrolyte interfaces. We obtain qualitative and quantitative agreement in the 2 V potential range for various salt concentrations.

From the bulk electrolyte solution to the electrochemical interface

This paper is aiming at presenting some relevant contributions of Jean-Pierre Badiali during the first ten years of his growing scientific activity. This presentation does not contain new materials but is based on a number of selected papers published in the seventies, a part of them written in French. The presentation is organized around three points. The first point, corresponding to his PhD thesis, is concerned with the study of ion-solvent and ion-ion interactions in a solution using complex dielectric permittivity measurements in the Hertzian and microwave frequency range. The second one is concerned with an analysis of the ion pair absorption band observed in the far infrared region in terms of an interionic potential energy. The third one is concerned with the metal-solution interface and his significant advances on (i) the Lippmann equation linking electrocapillary and electrical measurements and (ii) the contribution of the metal to the differential interfacial capacity.

Superhydrophobic films obtained from a spraying technique: Electrowetting dependence on the drying condition and ultraviolet irradiation

Superhydrophobic films were prepared using a spray technique. For these systems, the influence of the drying condition (atmospheric and vacuum) on their surface morphologies was investigated. Films obtained under vacuum exhibited a higher uniformity of surface morphology than those obtained under atmospheric pressure. For films dried under vacuum, electrowetting on dielectric (EWOD) effect was demonstrated. In the applied voltages from 0 to 100V, the variation range of the electrowetting contact angles was found be Δθ∼170. Before electrowetting saturation was achieved, the films displayed an electric breakdown. The influence of UV-C (254nm) irradiation times on the EWOD effect was also examined. The electrowetting experimental curves were observed be either nearly linear (0h and 3h) or nonlinear (12h and 24h). Young–Lippmann equation was able to describe the electrowetting behavior of irradiated films for 12h and 24h. The roughness of the films – obtained by atomic force microscopy – was observed to be nearly 14nm for films without irradiation and 80nm for those irradiated for 24h. The increase in the roughness was associated with the change of the electrowetting behavior after irradiation. These results pave the way for further studies on experimental factors that may control the EWOD effect.

Analysis of charging-induced structural damage in electrochemical systems.

Electrochemical charging of an electrochemical system results in Maxwell stress and a variation in the surface energy of the electrode. The charging-induced variation in the surface energy of the electrode and Maxwell stress introduce mechanical deformation and create stresses in the electrode. To relax the strain energy stored in the electrode, surface cracking and buckling can occur. Under the condition that the charging-induced change in the surface energy is the dominant factor controlling the in-plane deformation of a planar electrode, i.e. the bonding between the adsorbate and the substrate is weak, the variation in the surface energy of the electrode can be described by the Lippmann equation. Using the Lippmann equation, both the surface charge density on the electrode and the surface energy of the electrode are formulated as a function of the electrode potential. Analytical relations between the critical electrode potential and average damage size have been obtained for the charging-induced cracking and buckling in a planar, thin-film electrode. The results show that surface cracking will prevail over local buckling in accordance with experimental observations. Both critical electrode potentials are inversely proportional to the square root of the magnitude of the differential capacity of the electrical double layer at the electrode potential of zero charge.

Analysis of Electrowetting Phenomenon Using Image Processing Tool

Electrowetting has gained popularity in present days for its wide range of applications. This phenomenon can be described as change in the contact angle of solid-electrolyte interface caused by an application of potential difference between solid and the electrolyte. Application of voltage causes a hydrophobic surface to behave like hydrophilic surface. The electric energy counterbalances the free surface energy and lowers the surface tension [1, 2, 3]. The wide range of application of this phenomenon starts from electronic display, liquid lens with variable focal length in cellular phones, cameras, switches for optical fibres to biomedical applications like tumour detection, endoscopy etc. It is easy to operate and has fast response. In this paper we are studying the change in contact angle of the miniscule droplet with respect to variation in applied voltage in MATLAB 7.10.0 platform [4]. Image Processing tools are used on the liquid droplet obtained experimentally to find the angle made by the liquid meniscus with the horizontal plane. An algorithm is developed for automatic detection of boundary and measurement of the contact angle of the miniscule droplet. The experimental finding and the results obtained from the developed algorithm are in good agreement with each other. The guiding equation for the proposed work is based on Young- Lippmann equation.

Electrowetting on dielectrics on lubricating fluid-infused smooth/rough surfaces with negligible hysteresis

Low-voltage electrowetting on dielectrics on substrates with a thin layer of lubricating fluid to reduce contact angle hysteresis is reported here. On smooth and homogeneous solid surfaces, it is extremely difficult to reduce contact angle hysteresis (contact angle difference between advancing and receding drop volume cycle) and the electrowetting hysteresis (contact angle difference between increasing and decreasing voltage cycle) below 10°. On the other hand, electrowetting hysteresis on rough surfaces can be relatively large (~30°); therefore, they are not useful for most of the fluidic devices. In the present report, we demonstrate that using a thin layer of dielectric lubricating fluid on top of the solid dielectric surface reduces the contact angle hysteresis as well as electrowetting hysteresis below 2° on smooth as well as rough surfaces. Electrowetting on lubricating fluid-coated surfaces also show a threshold behavior and the threshold voltage depends on the viscosity of the lubricating fluid. Modified Lippmann equation is used to explain the electrowetting on lubricant-coated surfaces quantitatively. The experimental system can be modeled as two series capacitor, one each for dielectric lubricating fluid and solid dielectric, which jointly govern the electrowetting behavior, whereas the lubricating fluid also minimizes the contact angle hysteresis