Interface position definition

In Eq. 9, E is the interfacial tension, p the pressure, Vy the undisturbed velocity gradient tensor and Vy its transpose, tjm is the viscosity of the continuous phase, V is the total volume of the system, n is the unit vector orthogonal to the interface between the two phases, u is the velocity at the interface, dA is the area of an interfacial element and the integrals are evaluated over the whole interfadal area of the system, A. Since the constituents are assumed to be Newtonian all nonlinear contributions to the stress a(t) are caused entirely by the deformation of the droplet interface. The unit vectors n and u describe this deformation and can be computed using the Maffettone-Minale (MM) model for different frequencies and amplitudes. The MM model uses a second rank, symmetric and positive definite... 

By definition, electrode II at which oxidation is the predominant reaction is the anode, whereas electrode I at which reduction is the predominant reaction is the cathode. It is apparent that the removal of electrons from Ag will result in the potential of its interface becoming more positive, whilst the concomitant supply of electrons to the interface of Ag, will make its potential become more negative than the equilibrium potential ... 

For definiteness, the oxidation of copper to copper(l) oxide may be considered. Our picture of the process is that cation vacancies and positive holes formed at the Cu O/Oj interface by equation, 1.166 are transported to the Cu/CujO interface where they are destroyed by copper dissolving in the non-stoichiometric oxide. We require an expression for the rate of oxidation. 

At any interface between two different phases there will be a redistribution of charge in each phase at the interface with a consequent loss of its electroneutrality, although the interface as a whole remains electrically neutral. (Bockris considers an interface to be sharp and definite to within an atomic layer, whereas an interphase is less sharply defined and may extend from at least two molecular diameters to tens of thousands of nanometres the interphase may be regarded as the region between the two phases in which the properties have not yet reached those of the bulk of either phase .) In the simplest case the interface between a metal and a solution could be visualised as a line of excess electrons at the surface of the metal and an equal number of positive charges in the solution that are in contact with the metal (Fig. 20.2). Thus although each phase has an excess charge the interface as a whole is electrically neutral. 

At a definite value of the electrode potential E, the charge of the electrode s surface and hence the value of drop to zero. This potential is called the point of zero charge (PZC). The metal surface is positively charged at potentials more positive than the PZC and is negatively charged at potentials more negative than the PZC. The point of zero charge is a characteristic parameter for any electrode-electrolyte interface. The concept of PZC is of exceptional importance in electrochemistry. 

Electrochemical interfaces are sometimes referred to as electrified interfaces, meaning that potential differences, charge densities, dipole moments, and electric currents occur. It is obviously important to have a precise definition of the electrostatic potential of a phase. There are two different concepts. The outer or Volta potential ij)a of the phase a is the work required to bring a unit point charge from infinity to a point just outside the surface of the phase. By just outside we mean a position very close to the surface, but so fax away that the image interaction with the phase can be ignored in practice, that means a distance of about 10 5 — 10 3 cm from the surface. Obviously, the outer potential i/ a U a measurable quantity. 

This is the definition of the surface tension according to the Gibbs surface model [1], According to this definition, the surface tension is related to an interface, which behaves mechanically as a membrane stretched uniformly and isotropically by a force which is the same at all points and in all directions. The surface tension is given in J m-2. It should be noted that the volumes of both phases involved are defined by the Gibbs dividing surface X that is located at the position which makes the contribution from the curvatures negligible. 

Any surface (typically a piece of metal) on which an electrochemical reaction takes place will produce an electrochemical potential when in contact with an electrolyte (typically water containing dissolved ions). The unit of the electrochemical potential is volt (TV = 1JC1 s 1 in SI units).The metal, or strictly speaking the metal-electrolyte interface, is called an electrode and the electrochemical reaction taking place is called the electrode reaction. The electrochemical potential of a metal in a solution, or the electrode potential, cannot be determined absolutely. It is referred to as a potential relative to a fixed and known electrode potential set up by a reference electrode in the same electrolyte. In other words, an electrode potential is the potential of an electrode measured against a reference electrode. The standard hydrogen electrode (SHE) is universally adopted as the primary standard reference electrode with which all other electrodes are compared. By definition, the SHE potential is OV, i.e. the zero-point on the electrochemical potential scale. Electrode potentials may be more positive or more negative than the SHE. 

Concepts and terminology of adsorption processes on solid adsorbents are discussed by D. H, Everett, Reporting data on adsorption from solution at the solid/solution interface, Pure Appl. Chem. 58 967 (1986). See also D. H. Everett, Manual of Symbols and Terminology for Physicochemical Quantities and Units. Appendix II Definition, Terminology and Symbols in Colloid and Surface Chemistry, Butterworths, London, 1972 [published in Pure Appl. Chem. 31 577 (1972)]. The need for a relative definition of the amount of adsorbed substance stems from the fact that the actual position of an interface cannot be specified with absolute precision, even conceptually. 

The WE and CE combination represents a driven electrochemical cell. The presence of the RE allows the separation of the applied potential into a controlled portion (between the RE and the WE) and a controlling portion (between the RE and the CE). The voltage between the RE and the CE is changed by the potentio-stat in order the keep the controlled portion at the desired value. Consider the application of a potential Vin to the WE that is more positive than its rest potential, VffiSt, with respect to RE. By definition, polarization of the WE anodically (i.e., in a positive direction) would lead to an anodic current through the WE-solution interface and a release of electrons to the external circuit. These electrons would be transported by the potentiostat to the CE. A reduction reaction would occur at the CE-solution interface facilitated by a more negative potential across it. The circuit would be completed by ionic conduction through the solution. 

Note that this equation uses the unitless value of the Henry s law constant. If everything is at equilibrium, then there is no flow across the interface (F = 0), and thus, CWater = Cmf/ H, which is the definition of the Henry s law constant. By convention, if the flux is negative, the flow is from the atmosphere into the lake, and if the flux is positive, the flow is from the lake into the atmosphere. 

A schematic representation of the electrode-electrolyte interface is given as Figure 7.10, where the block used to represent the local Ohmic impedance reflects the complex character of the Ohmic contribution to the local impedance response. The impedance definitions presented in Table 7.2 were proposed by Huang et al. ° for local impedance variables. These differ in the potential and current used to calculate the impedance. To avoid confusion with local impedance values, the symbol y is used to designate the axial position in cylindrical coordinates. 

Performing macro-scale experiments it has been observed that the normal surface tension force induces higher normal stresses in the fluid on the concave side of the interface than on the other fluid on the convex side of the interface. In a micro-scale view we may say that this interfacial tension force is exerted by the interfacial material lying on the convex side of the surface upon the material lying on the concave side. The normal component of the surface force is thus frequently (not always ) defined positive into the mean curvature of the surface, in line with the physical observations. The direction of the normal component of the interface force given by (3.9) is determined by two factors, the interface normal unit vector n/ which we have defined positive into the curvature, and the mean curvature variable which we have chosen to define as an absolute value. That is, the variable used here determining the mean curvature of the surface Hi = ( i + K2)/ 2) is consistent with the definition... 

Figure 1. Model of A-B FGM structure (see definitions in the text). Points schematically represent potential for positive and negative sides of interface So-...

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