Quasistatic equilibrium

The elasticity depends on the rate of film expansion. Under quasistatic equilibrium conditions its values are very low and in such a case it is called Gibbs elasticity. When there is no equilibrium it is called Maiangoni elasticity. The largest value of the elasticity modulus, acquired when the adsorption layer behaves as insoluble one, is called Marangoni dilatation modulus Em). 

The film thickness is determined interferometrically. This technique allows to perform quasistatic equilibrium deformations and to study solutions with low (up to CMC) surfactant concentrations. 

The reactant properties and fuel cell condition determines the electrical potential difference between the anode and the cathode electrode. The following analysis assumes quasistatic equilibrium and a steady flow of gas and ions. 

To distinguish this case from the case with a stationary reference system, the solution is sometimes called a quasistatic equilibrium. 

A second equation is needed to determine the surface tension as a function of axial position. We adopt the quasistatic assumption that a is a unique equilibrium function of the surface excess concentration, T, even during dynamic events (17). A surface species continuity balance dictates how T varies along the interface. Upon neglect of surface diffusion and for h <1, the steady state form of this balance is... 

If the anisotropy is small enough that the differential term can be ignored, then the ratio of the surface energies is simply related to the cosine of the angle at which they meet. Note that one criterion for the application of Eq. 3 is that the facets are in local equilibrium. For this to be true, there must be no net growth or evaporation. If this is true, then thermal grooves at surface-grain boundary intersections should maintain a quasistatic profile and increase in width with the one quarter power of time [45]. 

Quasistatic process. One that involves passage through a large succession of very closely spaced equilibrium states. In this process the surroundings may be altered such that on the return path to the original system configuration the universe ends up in a different state. 

The equilibrium solubility was measured in a quasistatic apparatus. (See the table below.) Synonyms [2R[2R (4R, 8R )]]-3,4-Dihydro-2,8-dimethyl-2-(4,8,12-trimethyltridecyl)-2R-benzopyran-6-ol D-5-Tocopherol... 

Having solved the elastic boundary value problem and from it obtained the relevant interfacial concentrations, we are then prepared to obtain the concentration fields throughout the solid from which we compute the flux to or away from the various particles. Since we are assuming the situation to be quasistatic, the instantaneous concentration fields must satisfy an equilibrium condition, namely,... 

In quasistatic (or dynamic) techniques, a steady rate of boiling or evaporation is established, and it is assumed that the pressure attained in this steady state is the same as the equilibrium pressure. In careful experiments, pressures are measured at several evaporation rates to verify that they do not depend upon the rate within the experimental conditions. 

Also very important of course are processes leading from a metastable equilibrium state to a stable equilibrium state. These are irreversible, because when the (extra) constraint is released, even momentarily, the system is not in balance and proceeds in one direction, towards equilibrium. However, this inexorable progress towards equilibrium can be performed in one jump or can be halted in a succession of (metastable) equilibrium states called a quasistatic process. 

In many presentations of thermodynamics, quasistatic processes are either not mentioned or are said to be the same as reversible processes. In our usage, however, quasistatic processes are similar to reversible ones in that they are a continuous succession of equilibrium states, but these states are metastable equilibrium states, not stable equilibrium states. A quasistatic process is most easily imagined as resulting when one of the constraints on a metastable equilibrium state is released for an extremely short time, then re-imposed. While the constraint is released, the system changes slightly but irreversibly towards equilibrium, then settles down in its new metastable equilibrium state when the constraint is re-applied. This succession of events is repeated until the final state is reached. 

Look up the definitions of equilibrium, stable, metastable, reversible and quasistatic in any textbooks on thermodynamics or physical chemistry you have at hand, and reflect on the differences between them and the definitions in this text. 

We have tried to show that the affinity is a convenient representation of how far a system is from stable equilibrium, and increments in the progress variable allows us to consider the system at various stages as it progresses towards stable equilibrium. This progress is a part of the model we call a quasistatic reaction—a continuous succession of metastable equilibrium states in an overall irreversible reaction. 

In addition, the strong fields at the surface and interface at elevated temperatures may lead to field-assisted diffusion of mobile ion species such as protons and alkali ions, and strong illumination will require a new quasistatic equilibration, accompanied possibly by photodesorption (or adsorption), which might require long-time relaxation back to the dark equilibrium. 

In equilibrium (for / = 0 and constant X) and quasistatic transition, we have AStot = 0 and thus -ASm = AS. Stochastic entropy S(t) obeys the relation, TS = U — G, along the fluctuating trajectory at any time in the form ... 

For such theory, a,p,y,d,2., and are expansion coefficients that are extracted from the experimentally measured quasistatic hysteretic response of a single-crystal. Physically, the first three terms of the right hand side of the first row of the Helmholtz free energy expressoin defines the equilibrium, stress and electric field free variants of the system. The fourth term couples an externally specified electric field to the local state of polarization of the solid. Such contribution biases the stability of those variants that are closer (or parallel) to the applied field. The fifth term... 

Crystallization is bypassed. We speak of a frozen-in, supercooled, liquid-like structure. This type of quasistatic solid structure is thermodynamically controlled but not in thermal equilibrium and thus is not absolutely stable it tends to relax and slowly approach an equilibrium structure (whatever this may be in a complex multicomponent composition, it represents a minimum of the Gibbs free enthalpy). This also means that all... 

T(X2> In particular, according to the present quasistatic theory in which ( ) and (b) are assumed, a fiber initially in equilioriura in a state of homogeneous strain with X. < cannot be drawn without passing through a state in which the tension equals T(Xj ), which is, of course, greater than T, the equilibrium tension in a fully developed draw. 

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