Local concentration difference

There are no films or protective surface films on active metals, e.g., mild steel in acid or saline solutions. Passive metals are protected by dense, less readily soluble surface films (see Section 2.3.1.2). These include, for example, high-alloy Cr steels and NiCr alloys as well as A1 and Ti in neutral solutions. Selective corrosion of alloys is largely a result of local concentration differences of alloying elements which are important for corrosion resistance e.g., Cr [4],... 

The information is qualitative in nature. The area density of dots suggests local concentration differences, but the count rate at each point, which is fundamental information required for quantitation, is lost. 

Positive deviations of it1/2 with increasing time can also be evidence for convection within an electrochemical cell. Convection can be caused by external vibrations or by density gradients created by the local concentration differences resulting from the electrochemical perturbation. While the influence of external vibrations can be largely eliminated by isolation of the cell with a damped table, the natural convection due to unequal densities of O and R is an unavoidable consequence of the experiment, the importance of which depends on the particular species involved. The effect of natural convection at planar electrodes is most serious when the surface is mounted vertically. It is therefore desirable to carry out electrochemical experiments at surfaces facing up or down whenever possible. 

We note that earlier research focused on the similarities of defect interaction and their motion in block copolymers and thermotropic nematics or smectics [181, 182], Thermotropic liquid crystals, however, are one-component homogeneous systems and are characterized by a non-conserved orientational order parameter. In contrast, in block copolymers the local concentration difference between two components is essentially conserved. In this respect, the microphase-separated structures in block copolymers are anticipated to have close similarities to lyotropic systems, which are composed of a polar medium (water) and a non-polar medium (surfactant structure). The phases of the lyotropic systems (such as lamella, cylinder, or micellar phases) are determined by the surfactant concentration. Similarly to lyotropic phases, the morphology in block copolymers is ascertained by the volume fraction of the components and their interaction. Therefore, in lyotropic systems and in block copolymers, the dynamics and annihilation of structural defects require a change in the local concentration difference between components as well as a change in the orientational order. Consequently, if single defect transformations could be monitored in real time and space, block copolymers could be considered as suitable model systems for studying transport mechanisms and phase transitions in 2D fluid materials such as membranes [183], lyotropic liquid crystals [184], and microemulsions [185],... 

Local concentration differences of a particular element or compound in a given structure of a material... 

Many attempts have been made to synthesise organophosphorus compounds directly from the element with varying degrees of success.i In general mixtures of products are obtained, and the yields are frequently low and variable. The main difficulty is the insolubility of phosphorus in organic liquids and consequently the reactions are heterogeneous with the attendant problems of diffusion and local concentration differences. 

One could ask why the area densities may be different on the two sides of the barrier. This is due to the innate asymmetry in the metal—oxide-oxygen structure. One interface of the oxide may constitute the sink for defects whereas the other interface constitutes the source of the defects. The attendant concentration difference across the oxide layer leads to local concentration differences across the individual barriers. In other words, the area density differences are simply a manifestation of the concentration gradient which exists in the oxide for a given type of defect species. 

The mass flux of a solute can be related to a mass transfer coefficient which gathers both mass transport properties and hydrodynamic conditions of the system (fluid flow and hydrodynamic characteristics of the membrane module). The total amount transferred of a given solute from the feed to the receiving phase can be assumed to be proportional to the concentration difference between both phases and to the interfacial area, defining the proportionality ratio by a mass transfer coefficient. Several types of mass transfer coefficients can be distinguished as a function of the definition of the concentration differences involved. When local concentration differences at a particular position of the membrane module are considered the local mass transfer coefficient is obtained, in contrast to the average mass transfer coefficient [37]. 

The aqueous solutions have received attention for more than a century because they are of industrial, environmental and scientific importance. One of the features of the aqueous solutions of organic substances is their microheterogeneity, reflected in the fact that the local concentration differs from the bulk concentration. The microheterogeneities in solutions can be characterized by the following nanometer-level parameters (1) the correlation volume, i.e. the volume in which the concentration differs from the average concentration, (2) the excess (or deficit) number of molecules in the correlation volume compared to the number of molecules when they are randomly distributed, and (3) the inter molecular interactions between the molecules in the above volume. 

The ion concentrations and the electric potential inside these materials can be computed by the chemical and the electrical field equations. The local concentration differences form an osmotic pressure difference which results in a mechanical strain. Based on this, the swelling/bending of the polymer gel film may be obtained. 

Finally, the Landau-Ginzburg approach can be applied to microemulsions. In this approach the thermodynamic behavior of a system in the neighborhood of critical points is studied. For microemulsions this approach uses the expansion of the free energy in (spatially varying) order parameter fields that are identified as the local concentration differences of oil, water, and surfactant. We will not elaborate this approach but refer to a recent review by Gompper [25]. 

The functional (15) determines via the Boltzmann weight exp(—/ o[d>]) the probability of each configuration of the order parameter field (r) to occur in thermal equilibrium. In the ternary system under consideration, the order parameter field d>(r) is identified with the local concentration difference of oil and water. The local amphiphile concentration is considered to be integrated out in this model [41]. 

Local concentration differences caused by the interfacial mass transfer change the interfacial tension and, in turn, produce convections in the interface. By friction forces these convections enhance intensive motions on both sides of the interphase that can have regular (rolling cells) or irregular (eruptions) structures (Fig. 6.4-10). An example of Marangoni enhanced eruptions is shown in Fig. 6.4-11 (Wolf 1999). Such random motions have the potential to increase mass transfer rates by one order of magnitude. They are, however, not predictable with sufficient accuracy. 

As mentioned above, raising the pH is the most common way to perform deposition-precipitation. To avoid precipitation in solution, and to have local concentration differences in the suspension of the support minimized, it is better if the mixing and the generation of the precipitant can be carried out separately. It is crucial to maintain the concentration continuously below that of the supersolubility curve SS. 

Let i/ (r) describe the local concentration difference between oil and water, and p(r) the local surfactant concentration. What we have assumed in our model is that (i) the profiles of ij/ and p at oil/water interfaces do not depend on the average values of j/ and p (denoted hereafter as ij/ and p, respectively) and that (ii) the coarse-graining dynamics of ij/ based on the free energy becomes slow when the amplitude of p at the interface takes a certain... 

From the molecular viewpoint, the transfer of mass at the interface is stochastic and subsequently produces local concentration difference Ac from which the surface tension difference Ac is also established so as to induce interfacial circulation it is called Marangoni convection. Furthermore, due to the density at the interface is different from that of the bulk fluid by Ap, circulation between interface and the bulk fluid is also induced, which is called Rayleigh convection. Nevertheless, the creation of Act may be also due to the interfacial local temperature difference AT and the Ap may be achieved due to the temperature difference between interface and the bulk. Thus, there are AT-based besides Ac-based Marangoni convection and Rayleigh convection. 

Reaction Fast parallel reactions represented by Equation 2.59 belong to a category of reactions, where the product distribution depends upon the reactant mixing. If the reaction partner A3 is added to a solution containing Ai and A2 under conditions of immediate mixing (tmx hi, hz). the product distribution will depend on the intrinsic kinetics. But if the mixing time is on the same order as the reaction times, local concentration differences will appear and the product distribution will depend on the mixing intensity. 

The above theoretical approaches apply estimating MTCs for the forced convection of fluid flowing parallel to a surface. Typically, the fluid forcing process is external to the fluid body. In the case of natural or free convection fluid motion occurs because of gravitational forces (i.e., g = 9.81 m/s ) acting upon fluid density differences within (i.e., internal to) regions of the fluid. Temperature differences across fluid boundary layers are a major factor enhancing chemical mass transport in these locales. Concentration differences may be present as well, and these produce density differences that also drive internal fluid motion (i.e., free convection). 

In a similar manner it is possible to define a A parameter for the electrical experiment if the voltage drop over the layer is taken as the driving force (see Chapter 7). Ap stands for p(x=0) — p(x=s). The coordinate x=0 refers to the locus in the sample immediately adjacent to the layer, while x=s refers to the locus in the layer immediately adjacent to the gas phase. The latter is, for the case assiuued, in immediate equilibrium with the gas phase. Apart from a geometric factor, the constants of proportionality correspond to the effective conductivities (oq, <7 ) in the layer. The component or tracer fluxes can then, also, be regarded as driven by the local concentration differences , whereby the k value is defined ... 

In this book, we always choose to use the local concentration difference at a particular position in the column. Such a choice implies a local mass transfer coefficient to distinguish it from an average mass transfer coefficient. Use of a local coefficient means that we often must make a few extra mathematical calculations. However, the local coefficient is more nearly constant, a smooth function of changes in other process variables. This definition was implicitly used in Examples 8.1-1, 8.1-3, and 8.1-4 in the previous section. It was used in parallel with a type of average coefficient in Example 8.1-2. 

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