Thickness of the diffusion layer

The repulsion between oil droplets will be more effective in preventing flocculation Ae greater the thickness of the diffuse layer and the greater the value of 0. the surface potential. These two quantities depend oppositely on the electrolyte concentration, however. The total surface potential should increase with electrolyte concentration, since the absolute excess of anions over cations in the oil phase should increase. On the other hand, the half-thickness of the double layer decreases with increasing electrolyte concentration. The plot of emulsion stability versus electrolyte concentration may thus go through a maximum. 

The rate of dissolving of a solid is determined by the rate of diffusion through a boundary layer of solution. Derive the equation for the net rate of dissolving. Take Co to be the saturation concentration and rf to be the effective thickness of the diffusion layer denote diffusion coefficient by . 

The region of the gradual potential drop from the Helmholtz layer into the bulk of the solution is called the Gouy or diffuse layer (29,30). The Gouy layer has similar characteristics to the ion atmosphere from electrolyte theory. This layer has an almost exponential decay of potential with increasing distance. The thickness of the diffuse layer may be approximated by the Debye length of the electrolyte. 

From the ion density profiles it is obvious that the surface charge is screened within less than 10 A. Thus, the thickness of the diffuse layer is of the same order of magnitude as the one derived from the Debye... 

Figure 1.3 la to c shows how an increase in the concentration of dissolved oxygen or an increase in velocity increases /Y and thereby increases. It has been shown in equation 1.73 that /Y increases with the concentration of oxygen and temperature, and with decrease in thickness of the diffusion layer, and similar considerations apply to. Thus Uhlig, Triadis and Stern found that the corrosion rate of mild steel in slowly moving water at... 

The interchange reaction implies the removal of one atom of /I at the surface for each atom of B deposited. It therefore takes place with a minimum change in weight or dimensions of the article (A). U A and B have similar atomic weights, as in the case of iron and chromium, interchange reaction will produce little change in weight and no measurable increase in dimension, whatever the thickness of the diffusion layer. 

Example 5 A stainless steel pipe is to be used to convey an aerated reducing acid at high velocity. If the concentration of dissolved Oj is 10 mol dm (10 mol cm ) calculate whether or not the steel will corrode when (a) the acid is static, (b) the acid is moving at high velocity. Assume that the critical current density for passivation of the steel in the acid is 200/iAcm the thickness of the diffusion layer is 0-05 cm when the acid is static and 0-005 cm when the acid flows at a high velocity assume the diffusion coeffi-... 

In the thin-layer cavity cell technique, a cell is constructed to give a thin cavity on one wall of which the metal-plate working electrode is mounted. This wall is separated by a Teflon sheet in which a central aperture has been cut out, from the opposite wall of the cavity this wall contains entry and exit tubes for the test solution which is caused to flow past the working electrode provision is made for connections to the other electrodes. If the Teflon sheet is thin enough (about 0.05 mm), the distance between the two walls of the cavity is less than the normal thickness of the diffusion layer of the electrolyte when undergoing electrolysis, and so electrolysis within the cavity is rapid.26... 

Well-defined hydrodynamic conditions, with high rate of mass transport, are essential for successful use of electrochemical detectors. Based on the Nemst approximate approach, the thickness of the diffusion layer (<5) is empirically related to the solution flow rate (U) via... 

Electron-ion transduction allows local modulation of the ionic concentration in a solution at a distance from the electrode that is less than the thickness of the diffusion layer.171-173 The solution volume can be modified through the hydrodynamic conditions or the viscosity of the polymeric surrounding in order to reduce or enlarge the thickness of the diffusion layer. 

This treatment may be compared with that given in Chapter 4. The top of the stagnant film is assumed to have a gas concentration in equilibrium with the overlying air (i.e., Cg = fCnTg). The unknown values are the flux and the thickness of the diffusive layer 2. The thickness 2 has been determined by analyses of isotopes and Rn) that can be used to obtain the flux (Broecker and Peng, 1974 Peng et al., 1979). The... 

Figure 4 illustrates the dependence of on Aq for the case when r = 1 at several different values of [Fig. 4(a)] and when = 0.5 and at several different values of r [Fig. 4(b)]. From Fig. 4(a), one can see that takes a maximum around y = 0, i.e., Aq The volume ratio affects strongly the value of as shown in Fig. 4(b), which is ascribed to the dependence of the equilibrium concentration on r through Eq. (25). This simple example illustrates the necessity of taking into account the variation of the phase-boundary potential, and hence the adsorption of i, when one tries to measure the adsorption properties of a certain ionic species in the oil-water two-phase systems by changing the concentration of i in one of the phases. A similar situation exists also in voltammetric measurements of the transfer of surface-active ions across the polarized O/W interface. In this case, the time-varying thickness of the diffusion layers plays the role of the fixed volume in the above partition example. The adsorption of surface-active ions is hence expected to reach a maximum around the half-wave potential of the ion transfer. 

It can be seen that the dissolution rate constant kD is equivalent to the diffusion coefficient divided by the thickness of the diffusion layer (D/h). 

Convective diffusion to a growing sphere. In the polarographic method (see Section 5.5) a dropping mercury electrode is most often used. Transport to this electrode has the character of convective diffusion, which, however, does not proceed under steady-state conditions. Convection results from growth of the electrode, producing radial motion of the solution towards the electrode surface. It will be assumed that the thickness of the diffusion layer formed around the spherical surface is much smaller than the radius of the sphere (the drop is approximated as an ideal spherical surface). The spherical surface can then be replaced by a planar surface... 

An example of a vapor pressure profile is shown in Figure 11, where it is assumed that the relative humidity within the chamber is 80%, the critical relative humidity of the solid is 40%, and the thickness of the diffusion layer (8) is 1 cm. From the figure, note that the relative humidity profile is linear and we could have made the simplifying assumption that the convective term is negligible. By ignoring the convective term, Eq. (42) simplifies to... 

The important variables in Eq. (44) are the thickness of the diffusion layer (8) and the partial pressures of water vapor in the chamber and above the solid surface Pc and Ps). 

Electrolyte mixing is necessary to maintain the particles in suspension, unless the particles are neutrally buoyant, and to transport the particles to the surface of the electrode. The hydrodynamics of the electrodeposition system control the rate, direction, and force with which the suspended particles contact the electrode surface. Bringing the particles in contact with the electrode is a necessary step for the incorporation of particles into the metal matrix, although particle-electrode contact does not guarantee incorporation of the particle. Of course, an increase in flow can increase the plating rate as the thickness of the diffusion layer at the electrode surface decreases. 

The rate of agitation, stirring, or flow of solvent, if the dissolution is transport-controlled, but not when the dissolution is reaction-con-trolled. Increasing the agitation rate corresponds to an increased hydrodynamic flow rate and to an increased Reynolds number [104, 117] and results in a reduction in the thickness of the diffusion layer in Eqs. (43), (45), (46), (49), and (50) for transport control. Therefore, an increased agitation rate will increase the dissolution rate, if the dissolution is transport-controlled (Eqs. (41 16,49,51,52), but will have no effect if the dissolution is reaction-controlled. Turbulent flow (which occurs at Reynolds numbers exceeding 1000 to 2000 and which is a chaotic phenomenon) may cause irreproducible and/or unpredictable dissolution rates [104,117] and should therefore be avoided. 

At a rotating disc the thickness of the diffusion layer decreases with increasing rotation rate according to ... 

In contrast to the rotating disc electrode, mass transport to the ring is nonuniform. Nevertheless, the thickness of the diffusion layer Spj, which depends on the coordinate x in the direction of flow, and the rate of mass transport can be calculated. We consider a simple redox reaction, and rewrite Eq. (14.5) in the form ... 

V, where the plateau is reached and a quantitative determination can be done. The column effluent is pumped through the detector, and if this contains compounds that can be oxidized at the set potential the current through the electrode increases. The current is equivalent to the amount of compounds, but not necessarily the same for all kinds of compounds. This depends on the number of electrons that are involved in the electrode reaction, on the electrode kinetics, and on the thickness of the diffusion layer, d. This is expressed in Fick s first law ... 

Then an approximate analytical solution of the convective diffusion equation (43), which satisfies the boundary conditions, equation (44), is available under the assumption that the thickness of the diffusion layer <5, is small compared with the body radius r0 (p. 80 in [25]). As in the example of Section 4.1 (see equation (33)), the results of the derivation can be formally written in terms of the diffusion layer thickness, which now is ... 

In both regimes, speeding up electrolysis requires diminishing the time constant of the cell [equation (2.32)] by decreasing the volume-to-surface area ratio and/or the thickness of the diffusion layer by increasing the rate of stirring or of electrolyte circulation. 

During an electrode reaction in an unstirred solution, the thickness of the diffusion layer grows with time up to a limiting value of about 10- 4 m, beyond which, because of the Brownian motion, the charges become uniformely distributed. At ambient temperature the diffusion layer reaches such a limiting value in about 10 s. This implies that in an electrochemical experiment, the variation of concentration of a species close to the electrode surface can be attributed to diffusion only for about 10 s, then convection takes place. 

The slope of each concentration profile expresses the concentration gradient of species Ox at various times, 8C0x(x,t)/8x, where 8Cox(x,t) = Cox(x>t) C ox- The point at which the concentration gradient becomes zero (i.e. when C0x(.x, ) = C Qx, or COx(x,t)/C 0x = 1) identifies the thickness of the diffusion layer. 

The thickness of the diffusion layer (in metres) is approximately 6(Z>ox01/2-... 

There are a few electrochemical techniques in which the working electrode is moved with respect to the solution (i.e. either the solution is agitated or the electrode is vibrated or rotated). Under these conditions, the thickness of the diffusion layer decreases so that the concentration gradient increases. Since the rate of the mass transport to an electrode is proportional to the concentration gradient (Chapter 1, Section 4.2.2), the thinning of the diffusion layer leads to an increase of the mass transport, and hence to an increase of the faradaic currents. 

---