Hydrodynamic conditions

In chronoamperometry, the response of a simple, reversible electrode reaction on any type of electrode is given by the equation  

The second limit corresponds to the steady-state conditions under which the distance 8 and the current do not depend on time. This constant current is significant only on microelectrodes, while, on macroelectrodes, practically useful steady-state conditions can be established only by stirring the solution. The stirring can be achieved either by rotating a disk electrode, or by using a stationary electrode in the agitated solution [42, 56]. In electroanalysis, the main purpose of stirring is to increase the efficacy of accumulation of analytes on the electrode surface. 

The functions F(y), G(y), and H(y) are shown in Fig. III. 1.4. Around the center of the base of the cylinder, where the metal disk lies, the axial component of the solution velocity is most important, since the electroactive material is transported 

The current density on a stationary electrode immersed in a flowing solution is not uniform over the whole electrode surface. At an inlaid plate over which the solution flows, the diffusion layer thickness and the steady-state distance 8 increase downstream [57, 65, 66]  

Here v is the solution velocity and JC is the distance from the electrode edge in the direction of the flow. Similarly, the distance 5 at a tubular electrode is 

The rotating disk electrode is a small metal disk inlaid into an insulating cylinder having a large base [43-46]. The disk is situated in the center of the base. The cylinder is mounted on a metallic axle that is connected to an electromotor. The axle is perpendicular to the base and lies in the axis of the cylinder. The axle is connected to the metal disk by a wire, and bears a metallic bell that rotates in a mercury pool to obtain noiseless electrical contact with the elec- 

G(y) and H(y) are shown in Fig. III.1.4. Around the center of the base of the cylinder, where the metal disk lies, the axial component of the solution velocity is most important, since the electroactive material is transported towards the surface in this direction only. Under chronoamperometric conditions, a diffusion layer develops at the electrode surface and extends as far into the solution as the flux at the surface is not equal to the rate of mass transport in the bulk of the solution. Under steady-state conditions, the distance 6 depends on the electrode rotation rate [43]  

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The diffusion layer widtli is very much dependent on tire degree of agitation of tire electrolyte. Thus, via tire parameter 5, tire hydrodynamics of tire solution can be considered. Experimentally, defined hydrodynamic conditions are achieved by a rotating cylinder, disc or ring-disc electrodes, for which analytical solutions for tire diffusion equation are available [37, 4T, 42 and 43]. 

The detennination of biological affinity by mixing two species and measuring tlieir rates of association and dissociation presupposes tliat tire contribution of transport to tire association dynamics is precisely known. Well-defined hydrodynamic conditions are tlierefore a prerequisite for tire experimental detennination of affinities via rates. 

External Fluid Film Resistance. A particle immersed ia a fluid is always surrounded by a laminar fluid film or boundary layer through which an adsorbiag or desorbiag molecule must diffuse. The thickness of this layer, and therefore the mass transfer resistance, depends on the hydrodynamic conditions. Mass transfer ia packed beds and other common contacting devices has been widely studied. The rate data are normally expressed ia terms of a simple linear rate expression of the form... 

The mass-transfer coefficients are typically between 10 to 100 p.m/s, depending on hydrodynamic conditions and the values of D. 

This is essentially a corrosion reaction involving anodic metal dissolution where the conjugate reaction is the hydrogen (qv) evolution process. Hence, the rate depends on temperature, concentration of acid, inhibiting agents, nature of the surface oxide film, etc. Unless the metal chloride is insoluble in aqueous solution eg, Ag or Hg ", the reaction products are removed from the metal or alloy surface by dissolution. The extent of removal is controUed by the local hydrodynamic conditions. 

Metals. Most metals react with aqueous HCl foUowing equation 22. The reaction rate is dependent on the concentration of the acid, oxidi2ing, reducing, or complexing agents, and corrosion inhibitors, in addition to the metallurgical characteristics of the material and the prevailing hydrodynamic conditions (see Corrosion and corrosion control). 

A general flow map of different hydrodynamic conditions (Fig. 23) consists of regions of flooding, dispersion, and recirculation on a plot of N vs for a Rushton turbine. For a low viscosity aqueous/air system, the gas flow numbers for the three conditions are given hy FI = 30Fr[D/TY for flooding, = 0.2Fr° (F/r)° for complete dispersion, and =13FF D/TY for recirculation. 

A number of analytical solutions have been derived for iC as a function of channel dimensions and fluid velocity (30). In practice, the fit between theory and data for K is poor except in idealized cases. Most processes exhibit either higher fluxes, presumably caused by physical dismption of the gel layer from the nonideal hydrodynamic conditions, or lower fluxes caused by fouling (31). In addition, iCis a function of the fluid composition. 

Ultrafiltration equipment suppHers derive K empirically for their equipment on specific process fluids. Flux J is plotted versus log for a set of operation conditions in Figure 6 K is the slope, and is found by extrapolating to zero flux. Operating at different hydrodynamic conditions yields differently sloped curves through C. ... 

For very small AP, flux is linear with pressure. Figure 7 shows a graph of flux versus pressure. Curve A is the pure water flux from equation 1, curve B is the theoretical permeate flux (TPE) for a typical process. As the gel layer forms, the flux deviates from the TPF following equation 7 and curve D results. Changing the hydrodynamic conditions changes K and results in a different operating curve, curve C. 

In 1981, a novel flotation device known as the air-sparged hydrocyclone, shown in Figure 3, was developed (16). In this equipment, a thin film and swid flotation is accompHshed in a centrifugal field, where air sparges through a porous wall. Because of the enhanced hydrodynamic condition, separation of fine hydrophobic particles can be readily accompHshed. Also, retention times can be reduced to a matter of seconds. Thus, this device provides up to 200 times the throughput of conventional flotation cells at similar yields and product quaHties. 

The traditional view of emulsion stability (1,2) was concerned with systems of two isotropic, Newtonian Hquids of which one is dispersed in the other in the form of spherical droplets. The stabilization of such a system was achieved by adsorbed amphiphiles, which modify interfacial properties and to some extent the colloidal forces across a thin Hquid film, after the hydrodynamic conditions of the latter had been taken into consideration. However, a large number of emulsions, in fact, contain more than two phases. The importance of the third phase was recognized early (3) and the lUPAC definition of an emulsion included a third phase (4). With this relation in mind, this article deals with two-phase emulsions as an introduction. These systems are useful in discussing the details of formation and destabilization, because of their relative simplicity. The subsequent treatment focuses on three-phase emulsions, outlining three special cases. The presence of the third phase is shown in order to monitor the properties of the emulsion in a significant manner. 

Extraparticle Transport and Dispersion Mechanisms Extraparticle mechanisms are affecded by the design of the contacting device and depend on the hydrodynamic conditions outside the particles. 

External mass tran.sfer between the external surfaces of the adsorbent particles and the surrounding fluid phase. The driving force is the concentration difference across the boundary layer that surrounds each particle, and the latter is affected by the hydrodynamic conditions outside the particles. 

Particle-Bubble Attachment. In the above, principles leading to creation of desired hydrophobicity/hydrophihcity of the particles has been discussed. The next step is to create conditions for particle-bubble contact, attachment, and their removal, which is simply described as a combination of three stochastic events with which are associated the probability of particle-bubble colhsion, probabihty of attachment, and probability of retention of attachment. The first term is controlled by the hydrodynamic conditions prevaihng in the flotation unit. The second is determined by the surface forces. The third is dependent on the s irvival of the laden bubble by liq ud t irbulence and impacts by the other suspended particles. A detailed description of the hydrodynamic and other physical aspects of flotation is found in the monograph by Schulze (19 ). 

The factors to consider in the selection of cross-flow filtration include the cross-flow velocity, the driving pressure, the separation characteristics of the membrane (permeability and pore size), size of particulates relative to the membrane pore dimensions, and the hydrodynamic conditions within the flow module. Again, since particle-particle and particle-membrane interactions are key, broth conditioning (ionic strength, pH, etc.) may be necessary to optimize performance. 

Stable regiTTie The preferable hydrodynamic condition of the aerated liquid on a sieve tray. The aerated material exists as a stable froth gas-liquid contact is good. 

It is generally tme to say that, as speed increases, the oil viscosity decreases, that is, if hydrodynamic conditions exist. Relatively low viscosity oil will allow the oil to spread rapidly over the tooth surfaces before meshing and, in the case of forced lubrication, ease circulation. In the case of bath lubrication, it will eliminate the oil drag effect. 

Kassner used a rotating disc, for which the hydrodynamic conditions are well defined, to study the dissolution kinetics of Type 304 stainless steel in liquid Bi-Sn eutectic. He established a temperature and velocity dependence of the dissolution rate that was consistent with liquid diffusion control with a transition to reaction control at 860 C when the speed of the disc was increased. The rotating disc technique has also been used to investigate the corrosion stability of both alloy and stainless steels in molten iron sulphide and a copper/65% calcium melt at 1220 C . The dissolution rate of the steels tested was two orders of magnitude higher in the molten sulphide than in the metal melt. 

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. 

Thus, under the hydrodynamic conditions prevailing at high rotation rates, the one-electron product is removed more rapidly by convection than by the chemical reaction, while at slow rotation speeds the chemical reaction and further electron transfer predominates. The form of the electrode and the hydrodynamic conditions prevailing in the electrolysis solution are therefore parameters which require controlling but which give additional flexibility in the design of syntheses. 

The geometry of the reactor is of great importance owing to the fact that it is necessary to obtain good heat and mass transfer characteristics while working with laminar hydrodynamic conditions in order to assume a sufficient residence time compared to the reaction time. 

In the range of 500 to 900 rpm, Fig. 3 and 4 showed that impeller rotation speed does not affect significantly on reaction conversion for relatively long reaction time (above 60 minutes). Apparently, the hydrodynamic condition of liquid in the reactor was sufficiently turbulent by aeration. 

Actual concentration profiles (Fig. 1.28) in the very near vicinity of a mass transfer interface are complex, since they result from an interaction between the mass transfer process and the local hydrodynamic conditions, which change gradually from stagnant flow, close to the interface, to more turbulent flow within the bulk phases. 

Since the mass transfer coefficient, k, and the specific interfacial area, a, vary in a similar manner, dependent upon the hydrodynamic conditions and system physical properties, they are frequently combined and referred to as a "ka value" or more properly as a mass transfer coefficient. 

The archetypal, stagewise extraction device is the mixer-settler. This consists essentially of a well-mixed agitated vessel, in which the two liquid phases are mixed and brought into intimate contact to form a two phase dispersion, which then flows into the settler for the mechanical separation of the two liquid phases by continuous decantation. The settler, in its most basic form, consists of a large empty tank, provided with weirs to allow the separated phases to discharge. The dispersion entering the settler from the mixer forms an emulsion band, from which the dispersed phase droplets coalesce into the two separate liquid phases. The mixer must adequately disperse the two phases, and the hydrodynamic conditions within the mixer are usually such that a close approach to equilibrium is obtained within the mixer. The settler therefore contributes little mass transfer function to the overall extraction device. 

Ignoring the quite distinct functions and hydrodynamic conditions which exist in the actual mixer and settler items of the combined mixer-settler unit, it is possible, in principle, to treat the combined unit simply as a well-mixed equilibrium stage. This is done in exactly the way, as considered previously in Secs. 3.2.1 to 3.2.6. A schematic representation of an actual mixer-settler... 

Since the vapour phase dynamics are negligible, the vapour flow rate through the column is constant from plate to plate, at the rate of V, k mol/s. The liquid flow rates Ln, and the liquid holdup on the plate, however, will vary, under changing hydrodynamic conditions in the column. The corresponding notation, for any plate n in the column, is as indicated in Fig. 3.58. 

Levich124 has given the relationships between the limiting current i) and the bulk concentration C of the metal ion for plate electrodes, conical electrodes and rotated disc electrodes (RDEs) under hydrodynamic conditions anticipating his well known equations treated in Section 3.3.2.2 on hydrodynamic electrodes, we may assume the relationships concerned using the more general equation... 

As titrations require rapid and complete chemical reactions, it is mandatory to work under hydrodynamic conditions hence, with stationary electrodes, which are often used in voltammetric titrations, the solution is stirred by a mechanical or magnetic stirrer with rotating electrodes an additional stirring may sometimes be superfluous. 

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