Diffusion stationary

Under conditions of stationary (unidirectional and constant) mass transfer. Pick s first law describes the phenomenon of diffusion  

Laboratory tests of stationary diffusion of chloride ions in cementitious systems have been conducted since the 1970s for purposes of research and classification of different concrete compositions [5]. 

After a certain transition period (lag time, y, the flux of the species that diffuses through the sample becomes constant. If Q and C2, respectively, stand for the concentrations in the upstream and downstream chambers measured at time t from the beginning of the tesL L the thickness (m) of the sample, A the cross section (m ) and V the volume of the downstream chamber (m ). Pick s first law can be written as follows  

From this relationship the steady-state diffusion coefficient can be calculated. This kind of test can be used to compare the characteristics of different concretes with regard to chloride diffusion. A practical complication may be that concrete with low porosity may require a very long time to reach a constant flux. Values found for the steady-state effective chloride diffusion coefficient may vary from to 10 m /s for concrete with various binders and w/c [18, 19]. 

The reason for this layer formation in a stirred electrolyte is viscosity. While the concentration outside this layer is always kept equal to the bulk concentration by the flow of the electrolyte, the flow rate of the electrolyte in the layer is continuously decreasing and therefore approaches zero at the electrode surface. 

The flow rate decrease is linear for laminar flow and nonlinear for turbulent flow. The Reynolds number describes the border between laminar and turbulent flow. The Reynolds 

The Reynolds number has no dimension. The critical value for the transition from laminar to turbulent flow is of the order 10 to 10 . 

Pick s first law can be used to describe the diffusion to the electrode surface through the diffusion layer 

The number of moles per time interval dn/dt and per surface area A is proportional to the concentration gradient (c cJ/5. The constant D is the diffusion coefficient and is 

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When the liquid within the impeller is forced radially outward to the diffuser, a major portion of the velocity energy is converted into pressure energy by the stationary diffuser vanes (see Figure 3-63). This can also be accomplished by means of a volute, which is a part of the casing design (see Figure 3-64) [17]. 

Using the equation for the diffusion current i under the conditions of stationary diffusion ... 

The possibility that adsorption reactions play an important role in the reduction of telluryl ions has been discussed in several works (Chap. 3 CdTe). By using various electrochemical techniques in stationary and non-stationary diffusion regimes, such as voltammetry, chronopotentiometry, and pulsed current electrolysis, Montiel-Santillan et al. [52] have shown that the electrochemical reduction of HTeOj in acid sulfate medium (pH 2) on solid tellurium electrodes, generated in situ at 25 °C, must be considered as a four-electron process preceded by a slow adsorption step of the telluryl ions the reduction mechanism was observed to depend on the applied potential, so that at high overpotentials the adsorption step was not significant for the overall process. 

D. Diffusion Coefficient Divided by the Thickness of the Stationary Diffusion Layer, D/h... 

Although it is possible to control the dissolution rate of a drug by controlling its particle size and solubility, the pharmaceutical manufacturer has very little, if any, control over the D/h term in the Nernst-Brunner equation, Eq. (1). In deriving the equation it was assumed that h, the thickness of the stationary diffusion layer, was independent of particle size. In fact, this is not necessarily true. The diffusion layer probably increases as particle size increases. Furthermore, h decreases as the stirring rate increases. In vivo, as GI motility increases or decreases, h would be expected to decrease or increase. In deriving the Nernst-Brunner equation, it was also assumed that all the particles were... 

Recent experimental results on thermodynamic properties of high pressure supercritical fluids have opened up the possibility to study combustion and flames at very high pressures and in unusual environments. Stationary diffusion flames have been produced up to 2000 bar in dense aqueous mixed fluid phases. 

Various kinds of information can be expected from the high pressure combustion and flame experiments Reaction kinetics data for conditions of very high collision rates. Results about combustion products obtained at high density and with the quenching action of supercritical water, without or with flame formation. Flame ignition temperatures in the high pressure aqueous phases and the ranges of stability can be determined as well as flame size, shape and perhaps temperature. Stationary diffusion flames at elevated pressures to 10 bar and to 40 bar are described in the literature [12 — 14]. 

A comparison of the time developments of Y(r, t) in two limiting cases (pure contact reaction and strong tunnelling recombination) demonstrates their qualitative difference. In the latter case, the first stage is very short and is finished already at t a(R) x the further change of Y(r,t) is defined here entirely by the non-stationary diffusion. The relevant reaction rate for... 

The solutions of the stationary diffusion equations for spherical and disc microelectrodes are deduced in Appendix C. 

The hydrogen atoms absorption within the accepted model system is described by a non-stationary diffusion equation in the field of potential V under corresponding initial and boundary conditions [5]... 

Equation 4 is equivalent to Fick s second law (non-stationary diffusion), expanded by an additional source term which accounts for the production or consumption of species i caused by chemical transformations. Similar to this mass balance, an enthalpy balance may be also derived ... 

In the equilibrium state, this is, of course, zero. When the potential is increased, then the concentration (O) is depleted near the surface, while (R) is increased. Eventually a quasi-stationary state will be established, one in which the depletion of O at the electrode is balanced by a diffusion of O from the solution, while the excess of R will similarly be balanced by a diffusion of R away from the electrode to the solution. We can write for such a stationary diffusion state ... 

In the D-R Denver machine (Fig. 19-75), the pulp enters the top of the recirculation well A, while the low-pressure air enters through the air passage B. Pulp and air are intimately mixed and thrown outward by the rotating impeller C through the stationary diffuser D. The collector-coated mineral particles adhere to be removed in the froth product. 

Assuming a stationary diffusion layer outside the particle of thickness d one has for dXJdR... 

Interdiffusion within the film is treated as a quasi-stationary diffusion process across a planar layer (film). This means that the flux across the film adjusts itself rapidly to the changing boundary conditions and... 

Surface phenomena affect the particle sedimentation when a tangential surfactant concentration gradient exists near the particle surface. This situation is described by the stationary diffusion equation for the surfactant concentration outside the surface layer in the form = 0 [2,3], where the boundary condition, which reflects the substance conservation in a very thin surface layer, may be written as... 

Corrosion of horizontal refractory surfaces (e.g. the furnace bottom) again depends on the difference between the densities of the original and of the saturated melt. If dissolution of the refractory produces a solution of higher density, this remains stationary at the interface and corrosion proceeds by non-stationary diffusion. In the opposite case, the lighter solution will flow spontaneously upwards this process has to be compensated for by the downward flow of the higher-density melt, so that a system of cellular currents is established and non-uniform corrosion results, producing an unevenly pitted surface. 

Figure 6.6 Schematic concentration profile at the cathode for pulse plating conditions [6.101] pulsating diffiision layer thickness stationary diffusion layer thickness iJn Nemst diffusion layer thickness.

Helmholtz layer contains the second water molecule layer. From the Helmholtz double layer toward the bulk electrolyte are the diffusion layer and the hydrodynamic layer. In the diffusion layer, the concentration of species changes from that of the bulk electrolyte to that of the electrode surface. The diffusion layer does not move, but its thickness will decrease with increasing bulk electrolyte flow rate to allow higher reaction rates. The diffusion layer thickness is inversely proportional to the square root of the flow rate. The hydrodynamic layer or Prandtl layer has the same composition as the bulk electrolyte, but the flow of the electrolyte decreases from that of the bulk electrolyte to the stationary diffusion layer. 

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