Drop effect

Figure 10. Pelletizer pressure drop. Effect of polymer melt index (MI).

For the expressions used to calculate the mass average diameter and wall-drop effectiveness, readers are referred to Varone and Rohsenow (1990). 

The ohmic drop effect we are discussing deals only with the Ru portion ofthe cell resistance (Figure 1.5c). Indeed, the action of the potentiostat makes the working electrode potential independent not only of the possible shift of the counter electrode potential as the current varies, but also independent of the ohmic drop in the Rc portion of the cell resistance. In the case of cyclic voltammetry, the equation above becomes... 

There are two ways of handling the ohmic drop effect. One consists of equipping the instrument with a positive feedback loop that subtracts from E a tension, Rei, proportional to the current, thus eliminating, at least partially, the effect of the ohmic drop.14 One may even get the impression that total compensation, or even more, overcompensation, could be achieved. In fact, before total compensation is reached, oscillations appear as a result of the bandpass limitations of the operation amplifiers. The entire instrument can indeed be represented by a self-inductance, La, that is a... 

The above equations do not allow for kinetics associated with the mean free path discontinuity at the particle surface. A correction for this would increase the charging rate. As a first approximation, this can be allowed for by replacing Pp in Eqs. (75) and (77) with the product >p[l + (2A,/Z)p)]. This is based on the reasoning that ions migrating to within a mean free path of the particle surface will be deposited and that the ion concentration will drop effectively to zero within a mean free path of the surface. 

Labowsky, M. Fenn, J.B. de la Mora, J.F. A Continuum Model for Ion Evaporation From a Drop Effect of Curvature and Charge on Ion Solvation Energy. Anal. Chim. Acta 2000,406, 105-118. 

It must be emphasized again that the mid-peak potential is equal to E° for a simple, reversible redox reaction when neither any experimental artifact nor kinetic effect (ohmic drop effect, capacitive current, adsorption side reactions, etc.) occurs, and macroscopic inlaid disc electrodes are used, that is, the thickness of the diffusion layer is much higher than that of the diameter of the electrode. 

For zero expansion and taking into account the pressure-drop effect, the solution is (eq. (5.291))... 

The models of cases 1 and 4 give approximately the same results up to a pressure drop of 27% (1 m3/s). The difference between these two models is that in case 4, the pressure-drop effect is ignored. Thus, even for relatively high pressure drop, a simplified model that takes into account the expansion but not the pressure drop is able to approximate the real conversion. 

It is clear that ignoring the expansion, the deviation is very serious for the whole region of volumetric flow rates while ignoring the pressured-drop effect, but using the expansion factor the results could be veiy good up to a certain pressure-drop level, which is approximately 27% in our example. 

Then, the total pressure drop for the maximum mass superficial velocity of liquid is, for the single phases, 0.02 atm for the gas and 0.68 atm for the liquid, and for the two-phase system 1.43 atm. Thus, we can assume that the pressure-drop effect is minimal. 

What electrodes should be used to obtain a current density of 0.1 mA cm 2 if mass transfer and ohmic drop effects are neglected (Zinola)... 

A commonly employed method to minimise ohmic potential drop effects is to place the reference electrode very close to the working electrode by means of a Luggin capillary. The disadvantage of very close placement, which may be unacceptable, is disturbance of the fluid flow. To avoid this, other methods are sometimes used. For example, a rotating disc electrode has been described in which the reference electrode is placed in a tiny compartment within the rotating electrode assembly and linked to the solution via a tiny orifice (0.7 mm) drilled in the centre of the disc [88]. 

Owing to the small current measured, Ohmic drop (also called IR-drop) effects in solution are much less pronounced. This includes that ultra-micro electrodes can be used in highly resistive media (including non-aqueous solution) and/or without the use of supporting electrolyte. 

A first parameter to be studied is the applied potential difference between anode and cathode. This potential is not necessarily equal to the actual potential difference between the electrodes because ohmic drop contributions decrease the tension applied between the electrodes. Examples are anode polarisation, tension failure, IR-drop or ohmic-drop effects of the electrolyte solution and the specific electrical resistance of the fibres and yarns. This means that relatively high potential differences should be applied (a few volts) in order to obtain an optimal potential difference over the anode and cathode. Figure 11.6 shows the evolution of the measured electrical current between anode and cathode as a function of time for several applied potential differences in three electrolyte solutions. It can be seen that for applied potential differences of less than 6V, an increase in the electrical current is detected for potentials great than 6-8 V, first an increase, followed by a decrease, is observed. The increase in current at low applied potentials (<6V) is caused by the electrodeposition of Ni(II) at the fibre surface, resulting in an increase of its conductive properties therefore more electrical current can pass the cable per time unit. After approximately 15 min, it reaches a constant value at that moment, the surface is fully covered (confirmed with X-ray photo/electron spectroscopy (XPS) analysis) with Ni. Further deposition continues but no longer affects the conductive properties of the deposited layer. 

The electrode size is another important variable to analyze since the use of microelectrodes is very relevant for experimental electrochemical studies enabling the reduction of capacitative and ohmic drop effects, as indicated in Sect. 2.7. Specifically, it is of great interest to check the behavior of the system when the size of the electrode is reduced. In Fig. 4.20, the influence of the electrode radius on the... 

During the evaluation of our calculations we noticed, that the dissipation of the acoustic waves has an important influence on the temperature of the liquid. The dissipation caused an increase of the liquid temperature, which in its turn caused a decrease of the liquid viscosity and, as a result, the pressure gradient over the core decreased at constant liquid flow rate. This phenomenon is completely responsible for the pressure drop effect. It is a measurable effect and has to be taken into account when studying acoustic irradiation of porous materials. From the evaluation of the calculations we could also conclude, that the momentum transfer of the acoustic waves to the liquid, i.e. acoustic streaming, has a negligible effect on pressures and temperatures of the liquid, although the effect is measurable. 

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