Model contact resistance

In order to model the electrolyte properly, the transportation of mass, charge, and energy must be included in the model. Contact resistance between electrode and electrolyte can also be significant, which should be incorporated into the model. 

In accordance with this model, the current path is made through the contact resistance external collector - volume collectors (Rki), then goes through many other resistances, such as bulk resistance of the conductive particles (Rvi) and the contact resistance between the conductive particles in the volume of the electrode (Rci) at the end, there is contact resistance between the conductive particles and active mass particles (Rmi). 

In 1959, Little [69] extended the acoustic mismatch model to interfaces between solids. The experiments have revealed that in this case, the thermal contact resistance between solids is higher than that evaluated from the model and that data are less reproducible. 

The different behaviour of contact resistance in the two cases can be examined through the two models the just described acoustic mismatch model and the diffuse mismatch model which suppose that all the phonons are scattered at the interface. Hence these two models define two limits in the behaviour of phonons at a discontinuity. 

Some experiments outlined the frequency dependence of phonon scattering on surfaces [74]. Thus, Swartz made the hypothesis that a similar phenomenon could take place at the interface between solids and proposed the diffuse mismatch model [72]. The latter model represents the theoretic limit in which all phonons are heavily scattered at the interface, whereas the basic assumption in the acoustic mismatch model is that no scattering phenomenon takes place at the interface of the two materials. In the reality, phonons may be scattered at the interface with a clear reduction of the contact resistance value as calculated by the acoustic model. 

Contact resistance values calculated by the diffuse scattering model are higher than those obtained experimentally in the case that the two materials are similar (in density and... 

Ham JM, Kluitenberg GJ (1994) Modeling the effect of mulch optical properties and mulch-soil contact resistance on soil heating under plastic mulch culture. Agric For Meteorol 71 403 124. doi 10.1016/0168-1923(94)90022-1... 

Waldvogel and Poulikakos1501 extended the model and numerical techniques of Zhao et al.13681 by incorporating solidification and droplet-substrate contact resistance in the heat transfer model. They conducted both theoretical and experimental studies on the impact and solidification of molten solder droplets on a multilayer substrate. The theoretical model was based on the Lagrangian formulation, and accounted for a host of thermal-fluid phenomena,... 

It should be noted that it is difficult to obtain models that can accurately predict thermal contact resistance and rapid solidification parameters, in addition to the difficulties in obtaining thermophysical properties of liquid metals/alloys, especially refractory metals/al-loys. These make the precise numerical modeling of flattening processes of molten metal droplets extremely difficult. Therefore, experimental studies are required. However, the scaling of the experimental results for millimeter-sized droplets to micrometer-sized droplets under rapid solidification conditions seems to be questionable if not impossible,13901 while experimental studies of micrometer-sized droplets under rapid solidification conditions are very difficult, and only inconclusive, sparse and scattered data are available. 

Prasarma et al. [185] were also able to observe an optimum thickness of DLs for fuel cells experimentally. They demonstrated that the thicker DLs experience severe flooding at intermediate current densities (i.e., ohmic region) due to low gas permeation and to possible condensation of water in the pores as the thickness of the DL increases. On the other hand, as the thickness of the DL decreases, the mass transport losses, contact resistance, and mechanical weakness increase significantly [113,185]. Through the use of mathematical modeling, different research groups have reported similar conclusions regarding the effect of DL thickness on fuel cell performance [186-189]. 

Each tube is a sequence of cells electrically connected in series and this justifies the hypothesis that the current is the same for all the cells. Since the fuel flows in series through the various cells of the tube, fuel compositions vary from one cell to the next. As a consequence, cell voltage also varies from cell to cell, and this can be evaluated through a detailed evaluation of the local electrochemical kinetics of the reactor, as described in Section 6.2 of this work. When the model of the electrochemical kinetics is included into the overall model of the tube, an additional type of resistance is taken into consideration, i.e. the contact resistance (an approach... 

In the new model, the three-dimensional electric current path in the cell components is simulated precisely. The calculation of the electric current path inside the single cell and the calculations of chemical and thermo-fluid phenomena are connected to each other, i.e., it is a fully connected model. Using this model, it is possible to simulate the diagonal electric current in the electrolyte, and in addition, the geometry of the cell components can be considered in the calculation of the cell performance. Contact resistances among each cell component are also considered in the calculation. Here, a detailed calculation using the new model will not be mentioned. 

Access to contact resistance was first sought by modeling. Figure 1.11 shows equivalent circuits used for that purpose. Note that the bottom circuit includes head-to-toe diodes to account for non-linear contact resistance [35]. The model developed by Necliudov and coworkers also assumed a gate voltage-dependent mobility (this point will be discussed in more detail below). 

Fig. 2-15 Joint-roughness model for analysis of thermal contact resistance.

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