Phenomenological approach, historic

Most characterisation of non-linear responses of materials with De < 1 have concerned the application of a shear rate and the shear stress has been monitored. The ratio at any particular rate has defined the apparent viscosity. When these values are plotted against one another we produce flow curves. The reason for the popularity of this approach is partly historic and is related to the type of characterisation tool that was available when rheology was developing as a subject. As a consequence there are many expressions relating shear stress, viscosity and shear rate. There is also a plethora of interpretations for meaning behind the parameters in the modelling equations. There are a number that are commonly used as phenomenological descriptions of the flow behaviour. 

In solid-liquid mixing design problems, the main features to be determined are the flow patterns in the vessel, the impeller power draw, and the solid concentration profile versus the solid concentration. In principle, they could be readily obtained by resorting to the CFD (computational fluid dynamics) resolution of the appropriate multiphase fluid mechanics equations. Historically, simplified methods have first been proposed in the literature, which do not use numerical intensive computation. The most common approach is the dispersion-sedimentation phenomenological model. It postulates equilibrium between the particle flux due to sedimentation and the particle flux resuspended by the turbulent diffusion created by the rotating impeller. 

Summing up this study of the epistemological status of chemical radicals of the synthetic period with respect to historical development the following aspects seem notable. To begin with the more systematic topics Firstly, the classical (or phenomenological or thermodynamical) approach of stuff characterization appears not to come to terms with the chemical species radical in general. Only few exceptions are stable enough under normal conditions and can be observed. 

In Chapter 2, we approached alternating-current electrode polarization impedance from the phenomenological point of view, which parallels the historical development of this subject. Before we embark upon descriptions of electrochemical cells, ion-specific electrodes, and potentiometric techniques, it is necessary to discuss some of the electrochemical processes that occur at the interface between a solid electrode surface and a contacting electrolyte. 

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