Mixing process dynamic response

Mathematically speaking, a process simulation model consists of a set of variables (stream flows, stream conditions and compositions, conditions of process equipment, etc) that can be equalities and inequalities. Simulation of steady-state processes assume that the values of all the variables are independent of time a mathematical model results in a set of algebraic equations. If, on the other hand, many of the variables were to be time dependent (m the case of simulation of batch processes, shutdowns and startups of plants, dynamic response to disturbances in a plant, etc), then the mathematical model would consist of a set of differential equations or a mixed set of differential and algebraic equations. 

Because the most common impeller type is the turbine, most scale-up published studies have been devoted to that unit. Almost all scale-up situations require duplication of process results from the initial scale to the second scaled unit. Therefore, this is the objective of the outline to follow, from Reference [32]. The dynamic response is used as a reference for agitation/mixer behavior for a defined set of process results. For turbulent mixing, kinematic similarity occurs with geometric similarity, meaning fixed ratios exist between corresponding velocities. 

In a steady state continuous distillation with the assumption of a well mixed liquid and vapour on the plates, the holdup has no effect on the analysis (modelling of such columns does not usually include column holdup) since any quantity of liquid holdup in the system has no effect on the mass flows in the system (Rose, 1985). Batch distillation however is inherently an unsteady state process and the liquid holdup in the system become sinks (accumulators) of material which affect the rate of change of flows and hence the whole dynamic response of the system. 

This chapter will analyze the mixing process in more detail. The process was already introduced in chapter 4, but some special properties of the Laplace transform and some special cases of the mixing process will be reviewed. In subsequent chapters other types of processes will be analyzed for their dynamic behavior. The purpose of the Laplace transform is to analyze how the process output of interest changes if the process input is changed. This will result in knowledge about the behavioral properties of the system, such as order, stability, integrating or non-minimum phase response behavior. 

In turbulent flows, large scale eddies with coherent structmes are primarily responsible for the mixing of passive scalars. The large scale eddies embody themselves in the form of identifiable and organized distributions of vorticity. In addition, the mixing process involves all mechanisms typically found in vortex dynamics, such as stretching, breakup, concatenation, and self-induction of... 

The sensory technique used for assessing human perception of odors is called olfactometry. The basic technique is to present odorants at different concentrations to a panel of subjects and assess their response. The process favored by the U.S. National Academy of Sciences is dynamic olfactometry (16). This technique involves a sample dilution method in which a flow of clean, nonodorous air is mixed with the odorant under dynamic or constant... 

A wide variety of polymeric membranes with different barrier properties is already available, many of them in various formats and with various dedicated specifications. The ongoing development in the field is very dynamic and focused on further increasing barrier selectivities (if possible at maximum transmembrane fluxes) and/ or improving membrane stability in order to broaden the applicability. This tailoring of membrane performance is done via various routes controlled macro-molecular synthesis (with a focus on functional polymeric architectures), development of advanced polymer blends or mixed-matrix materials, preparation of novel composite membranes and selective surface modification are the most important trends. Advanced functional polymer membranes such as stimuli-responsive [54] or molecularly imprinted polymer (MIP) membranes [55] are examples of the development of another dimension in that field. On that basis, it is expected that polymeric membranes will play a major role in process intensification in many different fields. 

---