Basic Method Models


Straightforward processes in chemical engineering concern hydrodynamic, diffusion, heat conduction, adsorption and chemical processes.  These are typical non equilibrium processes and the relevant mathematical descriptions concern quantitatively their kinetics.  This provides a ground to utilize the laws of irreversible thermodynamics as mathematical structures creating the models of the easy processes.  The quantitative description of irreversible processes depends on the level of the process description.  From such a point of view, 1 can define 3 simple levels of description–thermodynamic, hydrodynamic and boltzmann levels.  These different levels if method descriptions type a all-natural hierarchy.  Thus, going up from one particular level to the subsequent, the description becomes richer, i.e., more detailed.  This method makes it possible for the kinetic parameters defined at a decrease level to be described via relevant kinetic parameters at an upper level.  The thermodynamic level utilizes quantitative descriptions by way of extensive variables.  If there is a distributed space, the volume have to be represented as a set of unit cells, exactly where the variables are the exact same but have different values in different cells.  The hydrodynamic is the next level, where a new in depth variable participates in the processes. 

This variable is the momentum.  Therefore, the hydrodynamic level of description can be deemed as a generalization of the decrease, thermodynamic level.  Here, the extensive variables are mass density, momentum, and power.  In the isolated systems they are conserved and the conservation laws of mass, momentum and  power are used.  The Boltzmann level is the subsequent upper level of description and concerns only the mass density as a function of the distribution of the molecules in space and their momenta.  The kinetics of irreversible processes employs mathematical structures following from Onsanger’s linear principle.  According to them, the imply worth of the time derivatives of the substantial variables and the imply derivatives of their adjoined intensive variables from the equilibrium are expressed by way of linear relationships.  The principle is valid close to the equilibrium and the coefficients of the proportionality are the kinetic constants.  When the process requires place far from equilibrium, the kinetic constants turn out to be kinetic complexes based on the corresponding intensive variables (in the case of fusion of two identical systems, the in depth variables double, whereas the intensive variables stay the same).

The hydrodynamic level is broadly applicable in the mechanics of continua.  Right here, the material point corresponds to a sufficient volume of the medium that is simultaneously sufficiently tiny with respect to the entire volume under consideration and at the identical time sufficiently massive with respect to the intermolecular distances of the medium.  Modeling in chemical engineering utilizes mathematical structures offered by the mechanics of the continua.  The principal purpose for this is the reality that these structures sufficiently well describe the phenomena in detail.  Furthermore, they employ physically effectively defined models with a low number of experimentally defined parameters.