Hydrodynamic methods concentration profile

A first model is used to compute the flowrates allowing to perform the separation with the greatest productivity. Then, the "mixed cell in series" model takes into account thermodynamic, hydrodynamic and kinetic properties of the system and compute the concentration profile inside the columns [14], In this model, we make the assumptions that the pressure drop inside the column is negligible compared to the pressure drop realized and controlled with the analogical valves, and we model the true moving bed assuming that the performance of SMB and TMB are equivalent. A mass balance equation is written for each stage and a classical Newton Raphson numerical method is used to solve the permanent state of the process [14],... 

The velocity and concentration profiles are developed along the HFs by means of the mass conservation equation and the associated boundary conditions for the solute in the inner fluid. This analysis separates the effects of the operation variables, such as hydrodynamic conditions and the geometry of the system, from the mass transfer properties of the system, described by diffusion coefficients in the aqueous and organic phases and by membrane permeability. The solution of such equations usually involves numerical methods. Different applications can be found in the literature, for example, separation and concentration of phenol, Cr(VI), etc. [48-51]. 

The confrontation of this elegant prediction by experiment has taken many years to complete because all experimental techniques available at that time did not have the proper spatial resolution. Spectroscopic methods such as EPR, NMR, IR are only sensitive to the fraction of monomers attached to the wall. Ellipsometry measures the first moment of the monomer distribution and vields an average length called the ellipsometric thickness Hydrodynamic methods, based on flow restric-tion in capillaries covered by the adsorbed layer, yield another average length related to the maximum extension of the adsorbed layer To study concentration profiles at the solid-liquid interface, one has thus to devise special tools. 

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