Laminar Flow Systems Research Articles

Residence time distribution in laminar flow systems. I. Hydrodynamic conception in study of distribution functions

Residence time distribution in laminar flow systems. I. Hydrodynamic conception in study of distribution functions

Diffusive mixing in continuous laminar flow systems

If the amount of mixing required at a local position of a system is measured by the absolute value of the excess concentration in that area, then it is shown that in a batch mixer, the local efficiency of mixing, described by the fractional decrease in the amount of mixing required per unit time is given by C 3 D/δ 2, while for a continuous mixer the local efficiency of mixing, described by the fractional decrease in the amount of mixing required per unit length, is given by C 3 D/δ 2 u x . In both cases C 3 is an approximately constant factor describing the shape of the concentration distribution and of order π 2, D is the appropriate chemical diffusion coefficient, δ is the local striation thickness and u x is the velocity component along the direct line from the entrance to exit. It is also shown that the relative rate of reduction of striation thickness is given by ▪ when u l is the velocity component along a striation segment of length, dl. Application of this relation to several simple types of flow is carried out and a brief discussion of the utility of the principles to continuous laminar flow mixer design is included.

The separation of ions with permselective membranes

AbstractThis study forms part of a project aimed at obtaining a better understanding of the behavior of nonideal permselective membranes. The object here was to determine the applicability of the Nernst‐Planck equations for studying the behavior of ions in aqueous solutions surrounding such a membrane during electrodialysis.Attention was confined to stagnant and laminar flow systems. The processes studied were transfer of hydrogen ions, silver ions, and mixtures of the two through the cation exchanging membrane Nepton CR‐61. The bulk solution concentrations on either side of the membrane varied from 0.01 to 0.20 N, and in all cases the only anions present were nitrate ions. Limiting currents for solutions of silver nitrate were predictable within 15%, with much of the uncertainty resulting from the difficulty in defining the limiting current. For mixtures of silver nitrate and nitric acid the limiting currents were predictable within the range of experimental accuracy but were found to be quite sensitive to small changes in the operating conditions. This sensitivity results from the very high relative mobility of the hydrogen ions. The relative transport of the two cations was primarily a function of relative concentration, relative diffusivities, current density, and ion exchange equilibria and was predictable with an accuracy limited only by the uncertainty of the ionic diffusivities and the ion exchange equilibria.The diffusivities of the cations in the membrane relative to the diffusivity of nitrate ion were estimated to be about ten times lower than in solution. This was explained by assuming that the cations tended to concentrate about the anionic fixed charges of the membrane thereby portially screening their effectiveness and reducing the mobility of the cations. In mixtures, the membrane diffusivity of the silver ions relative to the hydrogen ions was lower (by a factor of 1.4 to 3.6) than the relative diffusivity in solution. This indicated that silver ions were more easily concentrated about the fixed charges and thereby screened them from both the anions and hydrogen ions.

Mixing in Laminar-Flow Systems

Mixing in Laminar-Flow Systems