Solute boundary layer

With eveiy change in ion concentration, there is an electrical effect generated by an electrochemical cell. The anion membrane shown in the middle has three cells associated with it, two caused by the concentration differences in the boundaiy layers, and one resulting from the concentration difference across the membrane. In addition, there are ohmic resistances for each step, resulting from the E/I resistance through the solution, boundary layers, and the membrane. In solution, current is carried by ions, and their movement produces a fric tion effect manifested as a resistance. In practical applications, I R losses are more important than the power required to move ions to a compartment wim a higher concentration. 

In simple terms, the crystallisation process may be considered to take place in two stages—a diffusional step in which solute is transported from the bulk fluid through the solution boundary layer adjacent to the crystal surface, and a deposition step in which adsorbed solute ions or molecules at the crystal surface are deposited and integrated into the crystal lattice. These two stages which are shown in Figure 15.13, may be described by ... 

Analysis of Solute Boundary Layer. A closed-fonn solution of the... 

The boundary layer structure predicted by the analysis of Burton et al. (74) and by Wilson (80) is much more robust than just a description of the solute boundary layer caused by the rotational flow near a large crystal. 

When a stagnation flow on the melt-crystal interface is created by any mechanism and is intense enough to lead to a thin solute boundary layer, the velocity field in the boundary layer can be described by... 

Similarity Solution Boundary Layer with Uniform Temperature... 

Discrepancies between experimentally obtained and theoretically calculated data for cadmium concentration in the strip phase are 10-150 times at feed or strip flow rate variations. These differences between the experimental and simulated data have the following explanation. According to the model, mass transfer of cadmium from the feed through the carrier to the strip solutions is dependent on the diffusion resistances boundary layer resistances on the feed and strip sides, resistances of the free carrier and cadmium-carrier complex through the carrier solution boundary layers, including those in the pores of the membrane, and resistances due to interfacial reactions at the feed- and strip-side interfaces. In the model equations we took into consideration only mass-transfer relations, motivated by internal driving force (forward... 

A quantitative measure of the signiHcance of solution boundary layer effects is the mass-transfer Biot number ... 

Specification of initial conditions completes the statement of the problem. We emphasize that little can be done analytically (we will refer to what can be done later), and in general numerical solutions are required. The problems between the fluid dynamics and the surfacr tant concentration are coupled nonlinearly and we describe numerical methods and results later. In addition to the nonlinear nature of the problem, certain dimensionless groups are large and make the equations stiff, in the sense that either small time-steps are needed or boundary layer structures need to be resolved. For example, the Peclet numbers tend to be large in applications (see earlier) and solute boundary layers develop near the surface. Also, the bulk concentration constant k which appears in the mass balance equation (39) can be of order 10 - making that equation stiff. These issues are taken up in Section . 

Under the Cochran (1934) assumptions for a fluid flow near a rotating disk. Burton et al. (1953) introduced the solute boundary layer thickness as... 

---