Steady-state zones

Chapter 5 described the important details of dynamic (nonsteady-state) zone formation in one-dimensional systems. Omitted were other important aspects of zone formation and structure, including steady-state zones, two-dimensional zones, and the problem of statistical zone overlap. These topics will be examined in this chapter. 

In some steady-state methods of separation (isoelectric focusing, density-gradient centrifugation, and sometimes elutriation), component zones approach a stationary configuration centered about different points in space. Separation occurs by virtue of the different steady-state positions of the various solutes. In other systems (field-flow fractionation, zone refining, 

The unified treatment of this subject, presented below, is patterned after a paper previously published by the author [1]. 

A steady-state zone or layer is defined as one in which the concentration profile remains constant (or very close to constant) with the passage of time. Thus a necessary condition for the steady state is 

The reader may recall that the equation of continuity, Eq. 3.28, relates the derivative of flux density J to the accumulation rate dcldt dJ/dx = -del dt. Since dcldt is zero, dJ/dx must also be zero, a condition that is possible only for 

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Steady-state zone (loss rate at a constant value). 

Figure 11 shows typical CL oscillating responses of this system as perturbed by vitamin B6 pulses, which decrease the oscillation amplitude. Arrowheads indicate the times at which analyte pulses were introduced. Zone A corresponds to the oscillating steady state zone B to the response of the oscillating system to vitamin B6 perturbations and zone C to the recovery following each perturbation (second response cycle), which was the measured parameter. This... 

In Section V,A (Ref 66, p 157) theories are discussed which assume diverging flow in the steady-state zone, whiie in Section V,B those that assume parallel flow within the steady zone... 

Finally, we note that some component zones do not acquire Gaussian shapes because the controlling processes are quite unlike those described above. This situation applies to some of the steady-state zones described in the following chapter. 

We now concentrate on three classes of separations in which steady-state zones are described by Eq. 6.16. The specific separation techniques are discussed in more detail in subsequent chapters. 

Steady-State Zones in Free Space (Isoelectric Focusing and Isopycnic Sedimentation)... 

For steady-state zones, where H and N also lack definition, we turned to the peak capacity as a common denominator for different methods. We have learned how to estimate peak capacity for ID separations we now extend this concept to incorporate two axes. For this we must reconsider the matter of spot dimensions when migration occurs along both axes rather than just one. 

What value is assumed by the effective mean layer thickness of a steady-state zone held next to a wall by virtue of displacement at velocity W = 1.0 x 10 3 cm/s The zone consists of spherical particles of diameter 2.5 nm in an aqueous medium of viscosity Tf = 1.0 x 10 2 poise at 20°C. 

Basic Approaches to Separation Steady-State Zones and Layers, J. C. Giddings, Sep. Sci. Technol., 14, 871 (1979). 

In terms of organization, the text has two main parts. The first six chapters constitute generic background material applicable to a wide range of separation methods. This part includes the theoretical foundations of separations, which are rooted in transport, flow, and equilibrium phenomena. It incorporates concepts that are broadly relevant to separations diffusion, capillary and packed bed flow, viscous phenomena, Gaussian zone formation, random walk processes, criteria of band broadening and resolution, steady-state zones, the statistics of overlapping peaks, two-dimensional separations, and so on. 

EDTA, the abbreviation for ethyldiaminotetraethyl acid, usually is identified as H4Y. When dissolved at different pH values it exists in different forms. In strong acid solutions (pH < 1), it exists primarily as HgY. In the pH range of 2.67-6.16 it exists mainly in the form. At a pH > 10.26, it exists mainly in the Y form. The pH value employed for the separation of RE elements with EDTA as the chelate displacer is the key to a successful operation. The RE elements can be separated by using EDTA because the stability constants of the complexes they form are different. These stability constants increase with the increasing atomic number of the RE elements. In the steady-state zones obtained for the RE elements in the course of their separation, the pH value in each element separation zone is sizably different. The more stable the complex, the lower is the pH. Conversely, the less stable the complex, the higher is the pH. The pH values associated with some of the RE elements in their respective steady-state zones are listed in Table 8. 

Table 8 lists the pH values of the solution associated with some RE elements in their respective steady-state zones for a separation process... 

Table 8 pH Values of Different RE Elements in Steady-State Zone... 

Referring to the equation of continuity, as x approaches zero, the steady-state zones or layers are formed next to the phase s interface (but not for the bulk phases, where x 0). Separation then occurs by differential displacement permeation through the interface. Efficiency of the separation hinges directly on the distribution of solute in the steady-state layers. 

Field-flow fractionation experiments are mainly performed in a thin ribbonlike channel with tapered inlet and outlet ends (see Fig. 1). This simple geometry is advantageous for the exact and simple calculation of separation characteristics in FFF Theories of infinite parallel plates are often used to describe the behavior of analytes because the cross-sectional aspect ratio of the channel is usually large and, thus, the end effects can be neglected. This means that the flow velocity and concentration profiles are not dependent on the coordinate y. It has been shown that, under suitable conditions, the analytes move along the channel as steady-state zones. Then, equilibrium concentration profiles of analytes can be easily calculated. 

Generally, the concentration profile of analytes in FFF can be obtained from the solution of the general transport equation. For the sake of simplicity, the concentration profile of the steady-state zone of the analyte along the axis of the applied field is calculated from the one-dimensional transport equation ... 

Following the treatment given by Giddings [9], imposing for the condition of the steady-state zone of the analyte, which is characterized by the null flux density, and applying the equation of continuity, the general solution of the analyte concentration profile can be expressed in the form... 

Using (1) Giddings analysis [54] of the steady-state zones, formed next to the lEM-LM interfaces, and (2) theoretical considerations for onedimensional facihtated transport of a solute, applied to the BOHLM systems [46, 55], the equations for experimental determination of individual mass-transfer coefficients (fe,) were formulated. 

Thormann, W., Caslavska, J., and Mosher, R.A., Impactof electroosmosis on isotachophoresis in open-tubular fused-sUica capillaries Analysis of the evolution of a stationary steady-state zone structure by computer simulation and experimental validation. Electrophoresis, 16, 2016, 1995. 

The biofilm profiles suggest that progression of biofilm accumulation exhibits sigmoid behavior. Such progression can practically be divided into three zones (i) induction with biofilm thickness neighboring ca. 1 pm, (ii) exponential or log accumulation, and (iii) a plateau or steady-state zone. 

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