Radial equilibrium, column

The introduction of the sample valve, however, helped establish radial equilibrium early in the separation but, unless some special sample spreading device is employed at the front of the column, equilibrium will not necessarily occur at the point of injection. The stream splitting process is depicted in Figure 2. 

Equation (3) allows the calculation of the distance traveled axially by a solute band before the radial standard deviation of the sample is numerically equal to the column radius. Consider a sample injected precisely at the center of a 4 mm diameter LC column. Now, radial equilibrium will be achieved when (o), the radial standard deviation of the band, is numerically equal to the radius, i.e., o = 0.2 cm. 

Figure 3. Graph of Length of Column Traversed by the Solute Before Radial Equilibrium Is Achieved against Particle Diameter...

In a sedimentation equilibrium run, the stationary radial concentration profile, which is established after a few hours for a 1-mm column, is analyzed according to Equation (72) or, in case of polydisperse samples, Equations (74) or (75). Contrary to the sedimentation velocity experiment, the diffusion coefficient D is not required. 

Thus, to ensure radial equilibrium, either it must be achieved on injection by the use of a suitable sample distribution device, or by employing narrow bore columns where radial equilibrium is more quickly achieved. The latter alternative, however, will depend on the resolution required and will be discussed later under LC column design. 

Evaluation of Mweq. Sedimentation Equilibrium Experiments and the Archibald Method. At constant temperature the condition for sedimentation equilibrium is that the total potential jZi for each associating species i (i = A, B, or AnBw) be constant at every radial position r in the solution column of the ultracentrifuge thus... 

The plug-flow model indicates that the fluid velocity profile is plug shaped, that is, is uniform at all radial positions, fact which normally involves turbulent flow conditions, such that the fluid constituents are well-mixed [99], Additionally, it is considered that the fixed-bed adsorption reactor is packed randomly with adsorbent particles that are fresh or have just been regenerated [103], Moreover, in this adsorption separation process, a rate process and a thermodynamic equilibrium take place, where individual parts of the system react so fast that for practical purposes local equilibrium can be assumed [99], Clearly, the adsorption process is supposed to be very fast relative to the convection and diffusion effects consequently, local equilibrium will exist close to the adsorbent beads [2,103], Further assumptions are that no chemical reactions takes place in the column and that only mass transfer by convection is important. 

The concentrations of kraft lignin species were so low that ideal behavior could, with reasonable confidence, be expected to prevail. Thus, at equilibrium, the concentration of each solute species varies with radial distance r in the solution column according to... 

Example 8.1.22 below compares this optimal separation factor at total reflux at z = Le and the heavy fraction z = -L with the radial equilibrium separation factor (4.2.7) at any axial location in the column. 

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