Radial equilibrium

Using the simple radial equilibrium equation, the eomputation of the axial veloeity distribution ean be ealeulated. The aeeuraey of the teehniques depends on how linear F /r is with the radius. 

Hatch. J.E., Giamati, C.C., and Jackson, R.J., Application of Radial Equilibrium Condition to Axial-Flow Turbomachine Design Including Consideration of Change of Enthropy with Radius Downstream of Blade Row, NACA RM E54A20 (1954). 

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...

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. 

Fig, 4, Temporal behavior of the current required for radial equilibrium. 

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. 

The approximation is made by forfeiting the condition of radial equilibrium Eq. (1), but this is used later to estimate the errors from this assumption. 

The errors in the approximation can now be estimated by inserting Eq. (4) in the equation for radial equilibrium, (1), which leaves the residual term... 

---