Velocity, reduced

Recovery factor Reduced column length Reduced plate height Reduced velocity Relative retention ratio Retardation factor d Retention time Retention volume Selectivity coefficient Separation factor... 

All variables in the system can be expressed in reduced form. Velocity can be expressed as tt = where Uq is a fixed reference velocity and j/ is the dimensionless reduced velocity. Because time, /q, is the quotient of length, Lq, and velocity, Uq, the equation can be manipulated to yield... 

Because erosion-corrosion is directly linked to velocity and turbulence, reducing velocity and turbulence are important first steps in elimination. Reducing velocity and turbulence often requires design changes such as the following ... 

In 1972-1973 Knox et al. [3, 4, 5] examined, in considerable detail, a number of different packing materials with particular reference to the effect of particle size on the reduced plate height of a column. The reduced plate height (h) and reduced velocity (v) were introduced by Giddings [6,7] in 1965 in an attempt to form a rational basis... 

The reduced velocity compares the mobile phase velocity with the velocity of the solute diffusion through the pores of the particle. In fact, the mobile phase velocity is measured in units of the intraparticle diffusion velocity. As the reduced velocity is a ratio of velocities then, like the reduced plate height, it also is dimensionless. Employing the reduced parameters, the equation of Knox takes the following form... 

Figure 2. Graph of Log of Reduced Plate Height against Log of Reduced Velocity for Poorly and Well Packed Columns...

The curves represent a plot of log (h ) (reduced plate height) against log (v) (reduced velocity) for two very different columns. The lower the curve, the better the column is packed (the lower the minimum reduced plate height). At low velocities, the (B) term (longitudinal diffusion) dominates, and at high velocities the (C) term (resistance to mass transfer in the stationary phase) dominates, as in the Van Deemter equation. The best column efficiency is achieved when the minimum is about 2 particle diameters and thus, log (h ) is about 0.35. The optimum reduced velocity is in the range of 3 to 5 cm/sec., that is log (v) takes values between 0.3 and 0.5. The Knox... 

To compare the two equations, the reduced plate height (h) and reduced velocity (v)... 

It is not uncommon to supply air into the room with jets attached both to the ceiling and to the wall surfaces. Air jets can be parallel to both surfaces or be directed at some angle to one or both surfaces (Fig. 7.28). Studies of compact wall jets supplied parallel to both surfaces reported by Grimitlyn show that the correction factor value is in the range from 1.6 to 1.7, which means that restriction of entrainment from two sides reduces velocity decay by 20% to 30% compared to the case of a wall jet. 

FIGURE 22.9 Reduced plate height versus reduced velocity. Measured data V, toluene O, PS 2200 , PS 43,900 A, PS 77S.000. Theoretical lines solid lines, Giddings, infinite diameter column dotted line, Knox, infinite diameter column dashed line Knox walled column. (Reprinted from J. Chromatogr., 634, IS4, Copyright 1993, with permission from Elsevier Science.)... 

Reduce velocity Yes, but economic penalty Yes by increasing flow area... 

We have used the transformation of Eq. (1-62) the definition of % in Eq. (1-71) and = (ml2kT)llztya — v] furthermore is the (reduced) velocity vector of the first particle after the collision. Expanding the polynomials, we find noting that the collision... 

Rivers transport suspended sediments derived from the disintegration of basin surface layers. With reduced velocity, sediment is deposited in the river channel. The finest material is carried to the sea. It has been estimated that the average mechanical denudation rate for continents is 0.056 mm year (35). This is based on a total suspended load of 13.5 x 10 metric tons year (S). Presently, about two-thirds of the world s total suspended sediment load derives from Southern Asia and large Pacific Islands. Berner has estimated the increase in sediment loss in the U.S. and world since prehuman times to be approximately 200% (35). Current estimated erosion rate from the major land forms is provided in Table I. The relatively recent construction of large sediment trapping dams that normally caused sediment to be deposited in river valleys or transported to the ocean has drastically reduced sediment yields in great rivers. 

As noted in Table 49-3, slow cycling of the crossbridges permits slow prolonged contraction of smooth muscle (eg, in viscera and blood vessels) with less utilization of ATP compared with striated muscle. The ability of smooth muscle to maintain force at reduced velocities of contraction is referred to as the latch state this is an important feamre of smooth muscle, and its precise molecular bases are under smdy. 

Column Type Minimum Reduced Plate Height Minimum Reduced Velocity flow Resistance Parameter Separation Impedance... 

The possibility of obtaining significant improvements in performance by using semi-packed and open tubular columns is clearly illustrated by the values for the separation impedance in Table 1.17. Variation of the reduced plate height with the reduced velocity for an open tubular column is given by equation (1.82), assuming that the resistance to mass transfer in the stationary phase can be neglected... 

According to chromatographic theory, the reduced plate height is related to the reduced velocity by equation (4.2)... 

Because of the time required to develop sufficient data points to make a plot similar to that shown in Figure 4.11 it is useful to have a shorter method for assessing potential problems. For a good colunn the value of the reduced plate height should not exceed 3 or 4 at a reduced velocity of about 5 and 10 to 20 at a reduced velocity of about 100. 

Upon substitution of the reduced parameters given above the separation time for a packed column and an open tubular column would be Identical if d 1.73 dp given the current limitations of open tubular column technology the column diameter cannot be reduced to the point %diere these columns can compete with packed columns for fast separations. This is illustrated by the practical txanple in Figure 6.3 (57). Ihe separation speed cannot be Increased for an open tubular column by increasing the reduced velocity since the reduced plate height is increased... 

CEC plate heights were smaller than observed in HPLC and essentially independent of reduced velocity. 

A reduced velocity (Boure, 1966 Ishii and Zuber, 1970) involving the flow rate-versus-heating power ratio or its reciprocal [phase change number in Ishii and Zuber (1970)]. This group includes the specific volume ratio in Boure (1966) and in Ishii and Zuber (1970). 

Consider a process unit that develops a small hole, as shown in Figure 4-4. The pressure of the liquid contained within the process unit is converted to kinetic energy as the fluid escapes through the leak. Frictional forces between the moving liquid and the wall of the leak convert some of the kinetic energy of the liquid into thermal energy, resulting in a reduced velocity. 

A more vigorous treatment similar to the van Deemter equation but developed specifically for HPLC is the Knox equation, which uses a number of reduced parameters where h is the reduced plate height (h/dp) and vis reduced velocity (V dJD. ... 

Equation 5 Knox equation, with reduced plate height, h reduced velocity (m dpID ), V, coefficient B, describing axial diffusion (typical value 2) coefficient A, describing bed homogeneity (typical value 1-2) and coefficient C, describing mass transfer (typical value 0.05). 

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