Velocity interstitial

Peclet number for dispersion Pe = uUD where t/ is a Bnear velocity, L is a hnear dimension, and is the dispersion coefficient. In packed beds, Pe = udp/De, where u is the interstitial velocity and dp is the pellet diameter. 

By definition, the e]q>erlmentally determined average mobile phase velocity Is equal to the ratio of the column length to the retention time of an unretalned solute. The value obtained will depend on the ability of the unretalned solute to probe the pore volume. In liquid chromatography, a value for the Interstitial velocity can be obtained by using an unretalned solute that Is excluded from the pore volume for the measurement (section 4.4.4). The Interstitial velocity Is probably more fundamentally significant than the chromatographic velocity in liquid chromatography (39). 

Fig. 1.14 Propagators for water flowing with an average interstitial velocity of 610 pm s-1 through a sample of sandstone of 15.3% porosity. The curves in both plots refer to encoding times of A = 50, 85, 140, 220, 330, 500, 750, 1100 and 1650 ms. Left propagators in the z direction (along the flow axis) the disappearance of a pronounced peak near zero...

Ret< 1 Viscous or creeping flow in which pressure drop is linearly proportional to interstitial velocity and flow is dominated by viscous forces ... 

Ret < 150 Steady laminar inertial flow in which pressure drop depends nonlinearly on interstitial velocity and and boundary layers in the pores become pronounced with an inertial core appearing in the pores ... 

Extrapolation of laboratory results to the field scale is at best qualitative because of the complexity of the geochemical and hydrological systems in the Bengal Basin. Movement of As-contaminated groundwater towards a well screened in the uncontaminated aquifer is likely to contain both vertical and horizontal components of flow. For modeling purposes presented here, a relatively slow interstitial groundwater velocity of 3 m/yr (Stollenwerk et al. 2007) is compared with a more rapid interstitial velocity of 30 m/yr (McArthur et al. 2008). 

Richardson and Mijkle 63 1 have shown that, at high concentrations, the results of sedimentation and fluidisation experiments can be represented in a manner similar to that used by Carman" 4 1 for fixed beds, discussed in Chapter 4. Using the interstitial velocity and a linear dimension given by the reciprocal of the surface of particles per unit volume of fluid, the Reynolds number is defined as ... 

The friction group resistance force per unit particle surface (Ri) and the interstitial velocity. 

At any level in the transition region, there will be a balance between the mixing effects attributable to (a) axial dispersion and to (b) the segregating effect which will depend on the difference between the interstitial velocity of the liquid and that interstitial velocity which would be required to produce a bed of the same voidage for particles of that size on their own. On this basis a model may be set up to give the vertical concentration profile of each component in terms of the axial mixing coefficients for the large and the small particles. 

Here uR is the velocity at which the solute band moves along the column and u is the velocity of the mobile phase that is, u = (superficial velocity)/e, where superficial velocity is volumetric flow rate divided by cross-sectional area of column and s is the fractional volume of column occupied by mobile phase. Most column packings are porous, in which case s includes both interstitial and pore (intraparticle) voidage, as defined in the note to Table 19.1, and here u is less than the interstitial velocity. 

If now the cross-sectional area which determines the interstitial velocity for a given volumetric flow rate is proportional to the interparticle voidage, it follows that... 

C is the concentration of the analyte in the bnlk mobile phase is the interstitial velocity of the mobile phase... 

The lumped kinetic model can be obtained with further simplifications from the lumped pore model. We now ignore the presence of the intraparticle pores in which the mobile phase is stagnant. Thus, p = 0 and the external porosity becomes identical to the total bed porosity e. The mobile phase velocity in this model is the linear mobile phase velocity rather than the interstitial velocity u = L/Iq. There is now a single mass balance equation that is written in the same form as Equation 10.8. 

Moreover, examine die Wheeler-Jonas equation for the specified experimental conditions. On the basis of the results, predict the breakpoint time for lower interstitial velocities down to 1 m/s. 

In Figure 4.29, the breakpoint concentration for Cbl, = 1% is presented for different values of the interstitial velocity. 

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