Interstitial velocity measurement

The filtered conditionally averaged measurements picks up the flow between the bubbles. Far from the test bubble, the filtered conditionally averaged velocity tends to a constant value which corresponds closely to the interstitial flow concept introduced in 7.3.3, i.e. 

The inviscid model (7.35) suggests that the interstitial Eulerian velocity is related to the bubble rise velocity (v) and bulk fluid velocity U through, 

The contribution to the interstitial velocity is estimated from the flux transported by the wakes, i.e. 

For a 0.2%, the comparison with the inviscid blocking solutions appears quite satisfactory. For 0.2 a 10%, the influence of the wake is appreciable, but the 

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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). 

Boundaries and global mass conservation impose important constraints on the interstitial velocity. To relate these concepts to experimental measurements described later we focus on bounded channel flows generated by a stream of speed U through a cloud of bubbles injected into a channel and moving vertically with a speed v. When the average separation between the bodies is small relative to the separation of the channel walls, the dipole field and average flow is equivalent to a distributed dipole moment, and averaging (7.34) over the whole volume yields,... 

Figure 7.7 Normalised interstitial velocity versus voidage. The closed symbols are experimental measurements. The inviscid prediction (7.48), is plotted as a full line, while the wake corrected model (7.49) is plotted as open symbols.

Note that they used interstitial velocity in Eq. 5.43. Table 5.12 shows the measured Corey-type parameters. From these data, we can see that the residual oil saturations in P/0 were reduced by 0.05 to 0.06 compared with water/oil (W/0) kf curves, and the water relative permeabihties at So kw were rednced by 0.036 to 0.105. The oil relative permeabihty cnrves were not mnch changed. 

Fig. 8. Interstitial velocity profiles. Representative regions in the microcirculation. Circles represent locations of fluorescence photobleaching experiments. The arrows inside the circles represent the direction of the interstitial fluid velocity at these locations. The nearby values show magnitudes of the velocity in fim/s. (a) An area where interstitial flow parallels blood flow in the vessels, (b) Interstitial flow is opposite prevailing blood flow, (c) Fluid is absorbed from the interstitium into a postcapillary venule. (From Chary and Jain, 1989, with permission.) The photobleaching technique has provided the first and to date the only measurements in the literature of interstitial convective velocities. We have now further improved this technique to permit measurements of binding parameters (Kaufman and Jain, 1990, 1991, 1992a, b) and of transport parameters in light-scattering media (Berk et al., 1993).

The Taylor-Aris result for the dispersion coefficient (Eq. 4.6.35) has been applied to the empirical correlation of measured and calculated longitudinal dispersion coefficients in flow through packed beds and porous media (see Eidsath et al. 1983). Typically, the velocity in the Peclet number of the Taylor-Aris formula is identified with the superficial velocity, and the capillary diameter with the hydraulic diameter for spherical particles. An alternative velocity suggested by the capillary model is the interstitial velocity, and an alternative length is the square root of the permeability. In an isotropic packing of particles is about one-tenth the particle diameter (Probstein Hicks... 

From a theoretical standpoint, the interstitial velocity is the more important it determines the kinetic energy and the fluid forces and whether the flow is turbulent or laminar. From a practical standpoint, the superficial velocity is generally more useful it shows the flow rate in terms of readily measured variables. Both see common use. 

Northrup, M.A., et al.. Direct measurement of interstitial velocity field variations in a porous medium using fluorescent-particle image velocimetry, Chem. Eng. Sci.. 48( I), 13-22 (1993). 

Flow rate of wash liquid through the cake, usually expressed as the interstitial velocity u (flow rate per unit open area of the cake). The expected wash rates need to be known anyway, in their own right, for the washing process design. Predictions are relatively simple if the wash liquid properties are not too different from those of the mother liquor and if the specific cake resistance (and the medium resistance if not negligible) is known. Measurement of wash rate on an actual cake and medium is relatively simple (Buchner funnel, vacuum leaf, pressure leaf, pressure cell, pilot-scale or full-size filter, etc.). 

The above discussion shows how the presence of inaccessible pore volume causes salt peaks to move through a porous medium more slowly than polymer peaks. Only one final point remains to be made — the connected pore volume of a core, measured by saturation starting from an evacuated condition, is not just the polymer pore volume it is the total pore volume occupied by water, including that fraction inaccessible to polymer. With this as the pore volume, then the salt front velocity is the true interstitial velocity and the polymer moves faster its velocity is greater because it does not enter the inaccessible pore volume. 

Simcik M, Mota A, Ruzicka MC, et al CFD simulation and experimental measurement of gas holdup and liquid interstitial velocity in internal loop airlift reactor, Chem Eng Sci 66 3268-3279, 2011. 

Figures 3.2.13 and 3.2.14 show sufficiently good agreement between MRI measurements and simulation results for various heights in the bed and for two quite different Re numbers. The higher values of [I achieved for the lower Re number can be explained by a lower drag force exerted on the liquid film due to a lower gas velocity uG. In addition, smaller diameters dc of the collector bodies result in more interstitial pockets being formed per volume, giving more space for the liquid to accumulate therein.

The interstitial fluid content of the skin is higher than in the subcutaneous fat layer and normal fluid movement is intrinsically finked to lymphatic drainage as governed by mechanical stresses of the tissue. A model of temporal profiles of pressure, stress, and convective ISF velocity has been developed based on hydraulic conductivity, overall fluid drainage (lymphatic function and capillary absorption), and elasticity of the tissue.34 Measurements on excised tissue and in vivo measurement on the one-dimensional rat tail have defined bulk average values for key parameters of the model and the hydration dependence of the hydraulic flow conductivity. Numerous in vivo characterization studies with nanoparticles and vaccines are currently underway, so a more detailed understanding of the interstitial/lymphatic system will likely be forthcoming. 

If the dense phase expands this immediately affects the reactor model because more gas will then flow via the favourable interstitial phase. Most models readily allow for this change given that the true division of flow can be predicted. Unhappily it has so far only been possible to measure this division experimentally at fairly low flow rates, well below those employed in commercial reactors. Certainly at velocities up to about 15 cm/s much more gas flows interstitially through Geldart type A powders than minimum fluidisation flow (17). 

Here, once again, PeL and ReL are based on the interstitial liquid velocity. Bennett and Goodridge2 obtained data in a 7.62-cm i.d. column with 30.48- and 60.96-cm packed height. Their measurements with 0.635-, and 0.953-cm Raschig rings indicate that the liquid-phase Peclet number is independent of bed length and can be correlated to the liquid-phase Reynolds number by a relation... 

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