Liquid interstitial velocity

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. 

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). 

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, it has to be noted that for calculating the Peclet number in fixed beds, the actual velocity has to be used, i.e. the interstitial velocity, which influences the degree of mixing. In slurry bubble column reactors, the real velocity of the fluid is the bubble velocity, which is much higher than the gas superficial velocity. The mean bubble rise velocity for a batch liquid is (eq (3.201))... 

In Figure 5.2-22, the pressure-gradient, s(l -fi)(AP/Z), is plotted versus the interstitial mean gas velocity, ug, at constant gas densities. Along each line for a given density, the liquid flow-rates vary considerably, but the relationship between the pressure gradient and u(, is unique, and independent of the liquid mean velocity. 

Here, A is the cross-sectional area of fluid flow, V is the interstitial velocity of liquid, and M is the mass of tracer added. Michell and Furzer61 and Furzer and Michell35 claim that an accurate estimation of Ez can be obtained by fitting the experimental RTD with Eq. (3-8) by nonlinear regression techniques. The first and second moments are given by the relations... 

The interstitial velocity of the liquid in particulate region can be represented by a Richardson-Zaki type equation, assuming uniform-sized solids ... 

The net downward flow of liquid is the amount necessary to fill in the bubble cavities left behind the swarm per unit time, i.e., Cb bo- Hence the interstitial velocity of the downward flow of liquid through the bubble swarm is eb bo/(l b), and the ascending velocity of the swarm is reduced from Mb by this amount ... 

The relation given by Eq. (5-8) is obtained easily for a bulk recirculation flow of the continuous phase. We consider a bubble column of radius R in which the column liquid is in upflow centrally with a constant interstitial velocity Wju- Peripherally the liquid descends, forming a recirculation flow. For simplicity, it is assumed that gas bubbles distribute uniformly in the central upflowing liquid and ascend with it, and that no bubbles rise through the peripheral downflow. Here, the mean gas holdup of the upflow is b. and that averaged over the total column cross section is Cu. 

Tangential velocity along the bubble-emulsion interface Time-averaged interstitial velocity of liquid Interstitial mean liquid velocity, Eq. (4-15) Ascending velocity of bubbles... 

Area-averaged circulation velocity of liquid Mean interstitial velocity of upflow, Eq. (5-9) Interstitial velocity of gas in emulsion phase II along the column axis Slip velocity of bubble relative to liquid... 

Drop Velocity and Slip Velocity The hydrauhc characteristics of a static extractor depend upon drop diameter, liquid velocities, and physical properties. The average velocity of a dispersed-phase drop (Vj p) and the interstitial velocity of the continuous phase Vic are given by... 

The linear flow velocity, which is U in the liquid stream, increases upon entering the electrode to an interstitial velocity, W, given by... 

Due to the similarity between TMB and SMB processes (Section 6.6.2) the TMB approach is quite often used to estimate the operating parameters of SMB units. Operating parameters for TMB processes are the liquid flow rates in the four sections, Vj,TMB> and the volumetric flow rate of the adsorbent, Vads- To transfer these TMB parameters to SMB operating parameters (V/smb and tshift) the interstitial velocity in the SMB process must be equal to the relative velocity of fluid and adsorbent in the TMB process (Section 6.6.2.1). From this follow the relationships listed below ... 

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.). 

---