Dispersion liquid interstitial

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, PeL = LJLdp/EZL, Reu = dppLUL/pLi GaL = dlgpl/pl, UL is the interstitial liquid velocity, and EZL is the liquid-phase axial dispersion coefficient. Furzer and Michell28 correlated the Peclet number to the dynamic holdup by a relation... 

In fluidization, a suspension of fine solid particles behaves like a liquid during the upflow of a supportive gas or liquid phase. Thus the bed of fluidized solid itself may be analyzed similarly to liquid systems. The gas-lift effect produces internal recirculation, by providing a descending flow of high particle concentration and an ascending flow of low particle concentration. This effect resembles the circulation in bubble columns. Whereas bubble columns contain dispersed gas and a continuous liquid phase, the fluidized bed comprises the bubble phase and the emulsion phase in which particles have gained fluid-like properties by the interstitial gas flow. 

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... 

Consider a column experiment in which we have fluid flow in a saturated porous medium. If we introduce a small mass of tracer at a point in the flow field, we observe that, over time, the concentration is diluted in the direction of bulk liquid flow as a result of mixing with the interstitial fluid and is referred to as longitudinal hydrodynamic dispersion (Dl)- Mixing of the tracer perpendicular to the direction of bulk flow is referred to as transverse hydrodynamic dispersion (Dt ) and is frequently 20—50% smaller than longitudinal hydrodynamic dispersion. The dilution of the tracer occurs as a... 

Flow of liquids or gases through fixed beds is very important in chemical reaction engineering, since many commercially important processes involve reactors that contain beds of catalyst used to promote a desired reaction. The axial dispersion model has been used extensively to model these flows, even though two phases, fluid and solid, are present. Such a pseudo-homogeneous model assumes the same form we have described in the preceding section if the Peclet number is based on particle dimension and the interstitial fluid velocity is used. In this event... 

The other method of diffusion of a chemical through a liquid phase, molecular diffusion, is driven by concentration gradients. It is normally orders of magnitude slower in natural waters than eddy-driven processes, unless the water body is abnormally still and uniform in temperature (Lerman, 1971). Such situations are found only in isolated settings such as groundwaters and sediment interstitial waters. Even here, however, empirical measurements often indicate that actual dispersion exceeds that calculated from molecular diffusion alone. 

In a classic paper Lapidus and Amundson (1952) studied liquid chromatography for isothermal operation with linear, independent isotherms when mass transfer is very rapid, but axial dispersion is inportant. Although the two-porosity model can be used (Wankat, 1990), the solution was originally obtained for the single-porosity model. Starting with Eq. [18-551. we substitute in the equilibrium expression Eq. [18-6al to remove the variable q (solid and fluid are assumed to be in local equilibrium). Since the fluid density is essentially constant in liquid systems, the interstitial fluid velocity Vj ter can be assumed to be constant. The resulting equation for each solute is... 

As the proportion of liquid to particles is increased the liquid is free to move and the attractive force between particles decreases (funicular). When there is sufficient liquid to completely fill the interstitial pores between the particles (capillary) the granule strength falls further as there are fewer curved liquid surfaces and fewer boundaries for surface tension forces to act on. Clearly when the particles are completely dispersed in the liquid (droplet) the strength of the structure is very low. 

If we ignore any dispersion effects and employ only the interstitial velocity in the z-direction, (Vp Vg not being relevant), we get the time-dependent z-directional equation for particle mass concentration, Bp,rp< the liquid ... 

The third liquid-membrane technique is the hollow fiber contained liquid membrane (HFCLM). In the SLM/ ILM technique, the liquid membrane is in contact with the feed liquid/feed gas and the strip liquid/permeate gas. The membrane liquid may be lost by solubilization/volatiliza-tion in addition, there may be irreversible reactions with extractants, complexing agents inside the liquid membrane, which could reduce the performance over time. The HFCLM structure can take care of such problems. In this structure (Figure 8.1.50), the membrane module (cylindrical or otherwise) has two sets of porous hollow fiber membranes. The shell-side interstitial space between the fibers is filled with a liquid acting as the membrane. If this membrane liquid wets the membrane pores and is therefore present in the pores, the pressure conditions in the feed liquid and the sweep/strip fluid should be such (higher) that the membrane liquid is not dispersed in the feed/sweep/stilp fluids. If the membrane liquid does not wet the membrane pores, but the feed/sweep fluids do, then the membrane liquid pressure should be higher than the feed/sweep fluid pressures. 

Teflon. Results of dispersion experiments run before and after the polymer experiments are in good agreement with the liquid-filled porosity. In this paper, all velocities are interstitial velocities. In the first run where the velocity was 6.5 ft/D, breakthrough of the 0.5 normalized concentration occurred after 0.988 PV (370.5 cc) was injected. The second dispersion run at a velocity of 3.27 ft/D broke through at 0.964 PV (361.5 cc). The close agreement between liquid pore volume and breakthrough of the 0.5 normalized concentration data shows that the liquid-filled pore volume was not altered appreciably throughout the experiments. 

The equation is written in terms of concentration and therefore is suitable for a liquid feedstock. By use of an appropriate equation of state, equation 6.19 is readily adapted for a gas feed. The loading on the adsorbent q is expressed in units of mass/mass. The first term represents axial dispersion within the bed the axial dispersion coefficient is Dj The second term represents convective flow within the bed the interstitial velocity is u (and is equal to the superficial velocity divided by the bed voidage). The third term represents the accumulation of adsorbate in the fluid phase while the fourth term represents the rate of adsorption which may be a function of both the fluid phase concentration and the loading on the adsorbent. In general ... 

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