Continuous adsorptive bubble separation

In the bubble cell of any continuous adsorptive bubble separation process, the relative bubble velocity is the function of buoyancy component, the superficial gas velocity, and the superficial liquid velocity. The superficial velocity of gas and liquid are caused by the continuous entry of the gas and liquid phases into the bubble cell. Figures 4 (A) and 4 (B) show the relative bubble velocity in various two-phase bubble flow systems (43). 

In case of continuous adsorptive bubble separation processes, the following set of material balance equations at the steady state will be obtained. 

A few simple differences in the properties of immiscible phases make possible their relative displacement. Most simply, if the phases have different densities they will automatically acquire a relative motion in a gravitational field. Thus in adsorptive bubble separation methods, bubbles injected into a column of liquid rise toward the upper surface. Separation occurs by combining the relative enrichment of components at the bubble interface with the continuous displacement of bubbles through the liquid [33-35]. 

An adsorptive bubble separation process is assumed to be a continuous process in which the influent is continuously fed into the process system, while the effluent is continuously withdrawn from the process system. 

Lord Kelvin realized that, instead of completely drying out, moisture is retained within porous materials such as plants and vegetables or biscuits at temperatures far above the dew point of the surrounding atmosphere, because of capillary forces. This process was later termed capillary condensation, which is the condensation of any vapor into capillaries or fine pores of solids, even at pressures below the equilibrium vapor pressure, Pv. Capillary condensation is said to occur when, in porous solids, multilayer adsorption from a vapor proceeds to the point at which pore spaces are filled with liquid separated from the gas phase by menisci. If a vapor or liquid wets a solid completely, that is the contact angle, 0= 0°, then this vapor will immediately condense in the tip of a conical pore, as seen in Figure 4.8 a. The formation of the liquid in the tip of the cone by condensation continues until the cone radius, r, reaches a critical value, rc, where the radius of curvature of the vapor bubble reaches the value given by the Kelvin equation (r = rc). Then, for a spherical vapor bubble, we can write... 

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