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12-314 Coalescence Mechanisms in Mixing Flows As explained previously, coalescence between colliding drops occurs when the lm of continuous phase uid separating them thins to a critical thickness during contact Once the critical thickness is reached, a hole opens up which enlarges rapidly, resulting in coalescence and internal drop mixing Sometimes the combination is so rapid that internal pressures cause satellite drops to be ejected from opposite ends of the newly formed oscillating drop If the force holding drops in contact is brief and insuf cient drainage occurs, coalesce will not take place The approach forces needed to bring about lm drainage can be hydrodynamic, hydrostatic, or physicochemical As discussed above, hydrodynamic forces are bought about by shear (laminar or turbulent) and are of nite duration Such forces can be intense but are de nitely not constant during drop contact.

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Forces can also be due to gravity acting on density differences between the drops and the continuous phase Gravitational forces are constant and are of long duration They control coalescence times for drops approaching settled layers The lm thinning mechanism still applies even though there is no critical time beyond which departure occurs The time for an emulsion or suspension to settle completely can be quite long, particularly if the phases have similar densities or if interfaces contain surfactants, repulsive charges, or impurities Solid surfaces, particularly those easily wetted by the dispersed phase, can be major collectors of drops In the case of a rotating impeller, drops collect and coalesce on blade surfaces to form a condensed lm As this lm grows in thickness, it ows under centrifugal forces to the impeller tips and disperses into tiny drops This process is similar to the breakup of a cylindrical liquid jet.

A lm of dispersed phase can also collect on free surfaces, baf es, tank walls, and the impeller shaft, where the surface vortex meets the shaft In the case of emulsion and suspension polymerization, coalescence also leads to fouling of heat transfer surfaces Electrostatic forces are used in electrostatic precipitators to coalesce aqueous brine from crude oil Fibrous beds are used to coalesce owing drop suspensions where bers are chosen that will be wetted by the dispersed phase As the drop suspension is forced through the bed, drops coalesce and build up a wet layer on the bers This layer continues to thicken until drag forces caused by the ow result in break-off The departing drops, however, are much larger than the incoming drops, so the device achieves its desired function Centrifuges amplify gravitational forces The cream separator is a good example 12-31.

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5 Practical Classi cation of Coalescing Systems While it has been stated repeatedly that coalescence is highly complex and that scale-up is dif cult, not all liquid liquid systems are complex A simple way to characterize.

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As we expected, a 4K-by-8 single-port block RAM is inferred and two block RAMS are used to realize the circuit. 11.4.2

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