Surface renewal mechanisms

Marchello and Toor (M2) proposed a mixing model for transfer near a boundary which assumes that localized mixing occurs rather than gross displacement of the fluid elements. This model can be said to be a modified penetration-type model. Kishinevsky (K6-K8) assumed a surface-renewal mechanism with eddy diffusion rather than molecular diffusion controlling the transfer at the interface. 

In a series of papers between 1949 and 1954 Kishiuevskii and cowotkers24 27 proposed a surface-renewal mechanism which, in contrast to the theories described above, postulates that transfer into an eddy at the interface occurs predominantly by convective mass flow and not by molecular diffusion. The authors also dispute the noggestion drat the probability of replacement of a surface element is independen of its age. 

Comparisons between experimental observation and the predictions of (he Him theory on (he ons hand and various forms of surface-renewal theory on the other are reviewed briefly in Ref. 33 (Chap. 5). It is interesting that, although the evidence generally appears to favor the surface-renewal mechanisms, the two-film theory contributes to the design of complex processes in a manner Ihel continues to be very useful. An example of (his will be given later in the formulation of transfer unit relationships for pecked column design. 

Wasan DT, Ahluwalia MS. Consecutive film and surface renewal mechanism for heat and mass transfer from a wall. Chem Eng Sci 24 1535-1542, 1969. 

The first type of model considers the heat transfer surface to be contacted alternately by gas bubbles and packets of closely packed particles. This leads to a surface renewal process whereby heat transfer occurs primarily by transient conduction between the heat transfer surface and the particle packets during their time of residence at the surface. Mickley and Fairbanks (1955) provided the first analysis of this renewal mechanism. Treating the particle packet as a pseudo-homogeneous medium with solid volume fraction, e, and thermal conductivity (kpa), they solved the transient conduction equation to obtain the following expression for the average heat transfer coefficient due to particle packets,... 

The mechanism of transfer of solute from one phase to the second is one of molecular and eddy diffusion and the concepts of phase equilibrium, interfacial area, and surface renewal are all similar in principle to those met in distillation and absorption, even though, in liquid-liquid extraction, dispersion is effected by mechanical means including pumping and agitation, except in standard packed columns. 

From this relation 24) it is clear that the apparent over-all variation of 2 with D will depend on the relative importance of and ir as the turbulence is increased, v will increase faster than nd will depend less on D, becoming independent of D (i.e., varying as D ) in the limit of very high turbulence. At very low turbulence, however, k2 will vary with and for any narrow range of moderate turbulence the dependence on D will be to some power between 0 and 0.5. Experiments to test the mechanism of the surface renewal in a turbulent liquid are described below. 

Several different mechanisms have been proposed to provide a basis for a theory of interphase mass transfer. The three best known are the two-film theory, the penetration theory, and the surface renewal theory. 

The objective is to reduce volatiles to below 50-100-ppm levels. In most devolatilization equipment, the solution is exposed to a vacuum, the level of which sets the thermodynamic upper limit of separation. The vacuum is generally high enough to superheat the solution and foam it. Foaming is essentially a boiling mechanism. In this case, the mechanism involves a series of steps creation of a vapor phase by nucleation, bubble growth, bubble coalescence and breakup, and bubble rupture. At a very low concentration of volatiles, foaming may not take place, and removal of volatiles would proceed via a diffusion-controlled mechanism to a liquid-vapor macroscopic interface enhanced by laminar flow-induced repeated surface renewals, which can also cause entrapment of vapor bubbles. 

The objective of this entry is to introduce the readers to the fundamental principles of gas-to-liquid mass transfer, as well as its major applications. Therefore, the first section of the entry is on the three fundamental mechanisms of gas-to-liquid mass transfer the film theory, the penetration theory, and the surface renewal theory followed by the applications of gas-to-liquid mass transfer in unit operations that are widely used in various chemical processes. There is a vast pool of reported literature on different aspects of gas-to-liquid mass transfer processes, all of which is impossible to be included in this entry. Therefore, only typical gas-to-liquid mass transfer processes are presented here. 

The value of a varies with the system under consideration. For example, in equimolar counter diffusion, Na and Nb are of the same magnitude, but in opposite direction. As a result, a is equal to 1 and hence, Eq. (2) reduces to Eq. (1), where is equal to Convective mass transfer coefficients are used in the design of mass transfer equipment. However, in most cases, these coefficients are extracted from empirical correlations that are determined from experimental data. The theories, which are often used to describe the mechanism of convective mass transfer, are the film theory, the penetration theory, and the surface renewal theory. 

The fundamental principles of the gas-to-liquid mass transfer were concisely presented. The basic mass transfer mechanisms described in the three major mass transfer models the film theory, the penetration theory, and the surface renewal theory are of help in explaining the mass transport process between the gas phase and the liquid phase. Using these theories, the controlling factors of the mass transfer process can be identified and manipulated to improve the performance of the unit operations utilizing the gas-to-liquid mass transfer process. The relevant unit operations, namely gas absorption column, three-phase fluidized bed reactor, airlift reactor, liquid-gas bubble reactor, and trickled bed reactor were reviewed in this entry. 

The surface-renewal theory intends to provide a better representation of the physical mechanisms than the penetration theory, but it predicts the same dependency of the mass transfer coefficient upon the diffusion coefficient. The penetration theory can thus be looked upon as a special case of the surface renewal theory where the distribution function takes the form of (5.204). Moreover, both theories also contain an unknown fitting parameter and are thus in practice equivalent. For the quantitative determination of the transfer coefficient we need to relate s, t or tg to the measurable parameters of the system under consideration. For this reason these concepts have no predictive value. 

In liquid-solid fluidized beds, the presence of solids increases the turbulence in the system and provides additional surface renewal through the thermal boundary layer at the wall. Early studies have indicated that the heat transfer by particle convective mechanism is insignificant and that the convective heat transfer due to turbulent eddies is the principal... 

There are several possible mechanisms to explain the enhancement of absorption during surface renewal. The Marangoni Effect results from the fact that dilute solutions of water C10 %) exhibit abnormalities in regard to surface tension. Jones and Ray [8] have observed that absorption of ions at the surface continues until a specific number of sites are occupied. The concentration of these sites is about 5 per 10 surface molecules. If liquid vapor is continually condensed on the drop surface, new surface for sites is being formed at a rate fixed by condensation. A second mechanism for enhancement, Stefan flow, is a trapping of the gas molecules into the liquid phase by the condensing vapor flux. The Stefan flow flux can be expressed as [9] ... 

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