Model Higbie

The average transfer rate according to the Higbie model for surface age distribution then becomes ... 

Show that under the conditions specified in Problem 10.7 and assuming the Higbie model of surface renewal, the average mass flux at the interface is given bv ... 

According to the Higbie model, if the element is exposed for a time te, the average rate of transfer is given by ... 

Given that from the penetration theory for mass transfer across an interface, the instantaneous rate of mass transfer is inversely proportional to the square root of the time of exposure, obtain a relationship between exposure time in the Higbie model and surface renewal rate in the Danckwerts model which will give the same average mass transfer rate. The age distribution function and average mass transfer rate from the Danckwerts theory must be derived from first principles. 

Given that the instantaneous mass transfer rate = Kt 1/ 2, then for the Higbie model, the average mass transfer rate for an exposure time te is given by ... 

As explained in Section II,B,4, Van Krevelen and Hoftijzer (V4) computed approximated solutions for the film model, expressed by Eq. (26). It is interesting to note that other correlations giving implicit or explicit dependence between the enhancement factor E and the parameters Ha and El have been developed. Hikita and Asai (H7) have proposed an implicit expression for the Higbie model ... 

With the age distribution function for the classic Higbie model (Eq. 9.1.5), the average mass transfer coefficient is... 

The matrix [/c] in Eq. 9.3.30 is the matrix of mass transfer coeflicients at any time t. The matrix of time-averaged zero-flux mass transfer coeflicients is given for the Higbie model by... 

In searching for a more realistic model than one containing a fictitous film, Higbie [17] proposed the elimination of the film idea and replacing it with an imsteady-state model that permits turbulent conditions adjacent to the interface. Sometimes called the Higbie model, it contains the following elanents ... 

Given that the instantaneous mass transfer rate = then for the Higbie model, the... 

Laboratory absorbers for studying absorption into liquids may be divided into two groups. Some of them have effectively a quiescent liquid which comes into contact with gas for a desired time which can also be changed with relative ease. Strictly speaking these absorbers simulate the conditions which are foreseen by the Higbie model. Table 7 shows the main types and Danckwerts (2) discusses in some detail design characteristics and proper operation of many of these absorbers. These absorbers may also be used to obtain "process specific data" -such as, reaction kinetics, diffusivities etc. (2,73-75). 

Penetration theory can also be applied to turbulent conditions by assuming the turbulence spectrum to consist of large eddies, capable of surface renewal, and small eddies responsible for the presence of eddy diffusivity The small eddies are damped when an element of liquid reaches the interface so that, during its residence time there, mass transfer occurs in accordance with the assumptions of the penetration theory If all the eddies stay at the interface for the same interval of time we talk about penetration theory with regular surface renewal or the Higbie model If there is random distribution of residence times with an age-independent fractional rate of surface renewal, s, the term penetration theory with random surface renewal, or the Danckwerts nK)del, is employed In the case of the Higbie model, the mass transfer coefficient is the same as that given by eqn (18). For the Danckwerts model it takes the form... 

Enhancement fectors for second-order reaction for quiescent liquid or agitated liquid (film or Higbie models). Based on equation... 

According to the Higbie model and equation (243), the equation for the liquid-side controlled mass transfer is as follows ... 

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