Higbie’s penetration model

In [556] an attempt was made to describe the increase of k a values with increasing disperse phase fraction (here octene the droplets being stabilized by adding the anionic tenside sodium-dodecyl-sulfate) by a film variable hold-up model , that takes into consideration the change in oil/water fraction in the G/L film and diffusion in the droplets. It succeeded in approximating the test data much better than the two-film model or Higby s penetration model. The measurements by authors and other publications consulted, showed, however, that the linear relationship between the enhancement factor m for physical absorption and the fraction ... 

The gas-phase mass transfer is described by the stagnant film model whilst for the liquid phase Higbie s penetration model was used. The process of diffusion and simultaneous reaction in the liquid-phase penetration zone is given by the following balances [4] ... 

More recently, Kawase and co-workers have presented semi-analytical framework for the estimation of the volumetric mass transfer coefflcient in bubble column reactors with and without an internal draft tube [51,62,67]. They have essentially combined the Higbie s penetration model with the isotropic turbulence to deduce the following expression for gas-liquid mass transfer with power law liquids ... 

The addition of various surfactants and micelle forming agents on the biphasic hydroformylation of olefins was also considered as a tool for enhancement of the reaction rate. The relation between the extent of emulsification of the reaction mixture and the performance of hydroformylation reaction was also investigated. Mass transfer effects in biphasic hydroformylation of 1-octene in the presence of cetyltri-methylammoniumbromide (CTAB), was studied by Lekhal etal. [33], A mass-transfer model based on the Higbie s penetration theory was proposed to predict the rate of hydroformylation in a heterogeneous gas-liquid-liquid system under... 

Higbie s penetration theory was modified by Danckwerts, who assumed a residence time distribution for the active eddies at the interface. The same square root dependence of the k/ or kg value on diffusivity as in the penetration theory is obtained, but the resulting model is much more intellectually satisfying than the original penetration model. 

In surface renewal models the liquid surface is assumed to consist of a mosaic of elements with different age at the surface. The rate of absorption at the surface is then an average of the rates of absorption in each element, weighted with respect to a distribution function (t)—see Eq. 6.2-5. Under this heading of surface renewal theory we will also occasionally mention results of Higbie s [23] so-called penetration-theory, which can be considered as a special case in which every element is exposed to the gas for the same length of time before being replaced. The main emphasis of this section is on the Danckwerts [24] approach using the distribution function for completely random replacement of surface elements ... 

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... 

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