Higby

K. B. Higbie, J. R. Werning, Separation ofTantalum—Columbium by Solvent Extraction Bulletin No. 5239, U.S. Bureau of Mines, Washington, D.C., 1956. 

The stagnant-film model discussed previously assumes a steady state in which the local flux across each element of area is constant i.e., there is no accumulation of the diffusing species within the film. Higbie [Trans. Am. Jn.st. Chem. Eng., 31,365 (1935)] pointed out that industrial contactors often operate with repeated brief contacts between phases in which the contact times are too short for the steady state to be achieved. For example, Higbie advanced the theory that in a packed tower the liquid flows across each packing piece in laminar flow and is remixed at the points of discontinuity between the packing elements. Thus, a fresh liquid surface is formed at the top of each piece, and as it moves downward, it absorbs gas at a decreasing rate until it is mixed at the next discontinuity. This is the basis of penetration theoiy. 

Higbie, R., 1935. The rate of absorption of a pure gas into a still liquid during a short time of exposure. Transactions of American Institute of Chemical Engineers, 31, 365-389. 

The work of Higbie laid the basis of the penetration theory in which it is assumed that the eddies in the fluid bring an element of fluid to the interface where it is exposed to the second phase for a definite interval of time, after which the surface element is mixed with the bulk again. Thus, fluid whose initial composition corresponds with that of the bulk fluid remote from the interface is suddenly exposed to the second phase. It is assumed that equilibrium is immediately attained by the surface layers, that a process... 

Assuming that all the surface elements are exposed for the same time te (Higbie s assumption), from equation 10.113, the moles of A (nA) transferred at an area A in time... 

Average rates of mass transfer can be obtained, as previously, by using either the Higbie or the Danckwerts model for surface renewal. 

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

Equations 10.142 and 10.143 give the point value of NA at time t. The average values Na can then be obtained by applying the age distribution functions obtained by Higbie and by Danckwerts, respectively, as discussed Section 10.5.2. 

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 ... 

Obtain expressions for the average rates of transfer on the basis of the Higbie and Danckwerts assumptions. 

Given that, from the penetration theory for mass transfer across an interface, the instantaneous rale ol mass transfer is inversely proportional to the square root of the time of exposure, obtain a relationship between exposure lime in the Higbie mode 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 deri ved from first principles. 

In calculating Ihe mass transfer rate from the penetration theory, two models for the age distribution of the surface elements are commonly used — those due to Higbie and to Danckwerts, Explain the difference between the two models and give examples of situations in which each of them would be appropriate. 

Two rather similar models have been devised to remedy the problems of simple film theory. Both the penetration theory of Higbie and the surface renewal theory of Danckwerts replace the idea of steady-state diffusion across a film with transient diffusion into a semi-inhnite medium. We give here a brief account of surface renewal theory. 

The Ridgelimeter is the most commonly used device to standardize high methoxyl pectins for commercial use (Cox and Higby, 1944). This empirical Sag-test is a one-point, nondestructive measurement. 

Penetration theories (Higbie, 1935 Danckwerts, 1951 Dobbins, 1956) according to the penetration theory, diffusion of gases takes place into elements of water transported by turbulence to the surface. 

Anderson L, Higby GJ. The Spirit of Volunteerism—A Legacy of Commitment and Contribution. The United States Pharmacopeial Convention, Inc., Rockville, Maryland, USA, 1995. 

An alternative theory described in detail in Volume 1, Chapter 10, has been put forward by Higbie 2 , and later extended by Danckwerts and Danckwerts and Kennedy14 in which the liquid surface is considered to be composed of a large number of small elements each of which is exposed to the gas phase for an interval of time, after which they are replaced by fresh elements arising from the bulk of the liquid. 

All three of these proposals give the mass transfer rate N A directly proportional to the concentration difference (CAi — CAL) so that they do not directly enable a decision to be made between the theories. However, in the Higbie-Danckwerts theory N A a s/Dj whereas NA film theory. Danckwerts applied this theory to the problem of absorption coupled with chemical reaction but, although in this case the three proposals give somewhat different results, it has not been possible to distinguish between them. 

Chen J, Higby R, Tian D, Tan D, Johnson MD, Xiao Y, Keller KJ, Feng S, Shields PG (2008) Toxicological analysis of low-nicotine and nicotine free-cigarettes. Toxicology 249 194-203 Connolly GN, Alpert HR (2008) Trends in the use of cigarettes and other tobacco products, 2000-2007, JAMA 299 2629-2630... 

There are several theories concerned with mass transfer across a phase boundary. One of the most widely used is Whitman s two-film theory in which the resistance to transfer in each phase is regarded as being located in two thin films, one on each side of the interface. The concentration gradients are assumed to be linear in each of these layers and zero elsewhere while at the interface itself, equilibrium conditions exist (Fig. 5). Other important theories are Higbie s penetration theory and the theory of surface renewal due to Danckwerts. All lead to the conclusion that, in... 

Using Davidson s theoretical expression for bubble-cloud circulation and the Higbie theory for cloud-emulsion diffusion the interchange of gas between bubble and cloud is then found to be... 

Alternatives to the film theory are also in use. These models [Higbie (1935) Danckwerts (1950, 1955)] view that the liquid at the interface is continually washed away and replaced by fresh fluid from the main body of the liquid, and that this is the means of mass transport. These unsteady-state surface renewal theories all predict... 

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