Random surface renewal

Experiments have been carried out on the mass transfer of acetone between air and a laminar water jet. Assuming that desorption produces random surface renewal with a constant fractional rate of surface renewal, v, but an upper limit on surface age equal to the life of the jet, r, show that the surface age frequency distribution function, 4>(t), for this case is given by ... 

Danckwerts assumed a random surface renewal process in which the probability of surface renewal is independent of its age. If s is the fraction of the total surface renewed per unit time, obtain the age distribution function for the surface and show that the mean mass transfer rate Na over the whole surface is ... 

A detailed discussion of the relationship between drag reduction and the random surface renewal in turbulent pipe flow is available in Fortuin s report. 

Fortran JMH, KJijn PJ (1982) Drag reduction and random surface renewal in turbulent pipe flow Chem Eng Sci 37 611... 

The mode of random surface renewal exists for a surface that is in the main body of a suspension and is continually contacted by rising bubbles. The age distribution of elements on the surface is represented by that of a continuous-stirred tank reactor (CSTR), as given by... 

Experiments have been carried out on the mass transfer of acetone between air and a laminar water jet. Assuming that desorption produces random surface renewal with a... 

Random surface renewal is discussed in Section 10.5.2 where it is shown that the age distribution function is ... 

For the Danckwerts model, the random surface renewal analysis, presented in Section 10.5.2, shows that the fraction of the surface with an age between t and t + dt is a function of t = fit) dt and that f(t) = Kq s1 where s is the rate of production of fresh surface per unit total area. 

Figure 9.3. Surface age distribution according to Danckwerts the elements undergo random surface renewal at frequency s.

For the Danckwerts model, the random surface renewal analysis, presented in Section... 

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... 

DatKkwerts theory cf penetration with random surface renewal modifies diis picture by proposing an infinite range of ages for elements of the surface. The probability of an element of surface being rqrlaced by a fresh eddy is considered to be independem of the age of that element. Danckwerts introduced this modification by defining a surfiKe age distribution function, (r), such that the fraction of surface with ages between r and r -l- is 6(r)dir. If die probability of replacement of a surface element is independem of its age, Danckwetts showed that k = (sD), where s is the fractional rate of surface renewal. 

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