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Letter to the editor of the journal of aerosol science
Letters to the Editors Letter to the Editor of the Journal of Aerosol Science The Journal of Aerosol Science [4, 421 (1973)] published a review of "Topics in Current Aerosol Research" [Vol. 3, Part 2 (G. M. Hidy and J. R. Brock, Eds.), Pergamon, Oxford, 1972], which contains the survey entitled "The Theory of Thermophoresis and Diffusiophoresis of Aerosol Particles and Their Experimental Testing" by B. V. Derjaguin and Yu. I. Yaiamov. This review is signed by C. N. Davies. In view of the fact that the part of this review concerned with our work contains statements that may give a wrong idea of our work, we are compelled to correct these errors. Pointing out that the formula of the velocity of diffusiophoresis of small particles derived by us contains the second term which is absent in Waldmann's work, Mr. C. N. Davies contends firstly that the authors do not give any indication of how much difference it makes, and, secondly, that the relevant equations (1.95, 1.97, 1.111, 1.119) are incorrect. But, as a matter of fact, the authors state that if the masses of molecules of both gases, as well as the reflection diffusivities, are equal, and thus the first term becomes equal to zero, then the second term describes the diffusiophoresis velocity depending on the difference in the sizes of molecules. Hence, the second term introduces, not only quantitative, but also, which is more important, qualitative, changes into the laws of diffusiophoresis, as well as into those of barodiffusion. Mr. C. N. Davies does not substantiate in any way his contention that the equations mentioned are incorrect. Nor can the authors give credit to this contention in view of the errors made elsewhere in the review. It is easy to refute the statement of the dimensional inhomogeneity of the formulas (1.95) a. soo. For this purpose, the aforesaid values should be substituted by their dimensions, as IkTI = g cmS/seC,
Im, I = Im~l = g, I/9,,I = cmVsec, In, I = I ~ l
= cm-3,
]Pl = g/cm3,
instead of d-b do, dl, according to formula (1.40),
di-
mensions should be placed
Id-~l = I~ol/l~o-,l, Id01 = I~0l/la00l,
Idll = I~ol/la01l, instead of 6o, according to formula (1.39), dimensions should be placed I~0l = g~ cmT/sec instead of ao_l, aoo, aob according to formula (147a)~ dimensions l a0~l] = g~ cmZ/sec, l a001 = g cm3/sec, l a011 = gt cm~/sec. Hence [d_, I = c m4, Idol = cm/g½,
Idll = c m t and hence I/3'1 = ]/321 = giIdol = cm*. When substituting the aforesaid dimensions of the values k T , m b m2, nb n2, p, D12, d_b do, dl,/31,/32 in formulas (1.95), (1.97), (1.111), (1.119) their dimensions remain uniform. Therefore, remains unanswered the question which has been raised in our letter to Mr. Davies, as to what errors he has discovered in the formulas enumerated above. Finding that in the introduction the factor 7r is omitted in equation (2) (though it is an obvious misprint as ~r is included in equation (5.12), which is the basic equation in the discussion of the theory of thermophoresis), Mr. C. N. Davies indulges in writing: "The authors fail to do themselves justice because a ~r is omitted from equation (2) . . . . " Noticing misprints, Mr. C. N. Davies ignores some essential points, such as the use of the principle of symmetry of the Onsager kinetic coefficients for deriving all the basic effects discussed in our work, or the dusty gas model, which was first suggested by Derjaguin and Bakanov and is frequently erroneously called Mason's gas model. Ignoring this, Mr. C. N. Davies claims that the theory of Mason and Chapman is "brushed aside by Bakanov and Derjaguin". This theory, which treats 209
Copyright O 1975 by Academic Press, Inc. All rights of reproduction in any form reserved.
Journal of Colloid and Interface Science, Vol. 51, No. 1, April 1975
210
LETTERS TO THE EDITORS
thermophoresis as a limit case of the general theory of thermodiffusion of gases, was developed by Derjaguin and Bakanov in Ref. (36), i.e., four years before Mason and Chapman (42), whose work was cited in our survey on page 9. This method, as was pointed out by us, yields the same results as the direct method. Therefore, the above statement of Mr. C. N. Davies is likely to mislead the reader. Proceeding in the same spirit, Mr. C. N. Davies says that there is a difference of about 2% in the thermoosmosis coefficients for small particles and for specular reflection of molecules between the formula of Waldmann and that derived by Derjaguin and Bakanov. Mr. C. N. Davies writes further:--"Bakanov and Derjaguin give for both specular and diffuse reflection a similar formula with the constant 0.367 which reduces to 0.264 for condensation of the incident gas molecules followed by independent re-evaporation." If we ignore an insignificant difference of 2%, the difference from Waldmann's calculations published 2 years later will be a purely imaginary one based obviously on a misunderstanding. As is well known the diffuse reflection and condensation followed by independent reevaporation are indiscernable for steady-state processes. Therefore, Waldmann's constant 0.269 should be compared with the constant 0.264, calculated by the authors. Now, the constant 0.367 was calculated by us not for a genuine diffuse reflection, but for a diffuse reflection with the conservation of velocity. Furthermore, Mr. C. N. Davies dismisses as "vague" the objection to the cell method used by Schmitt (and many other authors). Our objection consists in the following : in the case of a gas which is nonhomogeneous with regard to temperature (or composition), the gas
Journal of Colloid and Interface Science, Vol. 51, No. 1, April 1975
slip occurs along the wall, so that the experimenter using this method must prove that the convection of gas in a measuring cell due to this slip does not significantly affect the measurement of the velocity of thermophoresis (or diffusiophoresis). Therefore, advocating a more dispassionate appraisal of our claim, Mr. C. N. Davies should have called "vague" its denial by Waldmann, for it was not based on the analysis of the role in gas convection of the slip in the layer adjacent to the wall. The authors are surprised by Mr. C. N. Davies's suggestion that they should discuss the causes of the difference between the theoretical formula (4.217) of the diffusiophoresis velocity of nonvolatile particles, derived by them, and the formula of Waldmann. The fact is that Waldmann's formula is an empirical one. Hence, there is no sense in discussing the cause of a difference between a theoretical and an empirical formula. Misleading also is the assertion of Mr. C. N. Davies that the velocity of diffusiophoresis of volatile particles is "slightly" increased in the ratio of the total number of vapor molecules per unit volume to the number of gas molecules. Actually, the formula {4.173) expresses an increment in the diffusiophoresis velocity depending on the ratio between the masses of molecules, but not on the ratio between their concentrations. B. DERJAGUIN YU. YALAMOV
Institute of Physical Chemistry, The USSR Academy of Sciences, Mosco% U. S. S. R. Received May 31, 1974; accepted October 17, 1974
Im, I = Im~l = g, I/9,,I = cmVsec, In, I = I ~ l
= cm-3,
]Pl = g/cm3,
instead of d-b do, dl, according to formula (1.40),
di-
mensions should be placed
Id-~l = I~ol/l~o-,l, Id01 = I~0l/la00l,
Idll = I~ol/la01l, instead of 6o, according to formula (1.39), dimensions should be placed I~0l = g~ cmT/sec instead of ao_l, aoo, aob according to formula (147a)~ dimensions l a0~l] = g~ cmZ/sec, l a001 = g cm3/sec, l a011 = gt cm~/sec. Hence [d_, I = c m4, Idol = cm/g½,
Idll = c m t and hence I/3'1 = ]/321 = giIdol = cm*. When substituting the aforesaid dimensions of the values k T , m b m2, nb n2, p, D12, d_b do, dl,/31,/32 in formulas (1.95), (1.97), (1.111), (1.119) their dimensions remain uniform. Therefore, remains unanswered the question which has been raised in our letter to Mr. Davies, as to what errors he has discovered in the formulas enumerated above. Finding that in the introduction the factor 7r is omitted in equation (2) (though it is an obvious misprint as ~r is included in equation (5.12), which is the basic equation in the discussion of the theory of thermophoresis), Mr. C. N. Davies indulges in writing: "The authors fail to do themselves justice because a ~r is omitted from equation (2) . . . . " Noticing misprints, Mr. C. N. Davies ignores some essential points, such as the use of the principle of symmetry of the Onsager kinetic coefficients for deriving all the basic effects discussed in our work, or the dusty gas model, which was first suggested by Derjaguin and Bakanov and is frequently erroneously called Mason's gas model. Ignoring this, Mr. C. N. Davies claims that the theory of Mason and Chapman is "brushed aside by Bakanov and Derjaguin". This theory, which treats 209
Copyright O 1975 by Academic Press, Inc. All rights of reproduction in any form reserved.
Journal of Colloid and Interface Science, Vol. 51, No. 1, April 1975
210
LETTERS TO THE EDITORS
thermophoresis as a limit case of the general theory of thermodiffusion of gases, was developed by Derjaguin and Bakanov in Ref. (36), i.e., four years before Mason and Chapman (42), whose work was cited in our survey on page 9. This method, as was pointed out by us, yields the same results as the direct method. Therefore, the above statement of Mr. C. N. Davies is likely to mislead the reader. Proceeding in the same spirit, Mr. C. N. Davies says that there is a difference of about 2% in the thermoosmosis coefficients for small particles and for specular reflection of molecules between the formula of Waldmann and that derived by Derjaguin and Bakanov. Mr. C. N. Davies writes further:--"Bakanov and Derjaguin give for both specular and diffuse reflection a similar formula with the constant 0.367 which reduces to 0.264 for condensation of the incident gas molecules followed by independent re-evaporation." If we ignore an insignificant difference of 2%, the difference from Waldmann's calculations published 2 years later will be a purely imaginary one based obviously on a misunderstanding. As is well known the diffuse reflection and condensation followed by independent reevaporation are indiscernable for steady-state processes. Therefore, Waldmann's constant 0.269 should be compared with the constant 0.264, calculated by the authors. Now, the constant 0.367 was calculated by us not for a genuine diffuse reflection, but for a diffuse reflection with the conservation of velocity. Furthermore, Mr. C. N. Davies dismisses as "vague" the objection to the cell method used by Schmitt (and many other authors). Our objection consists in the following : in the case of a gas which is nonhomogeneous with regard to temperature (or composition), the gas
Journal of Colloid and Interface Science, Vol. 51, No. 1, April 1975
slip occurs along the wall, so that the experimenter using this method must prove that the convection of gas in a measuring cell due to this slip does not significantly affect the measurement of the velocity of thermophoresis (or diffusiophoresis). Therefore, advocating a more dispassionate appraisal of our claim, Mr. C. N. Davies should have called "vague" its denial by Waldmann, for it was not based on the analysis of the role in gas convection of the slip in the layer adjacent to the wall. The authors are surprised by Mr. C. N. Davies's suggestion that they should discuss the causes of the difference between the theoretical formula (4.217) of the diffusiophoresis velocity of nonvolatile particles, derived by them, and the formula of Waldmann. The fact is that Waldmann's formula is an empirical one. Hence, there is no sense in discussing the cause of a difference between a theoretical and an empirical formula. Misleading also is the assertion of Mr. C. N. Davies that the velocity of diffusiophoresis of volatile particles is "slightly" increased in the ratio of the total number of vapor molecules per unit volume to the number of gas molecules. Actually, the formula {4.173) expresses an increment in the diffusiophoresis velocity depending on the ratio between the masses of molecules, but not on the ratio between their concentrations. B. DERJAGUIN YU. YALAMOV
Institute of Physical Chemistry, The USSR Academy of Sciences, Mosco% U. S. S. R. Received May 31, 1974; accepted October 17, 1974