- Email: [email protected]
Gas absorption with first-order chemical reaction in a spherical liquid film
Letters to the Editors 141 JANZ G. J. Estimation of thermodynamic properties of organic compounds Academic Press, New York 1958. A. F. Gas kinetics Butterworths, London 1955. [51 TROTMAN-DICKENSON A. F. J. Chem. Sot. 1960 218 1064. 161 Farrrs G. C., KNOX J. H. and TROTMAN-DICKENSON A. F. Progress in reaction kinetics (ed. by G. Porter) 1 107, Pergamdn Press, [71 KERR J. A. and TROTMAN-DICKENSON London 1961. 181 WU~ON D. J. and JOHNSTONH. S. J. Amer. Chem. Sot. 1957 79 29. [91 PITZER K. S. J. Amer. Chem. Sot. 1957 79 1804. .
Gas absorption with first-order chemical reaction in a spherical liquid 6lm (Received 20 December 1961) A RECENTpaper by RATCLIFFand HOLDCROFT[l] gives an equation for the rate of gas absorption with first-order chemical reaction in a spherical liquid film. The applicability of the same appears to be questionable, except for the limiting case of purely physical absorption. In fact, the equation given in the paper leads, in the case of very high values of the dimensionless reaction rate kR/uo+, to a direct proportionality between gas absorption rate and kinetic constant, while in this case, for other geometries of the liquid film, the gas absorption rate is proportional to the square root of k. This discrepancy is due to the fact, that in the mathematical derivation of the equation given by the authors, an approximation is introduced which is valid only for very low kR/uo+ values. In fact, equation A. 11 of the paper contains the term : Y
20
G = 2c+R2-\/(Dr)
s
: [y’(kr)erf
z/(kt) + e-Et/l/t]sen BdtI (1)
where :
t = R/u;
0 sin%& s0
(2)
For very high k/Rue+ values, equation (1) becomes: G = 4rR2cfZ/Dk
(3)
which gives the required square root of k. For very low kR/u$ values, equation (1) yields:
s x
G = 2c+Raz/(Dnuo+/R)
s
0
*
f’(d - y2/4DB2)exp(-82)B-2dS yl2JDd
where the function to be integrated has its largest values in the vicinity of the lower integration limit. In this vicinity, y*/4Dp2 is close to 4, and therefore this term cannot be neglected with respect to 4, as done by the authors, even if the integral for y = 0 is required. Only when kR/uo+ tends to zero,f’(+) tends tof’(O), and therefore the approximation introduced by the authors is correct. On the other side, the equation given is admittedly sensitive only for large k values, when it is not correct; for very low k values, it degenerates into the correct equation for physical absorption, originally given by Davidson [2], but cannot be used sensitively in order to evaluate k values. If the above discussed substitution has to be avoided, the mathematical treatment chosen by the authors does not lead itself to any simple way of getting further than equation A.11. and a somewhat simplified approach is in order. Neglecting the sphericity effect as far &the stretching of the liquid tilm is concerned, the differential equation A.1 of the paper may be treated in the classical way, yielding:
sen @de @ o sent&da
(4)
which coincides with the equation given by KRAMER~(31, calculated neglecting the stretching effect. Equation [4] differs very slightly from the exact equation given by DAVIDSON [2]; it seems therefore reasonable to assume that the stretching effect may be neglected also in the chemical absorption problem. The agreement between predicted and experimental values of k given in the paper is possibly due to the fact that the dimensionless reaction rates involved are indeed low. In fact, carbon dioxide absorption in carbonate-bicarbonate buffer solutions proceeds at a rate which, on a table-tennis ball absorber, and in the range of liquid flow-rates used, is little different from the rate of physical absorption [4]; l,l-dimethoxyethane absorption in acid solutions involves even lower values of k, as reported in the paper. The notation of the original paper has been used. The symbol UO+indicates the surface velocity of the liquid at the equator of the sphere. G. kiTARITA Zstituto di Chimica Zndustriale, University of Naples, Italy.
REFERENCES RATCLIFFG. A. and HOLDCROF~J. G. Chem. Engng. Sci. 1961 15 100. DAVIDSONJ. F. and CULLENE. J. Trans. Inst. Chem. Engrs. 1957 35 51. LYNN S. et al. Chem. Engng. Sci. 1955 4 63. DI BLMIO G. Chem. Eng. Thesis, University of Naples, Naples, Italy, 1961.
708
Gas absorption with first-order chemical reaction in a spherical liquid 6lm (Received 20 December 1961) A RECENTpaper by RATCLIFFand HOLDCROFT[l] gives an equation for the rate of gas absorption with first-order chemical reaction in a spherical liquid film. The applicability of the same appears to be questionable, except for the limiting case of purely physical absorption. In fact, the equation given in the paper leads, in the case of very high values of the dimensionless reaction rate kR/uo+, to a direct proportionality between gas absorption rate and kinetic constant, while in this case, for other geometries of the liquid film, the gas absorption rate is proportional to the square root of k. This discrepancy is due to the fact, that in the mathematical derivation of the equation given by the authors, an approximation is introduced which is valid only for very low kR/uo+ values. In fact, equation A. 11 of the paper contains the term : Y
20
G = 2c+R2-\/(Dr)
s
: [y’(kr)erf
z/(kt) + e-Et/l/t]sen BdtI (1)
where :
t = R/u;
0 sin%& s0
(2)
For very high k/Rue+ values, equation (1) becomes: G = 4rR2cfZ/Dk
(3)
which gives the required square root of k. For very low kR/u$ values, equation (1) yields:
s x
G = 2c+Raz/(Dnuo+/R)
s
0
*
f’(d - y2/4DB2)exp(-82)B-2dS yl2JDd
where the function to be integrated has its largest values in the vicinity of the lower integration limit. In this vicinity, y*/4Dp2 is close to 4, and therefore this term cannot be neglected with respect to 4, as done by the authors, even if the integral for y = 0 is required. Only when kR/uo+ tends to zero,f’(+) tends tof’(O), and therefore the approximation introduced by the authors is correct. On the other side, the equation given is admittedly sensitive only for large k values, when it is not correct; for very low k values, it degenerates into the correct equation for physical absorption, originally given by Davidson [2], but cannot be used sensitively in order to evaluate k values. If the above discussed substitution has to be avoided, the mathematical treatment chosen by the authors does not lead itself to any simple way of getting further than equation A.11. and a somewhat simplified approach is in order. Neglecting the sphericity effect as far &the stretching of the liquid tilm is concerned, the differential equation A.1 of the paper may be treated in the classical way, yielding:
sen @de @ o sent&da
(4)
which coincides with the equation given by KRAMER~(31, calculated neglecting the stretching effect. Equation [4] differs very slightly from the exact equation given by DAVIDSON [2]; it seems therefore reasonable to assume that the stretching effect may be neglected also in the chemical absorption problem. The agreement between predicted and experimental values of k given in the paper is possibly due to the fact that the dimensionless reaction rates involved are indeed low. In fact, carbon dioxide absorption in carbonate-bicarbonate buffer solutions proceeds at a rate which, on a table-tennis ball absorber, and in the range of liquid flow-rates used, is little different from the rate of physical absorption [4]; l,l-dimethoxyethane absorption in acid solutions involves even lower values of k, as reported in the paper. The notation of the original paper has been used. The symbol UO+indicates the surface velocity of the liquid at the equator of the sphere. G. kiTARITA Zstituto di Chimica Zndustriale, University of Naples, Italy.
REFERENCES RATCLIFFG. A. and HOLDCROF~J. G. Chem. Engng. Sci. 1961 15 100. DAVIDSONJ. F. and CULLENE. J. Trans. Inst. Chem. Engrs. 1957 35 51. LYNN S. et al. Chem. Engng. Sci. 1955 4 63. DI BLMIO G. Chem. Eng. Thesis, University of Naples, Naples, Italy, 1961.
708