Chemical Engineering Science 59 (2004) 729 www.elsevier.com/locate/ces Letter to the editor Reply to the Comments by I. Fort on “The role of convection and turbulent dispersion in blending”  We are aware of Professor Fort’s pioneering work and it has been referred in our recent comprehensive review on mixing (Nere, et al., 2003). It has been indicated in his letter that the ratio of mixing time to circulation time  mix = C is proportional to (T=D) a . It has been reported in the past literature that the value of the exponent ‘a’ is between 1.8 and 2.5. Indeed, a similar dimensionless parameter  mix = C has been used for correlating mixing time in the case of jet mixers (Grenville and Tilton, 1996, 1997). In our previous paper (Patwardhan and Joshi, 1999), we have observed that the mixing time could be correlated with the help of secondary ow number, N QS , rather than the pri- mary pumping capacity, N QP . This implies that the circula- tion time should preferably be calculated based on the total ow (primary + entrained) generated by the impeller. The following correlation has been reported based on the ex- perimental measurements and CFD simulations for a wide variety of axial ow impellers having a constant T=D ratio:  mix U tip R ˙ 1 N QS ; where U tip is the impeller tip speed and R is the radius of the tank. Substituting for the U tip , the above equation can be re-arranged in terms of the mixing time and circulation time  mix  C = Constant : Thus, our results are in agreement with those mentioned by Professor Fort and the previous literature. In the letter, Professor Fort has pointed out that the cir- culation time should be calculated based on the total volu- metric ow rate of the liquid. Thus, the energy eciency of the blending process should be dependent upon N QS =N 1=3 P or N 3 QS =N P ratio rather than N 3 QP =N P ratio. In fact, we have shown in our earlier paper (Patwardhan and Joshi, 1999) that the following correlation is able to correlate the data of a large number of axial ow impellers:  mix = 12:66N 1=3 P T 2=3 N QS (P=M ) 1=3 : The impeller pumping capacities N QP and N QS are related to each other. However, the ratio N QS =N QP depends upon the shape of the impeller blades. This subject has also been  doi of original article 10.1016/S0009-2509(03)00130-1 addressed earlier (Patwardhan and Joshi, 1999). Thus, the energy eciency of the impeller for the purpose of homog- enization should therefore be dened as N 3 QS =N P rather than N 3 QP =N P . As pointed out by Professor Fort in his letter, the main conclusion of our approach in the article is as follows: Out of the total kinetic energy associated with the uid (mean kinetic energy + turbulent kinetic energy), mean kinetic en- ergy contributes signicantly more to the process of homog- enization than the turbulent kinetic energy. This has been demonstrated in our article with the help of experiments on two widely dierent systems: jet mixers (out of the total energy input practically everything is supplied as mean ki- netic energy) and ultrasonic mixers (out of the total energy input practically everything is supplied as turbulent kinetic energy). We are thankful to Professor Fort for commending our model, which has a deeper insight in to the mechanism of homogenization. A.W. Patwardhan A.B. Pandit J.B. Joshi Institute of Chemical Technology University of Mumbai Matunga, Mumbai 400 019 India E-mail address: awp@udct.org (A.W. Patwardhan). References Grenville, R.K., Tilton, J.N., 1996. A new theory improves the correlation of blend time data from turbulent jet mixed vessels. Chemical Engineering Research Design 74 (A), 390–396. Grenville, R., Tilton, J., 1997. Turbulence for ow as a predictor of blend time in turbulent jet mixed vessels. Recent Progess en Genie des Procedes, Proceedings of the ninth European Conference on Mixing, Vol. 11(51), France, pp. 67–74. Nere, N.K., Patwardhan, A.W., Joshi, J.B., 2003. Liquid phase mixing in stirred vessels: turbulent ow regime. Industrial and Engineering Chemistry Research 42, 2661–2698. Patwardhan, A.W., Joshi, J.B., 1999. Relation between ow pattern and blending in stirred tanks. Industrial and Engineering Chemistry Research 38, 3131–3143. 0009-2509/$ - see front matter ? 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2003.11.012