Mass Transfer to Newtonian and Non-Newtonian Fluids in Short Annuli INTRODUCTION zyxwvutsrqpon Mass transfer to fluids flowing through annuli is frequently encountered in many industrial processes. Corrosion, scaling and descaling, annular condensers, transpiration and film cooling of annular ducts, and annular electrochemical reactors are some typical examples of the practical application of mass transfer in annular systems. Cases of mass transfer in fully developed laminar and turbulent annular flows with both developed and developing concentration boundary layers have been adequately dealt with by several workers (Ross and Wragg, 1965; Wragg and Ross, 1967, 1968; Turitto, 1975; Pickett, 1977; Remorino et al., 1979). Cases of developing annular flows with developing concentration boundary layers have received little attention (Pickett, 1977). Further, except zyxwvutsrqp for the work of Remorino et al. (1979), almost all reported studies of mass transfer in annuli are limited to Newtonian fluids. The present paper reports new experimental data on mass transfer to non-Newtonian fluids and shows that Newtonian rela- tions could easily be extended to such fluids. New design equations for both developing laminar and turbulent flows in short annuli are also presented. BACKGROUND Newtonian Fluids Ross and Wragg (1965) have made the most comprehensive theoretical and experimental contributions regarding the study of mass transfer in fully developed laminar and turbulent flows in an annulus. For fully developed laminar flow, extension of the Le- veque solution to an annulus gave (1) where zyxwvutsrqp +(a) is a function of aspect ratio zyxwvutsrq a(=Di/D,) and is given by zyxwvutsrqpon Sh zyxwvutsrqp = 1.614[4(a). Re - Sc(de/l)]1/3 For fully developed turbulent flow with L/de < 2, Ross and Wragg (1965) showed that their data agree well with the equation U. K. GHOSH and S. N. UPADHYAY Department of Chemical Engineering and Technology Institute of Technology Banaras Hindu University Varanasi 221055, India Sh = 0.276 Re058 - S~’/~(d,/L)1/3 (3) developed analytically for very short parallel plates in a fully de- veloped flow (Pickett, 1977). A more recent analysis by Pickett (1977), however, indicates that (41 gives a better agreement with the experimental data. For L/de > 2, Lin et al. (1951) obtained good agreement with the Chilton- Colburn equation (5) A theoretical analysis of the m a s transfer problem for an annulus with short transfer surfaces and having no hydrodynamic entrance length is difficult to make. The only reported experimental data on mass transfer from short electrodes in developing laminar flow are those of Carbin and Gabe (1974), who correlated their results (6) Considering the similarity between Eqs. 1 and 6, Pickett (1977) recommended the use of Eq. 1 for design purposes, ignoring the hydrodynamic entrance effects, if any. Sh = 0.145 Re2l3. Sc1/3(d,/L)1/3 Sh = 0.023 Reo - Sc U3 by Sh = 3.93 Reo 32 * Sco 33(de/L)0 35 Non-Newtonian Fluids For fully developed laminar annular flow of a nowNewtonian fluid obeying the power law model r = K k)n (7) Equation 1 can be written as (Remorino et a]., 1979) where Re, and Sc, are modified Reynolds and Schmidt numbers, respectively, for power law fluids and Fredrickson and Bird (1958) have reported the numerical values of X(a,n) and Q(a,n). Remorino et al. (1979) have shown that ex- perimental data for both Newtonian and non-Newtonian fluids (n = 0.77 to 1.0) can be successfully represented by Eq. 8. AlChE Journal (Vol. 31, No. 10) October, 1985 Page 1721