The error in B values and corrected values are described in detail elsewhere (1). The error in B values, which was due to a typographical error in a numerical program used earlier ( 8 ) , amounted to about 7% in the G region of interest in withdrawal. Comparison of the new B values with equivalent values obtained independently by another numerical technique (2) confirmed that the new values are accurate to at least four significant figures.The error due to the previous use of the improper range of G has been discussed and minimized, as described elsewhere ( 5 ) . The previous range used, namely G of 0.03 to 3 (8), was replaced by choosing the G range so as to minimize the error in curvature in Equation (3). Comparing the magnitude of each term in Equation ( 3 ) , using a = 2.4 and /iI = 0.85 as reasonable estimates, indicated that the region for which the 4 correlation should be most precise occurs at Go of 1 to 30 and higher. A log-log plot of + vs. G in this region indicated a /iI of unity and a = 3.36. Thus the more accurate description of top curvature for a static menisci on a cylinder is ( 5 )Use of the new OL and /iI values corrects the previous errors in Equation ( 4 ) . As a check, Cs values obtained using empirical Equation (7) were compared with theoretical values of four to five place accuracy for a range of G (0.003 to 30). The new curvature values from Equation (7) were found to be accurate to within 0.5% for all G and, furthermore, to be accurate to within 0.1% for all G < 0.02 and all G > 2. The largest differences of 0.3 to 0.5% were noted at G from 0.07 to 0.7.
THE NEW DYNAMIC CURVATURE EXPRESSION [EQUATION (811Using Equation (7) and the static to withdrawal transformation described above, the curvature for the top of a withdrawal meniscus is now given as 3.36 (SG) 1 C L +--1 + 3.36(SG) 2 ( S G )
Equation (8) is a new equation.Comparison of C, of Equation (8) with C,* of Equation ( 5 ) indicates that the old C,' value has errors of 2 to 6% in the GS range of 0.3 to 3 and errors of about 6% in the GS range of 3 to 30.Use of the C, of Equation ( 8 ) is recommended in all available continuous withdrawal theories for cylinders (6), including Equation ( 6 ) for Newtonian fluids (7, l o ) , the special-case Newtonian theories for low speeds ( 9 ) , and the theory for non -Newtonian fluids ( 4 ) . The effect of the improved precision should be most apparent at larger radii (larger G ) and higher speeds (thicker films and larger S) or both (larger GS).Most reported data for continuous-phase mass transfer in agitated extraction vessels are expressed in terms of Kcu, the mass transfer coefficient per unit volume. Recently Schindler and Treybal (17) report some area-free coefficients for the continuous extraction of water-saturated ethyl acetate with water itself. The object of this paper is to describe other data for area-free coefficients that pertain to continuously worked extractors of similar design. The system, however, differs in that it is ternary: a solute is extracted from the dispersed phase int...
