Portion of Unstable Particles on the Wall Surface. The portion of unstable particles on the wall surface is equal to the sum of the unstable particles at times 0, 1, 2, ..., t,+ + Nand is given by t,++N-1 N-1 U(t,+,r,U = c (7 + [Ii -+ + c (7 + 5)' -i=O i=O N-2 yta+[ (i + l)(y + t)i (A15) i=O Literature Cited Cantwell, B. J. Organized motion in turbulent flow. In Annual Reviews of Fluid Mechanics; Dyke, M. V., et al., Eds.; Annual Reviews: Palo Alto, CA, 1981; Vol. 13, pp 457-515. Cleaver, J. W.; Yates, B. The effect of re-entrainment on particle deposition. Chem. Eng. Sci. 1976, 31, Reed, J. The adhesion of particles undergoing an elastic-plastic impact with a surface. J. Phys. D: Appl. Phys. 1984,17, 677-689. Saffman, P. G. The lift on a small sphere in a slow shear flow. J. Fluid Mech. 1965,22,385-403. Schlichtina, H. Boundary-Layer Theory; McGraw-Hik New York, 327-332. --1955; Chapter la. Tsai. C. J.: Pui. Y. H.: Liu. B. Y. H. CaDture and rebound of small particles upon impact k t h solid surfaces. Aerosol Sci. Technol. Vatistas, N. The effect of adhesion time on particle deposition. Chem. Eng. Sci. 1989,44, 1603-1608. Vatistas, N. The adhesion of particles to surface under turbulent flow conditions. In Particles on surface 3 detection, adhesion, and removal; Mittal, K. L., Ed.; Plenum Press: New York, 1991; in press. Wall, S.; John, W.; Wang, H. C.; Goren, S. L. Measurements of kinetic energy loss for particles impacting surfaces. Aerosol Sci. Technol. 1990, 12,926-946. Yung, B. P. K.; Merry, H.; Bott, T. R. The role of turbulent bursta in particle reentrainment in acqueous system. Chern. Eng. Sci.Extraction of citric acid from aqueous solutions with TAA, a mixture of tertiary aliphatic amines, dissolved in l-octanolln-heptane mixtures, and coextraction of water have been studied as a function of acid, amine, and octanol concentrations at different temperatures. Using a "chemical modeling" approach, two complexes [acid-amine.hllH20 and a~id.(amine)~-h~~H~O] have been assumed to exist in the organic phase, and the corresponding equilibrium constants, apparent enthalpies, and entropies of complex formation have been evaluated. The overall equilibrium constants, Bill and Fl2, and hydration numbers, hll and hI2, have been correlated with the concentration of amine and with various properties of the mixed solvents. The solubility of water in acid-free organic phase has been found to be the best fitting parameter. According to IR spectra, the amineacid interaction is represented by an equilibrium between the extreme types of an H-bond ("neutral" O-H.-NR3 and ionic O--. H-+NR3). A mathematical model of acid extraction and water coextraction has been formulated. Multicomponent solid particles were suspended in vertical bubble columns of 7-cm diameter and 4.85-m height and 15-cm diameter and 2.7-m height. Axial changes in holdups of gas and solids in the column were determined by sectioning the column simultaneously with 20 horizontal plates for the 7-cm-diameter column and 11 such plates for the 15-cm-diameter column...