Mass Transfer To Drops Moving Through Power Law Fluids In The Intermediate Reynolds Number Region

The mass transfer rate to fluid spheres is calculated for power law and Newtonian fluids by using the intermediate Reynolds number stream functions of Nakano and Tien (1970) and Yamaguchi et al. (1974), respectively. The Sh increases with increases in Re and Pe and decreases in n. Better results are obtained with Nakano and Tien\u27s functions when Re \u3e 10 and with Yamaguchi\u27s functions when Re \u3c 10. Copyright © 1976 American Institute of Chemical Engineer

Mass Transfer In Dispersed And Continous Phases For Creeping Flow Of Fluid Spheres Through Power Law Fluids

The diffusion equation was numerically solved by an implicit finite-difference method for the purpose of calculating the continuous phase Sherwood number, Sh, for mass transfer from an internally circulating Newtonian droplet traveling through a non-Newtonian power-law-type continuous phase in the creeping flow regime. The Mohan stream functions were used in the calculations in order to approximate the velocity profile inside and outside the droplet. The calculated Sh is presented as a function of the Peclet number, Pe, power-law index, n, and a viscosity ratio parameter, X. Sh increases as n decreases in the pseudoplastic region. The dependence of Sh on n is important when Pe is greater than 102, except when both X \u3e 1 and Pe \u3e 104. When used with the Mohan stream functions, the Baird and Hamielec short-range diffusion equation provides a close approximation for Sh when X \u3c 3, provided that Pe \u3e 104. The mass transfer model for the dispersed phase was also numerically solved in order to determine the effect of continuous phase pseudoplasticity, n. Although a slight increase in the total amount of mass transferred, Amt, with a decrease in n was determined, it is concluded that the power-law behavior in the continuous phase does not affect to any appreciable extent the internal mass transfer, either with or without chemical reaction in the fluid sphere. Amt increases with decreasing X, and this dependency is particularly important when mass transfer occurs with chemical reaction in the dispersed phase. © 1976, American Chemical Society. All rights reserved

Sufficiency Conditions For Constrained Optima

Sufficiency conditions for constrained optimization problems were derived by the use of constrained second total derivatives. The results are in a simpler form than the Schechter and Beveridge relation. The sufficiency conditions of Phipps were corrected. © 1971, American Chemical Society. All rights reserved

Diffusion Coefficients Of N-Heptane And N-Decane In N-Alkanes And N-Alcohols At Several Temperatures

The diffusion coefficients of the solutes n-heptane and n-decane were measured in the series of alkane solvents n-hexane through n-decane and in the alcohol solvents n-hexanol and n-heptanol. Mutual and self-diffusivities in most cases were measured at the temperatures of 20°, 25°, 30°, and 40°C. Concentrations of the diffusion species were in the infinitely dilute region. An unsteady state porous frit technique was used with carbon-14 tagged diffusion species. The diffusion coefficients measured were compared with various liquid diffusivity prediction correlations. © 1974, American Chemical Society. All rights reserved

Diffusion Coefficients Of D-glucose In Aqueous Carboxymethylcellulose And Carboxypolymethylene Solutions

A micro interferometric method was used to determine pseudo-binary, molecular diffusion coefficients for diffusion of D-glucose in aqueous carboxymethylcellulose (CMC) and aqueous carboxypolymethylene (Carbopol) solutions. An initial solute concentration of about 9 wt. % D-glucose in the aqueous polymer solutions was used. The polymer concentrations for the CMC solutions ranged from 1.2 to 2.2 wt. % and for the Carbopol solutions from 0.18 to 0.28 wt. %. Diffusion coefficients were determined as a function of reduced solute concentration, both with and without the effect of solution volume change during diffusion being considered. © 1969, American Chemical Society. All rights reserved

A Liquid Extraction Column With Reciprocated Wire Mesh Packing

In a new type of pulsating, liquid extractor, pulsating energy is added to the counter currently flowing liquid streams by a stainless-steel wire mesh packing which is reciprocated vertically in a 3-inch i.d. extraction column. The mass transfer performance and flooding characteristics are studied as a function of the frequency and amplitude of reciprocation, the total solvent and feed throughputs, and choice of phase dispersion. The benzene-HAc-H2O and MIBK-HAcH2O systems were used. Extraction data for the benzene system were correlated in terms of a dimensionless pulse velocity group. Operating throughputs are significantly higher than those achieved with other designs of mechanically aided extractors, while maintaining high rates of extraction. © 1969, American Chemical Society. All rights reserved