Mass transfer coefficients from packed beds of benzoic acid spheres to water and propylene glycol solutions were measured in the very low Reynolds number, Nr/, range of 0.0016 to 55. Studies using bed heights from l/i to 4 inches showed the mass transfer, J, to be affected only slightly. No effects on J were found on diluting the bed by a factor of 1 0 to 1 with inert spheres. Varying the Schmidt number, Nsc, from 950 to 70,600 had no effect on J when Nsc2/3 was used. Data obtained from internal samples gave the same J values as from outlet samples and showed that axial mixing effects were small. Gupta and Thodos experimentally found J to be inversely proportional to the void fraction and this was shown to be very similar to that derived by Pfeffer. Equations are proposed for liquids for the entire range of Nr/ from 0.0016 to 1500. nil ass transfer of fluids in packed beds of spherical particles * " * is encountered in many different processes at very low velocities in chromatography, ion exchange, combustion of fine particles, and petroleum reservoir engineering. Relatively few data on liquids are available covering the effects on J of wide variations of Schmidt number, A/, at very low Reynolds numbers, //, below 0.05, of variations of bed length, and of dilution of the bed with inert spheres.Williamson, Bazaire, and Geankoplis ( 16) obtained mass transfer coefficients for packed beds of benzoic acid spheres and water in the A// range of 0.05 to 55. They correlated the data of others (6, 11) using A"Sc°-5S instead of /2'3. Mc-Cune and Wilhelm (7 7) used modified spheres of 2-naphthol and water and obtained J values for a ,Ylie' rangie of 14 to 1440. Gaffney and Drew (6) studied mass transfer of modified spheres with liquids in a -Yr/ range of 0.4 to 765 using a wide range of A/.Pfeffer (12) derived a theoretical equation relating J to A// which holds for high Peclet numbers and low ,YR/ or mainly liquids. He also derived an expression for the effect of ( on J. Gupta and Thodos (8) experimentally determined J to be proportional to 1/e for gases in the high A"Re' region. They also correlated all the mass transfer data on gases for a ArRe' range of 12 to 2140. Bradshaw and Bennett (7) showed that the J value of liquids should be lower than the J of gases at low A// because of the higher Schmidt number of liquids.DeAcetis and Thodos (3), Bradshaw and Meyers (2), Bradshaw and Bennett (7), and McCune and Wilhelm (77) studied effects of bed height on J at high Reynolds numbers. De-Acetis and Thodos (3) also studied dilute beds-i.e., the effect of inert spheres mixed with the active spheres in a packed bed.In the present work mass transfer coefficients of benzoic acid spheres in water and propylene glycol solutions w'ere obtained in packed beds in the A'R/ region of 0.0016 to 55. The effects of bed height, dilute beds, and internal sampling were also studied. The data were correlated and equations presented. Experimental MethodsThe apparatus used and the experimental methods are very similar to those used by Williamson...

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The adsorption isotherms on activated carbon were measured for the following six systems: benzaldehyde, phenol, and potassium chloride in water; benzene, isopropylbenzene, and phenol in cyclohexane. The systems isopropylbenzene and benzene each in cyclohexane and potassium chloride in water proved to be slightly adsorbing systems, whereas the benzaldehyde and phenol each in water were highly adsorbing systems. The rate of diffusion of the slightly adsorbing solutes was interpreted by assuming that the intraparticle diffusion was due to pore volume diffusion. The results indicated that the tortuosity factor for activated carbon is 3.5. The effective pore volume diffusivity and the tortuosity factor were not affected by the concentration of the solute, solute molecular size and the particle diameter. The external mass transfer resistance was negligible when pore volume diffusion was the controlling intraparticle diffusion mechanism.

Experimental data were obtained on the effect of bed length of packed spheres on axial diffusion coefficients with the frequency response technique used. Lengths of packed section of 6 to 174 cm. were used. The end effects were eliminated by using a novel experimental technique for analyses of the inlet and outlet streams. No effects of length on DL were found.When the end effects were artificially introduced by using void analytical sections a t the two ends, then large effects of length on DL were found. These void sections were the cause of length effects found by other experimenters. The DL drops as the length of bed is increased. Above about 65 cm. length the DL remains constant with increase in length. The over-all results are in general agreement with the data of others.An understanding of the behavior of fluids in empty tubes and packed beds is very important in the study of heat, mass, and momentum transfer. Much experimental data exist on radial mass transfer or diffusion coefficients perpendicular to the axial flow of the liquid or gas. Recently Ebach and White ( 3 ) , Carberry and Bretton ( l ) , and Strang and Geankoplis (7) presented experimental correlations for packed beds of spheres for the effect of liquid velocity, particle diameter, and viscosity on the axial diffusion coefficient.However no comprehensive experimental study has been made of the elimination of end effects and the effect of column length on DL for liquids. McHenry and Wilhelm ( 5 ) obtained data on gases for different lengths and eliminated end effects by calculation. Carberry and Bretton (1) presented experimental points obtained at five different bed lengths and different velocities using liquids.To investigate the axial difhsion of a flowing system experimentally the outlet response resulting from an inlet disturbance is measured. This disturbance can be a step or pulse function or a continuous sine-wave function. The sine wave is used in the frequency response experiments. Ebach and White ( 3 ) discuss these methods in detail.In the present work DL values were obtained for glass spheres in packed beds with water used. End effects were experimentally eliminated which removed the column length effect on D,. The effect of length was also determined by introducing end effects artificially and varying the length. It is assumed that C is a function of Z and t only, that there are no radial gradients, and that U is constant. Carberry and Bretton (1) discuss in detail the assumptions implied in this model. Their data and that of others ( 3 ) suggest that Equation ( 1 ) does not apply owing to the fact the amplitude does not dampen as the square root of time or bed length. However in the present work it will be shown that it does apply under the carefully designed conditions of experimentation.Two boundary conditions are imposed at the inlet and the outlet of the bed respectively: UThis can be compared to the phase shift measured experimentally. Deisler and Wilhelm (2) discuss in detail the addition of nr radians to the .fHixp.. Eq...

The transition region of diffusion for a binary gas mixture was experimentally investigated in an isobaric open system of fine glass capillaries in parallel. Results were obtained over a 675/1 pressure range from 0.444 to 300.2 mm of Hg absolute in the transition region between Knudsen and molecular (ordinary) diffusion and confirm the theoretical equation for the flux in true capillaries in an open system. This equation has been derived by others using a momentum balance with various assumptions, such as additivity of the momentum transfer rates for the Knudsen and molecular regions, etc. These assumptions seem to be confirmed. This appears to be the first known experimental confirmation of this equation for capillaries over a wide pressure range. Experimental flux ratios obtained in the transition region confirm the predicted inverse square root relationship with the molecular weights. Data for counterdiffusion in an open system near the Knudsen region tend to confirm the Knudsen equation and data in the molecular region also substantiate the Stefan-Maxwell relations.

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