Showing papers in "Aiche Journal in 1971"

Multicomponent separation calculations by linearization

Abstract: A new approach to separation calculations has been developed which has many practical advantages. The equations of conservation of mass and energy and of equilibrium are grouped by stage and then linearized. The resulting set of equations has a block-tridiagonal structure which permits solution by a simple technique. Thus a new way to apply the Newton-Raphson technique to separation calculations is devised. The method has been tried on a number of problems chosen to exhibit characteristics which cause other solution technique to fail. Most problems are solved with ten iterations or less.

Permeation through liquid surfactant membranes

Abstract: A novel separation technique based on the selectivity of a liquid membrane composed of surfactants and water is described. The permeation mechanism is discussed in terms of surfactant concentration, surfactant structure and chain length, the nature of permeate, and the solubility of permeate in water.

Drop‐size distributions from pneumatic atomizers

Abstract: A study was made of the atomizing characteristics of convergent-type pneumatic nozzles. Drop-size correlations were obtained for the following ranges: drop size, 6 to 350 μ, mass median diameter; mass flow ratio, 0.06 to 40; relative velocity, 250 ft./sec. to sonic velocity; and viscosity. 1 to 50 cp. The technique employed was to spray cool a molten wax, and melts of wax-polyethylene mixtures. The most important operating variables in pneumatic atomization are the dynamic force of the atomizing gas, and the mass flow ratio of air to liquid. The cumulative volume drop-size distribution of spray from a pneumatic nozzle was fitted by a modified logistic equation. Empirical correlations developed in the study can be used to design nozzles or to predict drop size for sprays produced by the types of nozzles studied. In particular, this study provides new experimental data on the performance of pneumatic atomizers in producing relatively large drops.

Liquid bridges between cylinders, in a torus, and between spheres

Abstract: Recently, there has been a revival of interest in the classical problems concerning the configuration of a mass of liquid which bridges a gap between solid surface, being supported by capillary attraction. These liquid bridges are concepts in theories of oil recovery from porous media, adsorption hysteresis in porous adsorbents, capillary condensation, particle sedimentation, soil properties, and space exploration. The stability of a capillary liquid bridge of given volume between 2 small, solid, equal, separated spheres is investigated by formulating and treating a minimum energy problem in the calculus of variations and by experiment. A conjecture is made that in the case of 2 solutions, one and only one is minimizing, and that the case of one solution represents the limiting stable bridge. This theory agrees accurately with the stability experiments. Furthermore, it is possible to predict the cohesive force. For the case of spheres in contact, the theory presented is in agreement with some experimental work and also with the theory of Fisher and calculations of cohesive force based on Melrose and Wallick's solution to the bridge problem. For the case of separated spheres, the agreement with the only available experimental data is excellent except for close separations. (18more » refs.)« less

Membranes which pump

Abstract: Carrier-containing membranes which can pump a specific ion from a region of low concentration into a region of high concentration have been constructed. This pumping is a large effect, proportional to the amount of carrier present. The main requirement for this type of transport is that the carrier react competitively with two simultaneously diffusing solutes. One solute is pumped; the second supplies the energy for the pumping. A theory based on the assumption that the two carrier reactions are fast predicts that the amount pumped is proportional to the carrier concentration, that the pumping stops when the concentration gradient of the energy supplying solute reaches zero, and that the effect goes through a maximum when the solubility in the membrane of the solute being pumped decreases. These predictions are in agreement with experimental results for sodium transport across membranes containing a variety of carriers, including stearic acid, lecithin, and monensin.

The dynamics of thin liquid films in the presence of surface‐tension gradients

Abstract: The climbing of Marangoni films up vertical solid surfaces was investigated experimentally and theoretically. The system considered was a nonisothermal plate with its warm end partially immersed in a nonvolatile liquid. Observed film thicknesses and rates of climb were in agreement with an approximate hydrodynamic model obtained by assuming the supply capacity of the film to be rate limiting. The results of this study confirm the hypothesis is that previously observed liquid films formed against gravitational forces above equilibrium menisci are produced by surface-tension inequalities. It is pointed out that hydrodynamic processes cannot allow for the advancement of the leading edge of Marangoni films and a separate physicochemical process is required to explain spontaneous spreading of these films. Evidence is presented for the formation of much thinner primary films ahead of the secondary bulk films described by hydrodynamics. These primary films appear to be produced by a combination of multilayer adsorption and/or surface diffusion. The kinetics of these diffusional processes may limit spreading rates when surface-tension gradients become sufficiently large. Finally, the Marangoni films were found to be unstable in a manner hithertonot considered.

Polymerization in expanding catalyst particles

Abstract: Four models are presented to describe polymerization in expanding catalyst particles. The globules are presumed to be expanding with accumulating polymer, and catalytic reaction sites are dispersed throughout the polymer matrix which is forming about them. Monomer must diffuse through the polymer to polymerize at the catalyst sites. The Thiele modulus (α), , is a ratio of characteristic diffusion time to reaction time which is a measure of the importance of diffusion relative to reaction. Polymerization rates are predicted by the models which are generally dependent on the controlling mechanism. Broad molecular weight distributions are predicted for cases of diffusion control (large α) for those models in which catalyst sites are not equally accessible to monomer. Polymerization rates decline toward an asymptotic final value as the particles expand in diffusion-controlled cases. Most of the decline which would be readily observable in a laboratory experiment would have occurred by the time the particle radii had increased to about three times their original value.

Separation of nitrogen and methane via periodic adsorption

Abstract: The periodic process utilizes a rapid pressure swing cycle in an adsorbent bed to effect the separation of gas mixtures. During the first portion of a cycle the compressed gas mixture flows into the adsorbent-filled column. Next, while the feed gas is restrained, an exhaust orifice is opened at the feed end of the column providing depressurization. The product stream is enriched in the component exhibiting the lowest coefficient of adsorption. A mathematical model based upon the assumption of instantaneous equilibrium between the gas phase and the adsorbed gas was formulated and solved to simulate the periodic, adsorption process. The measured nitrogen content of the product gas stream was found to correlate with the ratio of the product gas rate to the feed gas rate. At 24°C. the calculated pressure response, feed gas flow rate, and product gas composition correspond favorably with related experimental measurements for all values of the feed gas pressure, cycling frequency, and product gas flow rate within the ranges investigated.

Kinetics of ozone decomposition and reaction with organics in water

Abstract: The decomposition of ozone in water is found to be second order at pH 2 and 4 with the rate insensitive to pH. At pH 6 the reaction order is 3/2 to 2 and at pH 8 it is first order. Above pH 6 the rate increases rapidly with pH. Ozonation can greatly reduce the organic matter in waste water. The reaction rate of ozone with organics in flocculated secondary sewage effluent is found to depend on the rate of ozone decomposition, which is independent of the subsequent reaction with the organics.

An exact analysis of low peclet number thermal entry region heat transfer in transversely nonuniform velocity fields

Abstract: A theoretical method is described for obtaining the exact solution to the problem of thermal entry region heat transfer which takes into account both transverse non-uniformity in the velocity field and axial conduction. To allow for the effect of upstream conduction, the fluid temperature was taken to be uniform at × = – ∞, and the first 20 eigenvalues and the corresponding eigenfunctions were determined separately for the heated and adiabatic regions. Both the temperatures and temperature gradients were then matched at × = 0 by constructing a pair of orthonormal functions from the nonorthogonal eigenfunctions. Nusselt numbers calculated for pipe flow subject to the boundary condition of uniform wall heat flux show virtually perfect agreement with those reported recently by Hennecke, who solved the governing partial differential equation numerically. To illustrate its general applicability, the present method was further employed to analyze the corresponding problem in parallel-plate channel flow, for which no solution has hitherto been reported.

Bubble coalescence in viscous fluids

Abstract: The gravity-driven coalescence of 1- to 2-cm. diameter air bubbles in glycerine and in water has been studied by high-speed cinematography. The resulting coalescence behavior can be correlated by a simple model which assumes that each bubble trails a wake, and that the bubble coalescing from below accelerates when it enters the wake of the preceding bubble and thus overtakes the first bubble. The predictions of the model are not significantly altered by different assumed wake configurations.

Transfer of surface‐active agents across a liquid‐liquid interface

Abstract: Analytical solutions are obtained for the transfer of an adsorbing solute across a liquid-liquid interface taking into account the effects of molecular diffusion in both bulk phases, adsorptive accumulation at the interface, and energy barriers to adsorption and/or desorption. These solutions show that while adsorptive accumulation alone affects the transfer rate but little, the presence of an adsorption or desorption barrier can significantly affect the bulk concentration profiles and decrease the mass transfer rate. The presence of a desorption barrier is shown to cause the dynamic interfacial tension to pass through a minimum below the steady state value. For some systems it is conceivable that the interfacial tension minimum would be sufficiently low that a slight agitation would result in spontaneous emulsification. Dynamic interfacial tension data for oil-water systems with interface ages from 0.05 to 1.5 sec. are obtained using a laminar contracting liquid jet. The data indicate the presence of a small net desorption barrier to the transfer of normal and isobutyric acids from oil to water and large barriers to both the adsorption and desorption of 1,5 pentanediol.

Mixing and product distribution for a liquid‐phase, second‐order, competitive‐consecutive reaction

Abstract: Mixing effects for the homogeneous, liquid-phase, second-order, competitive-consecutive reaction of iodine (B) with L-tyrosine (A) to form 3-iodo-L-tyrosine (R) and 3,5-diiodo-L-tyrosine (S) were determined for the following conditions: vessel volume, 5 and 36 liters (baffled and unbaffled); turbine diameter (2 to 6 in.) and speed (95 to 1,600 r.p.m.); feed inlet locations (3), addition rate (0.25 to 18 min.), and distribution; temperature (11° to 43°C.); initial A concentration (0.1 to 0.4 g.-mole/liter); and kinematic viscosity (0.765 to 6.35 centistokes). A was initially charged to the reactor and an equimolar quantity of feed B was added over a time period. Yields of R are less than that expected for perfect mixing owing to local regions of excess B concentration that exist for time periods during which R over-reacts to S. Agitation power for a given yield is less in unbaffled vessels without an air-liquid interface than for baffled vessels. The local fluctuating velocity u′ where feed is introduced correlates the mixing variables and predicts mixing requirements for maintaining yields of R on scale-up. Regions of excess B concentration are related to a concept of partial segregation. The extent of reaction occurring under this condition is correlated by the dimensionless group (k1bτ) (a0/b), where τ is a microtime scale of mixing related to u′ and the characteristic length of a microscale eddy. The magnitude of this group provides a criterion for predicting the importance of mixing effects on other reaction systems.

A corresponding states correlation of saturated liquid volumes

Abstract: A corresponding states correlation is presented for the prediction of saturated liquid volumes. Parameters required are the critical temperature, the acentric factor, and a scaling volume. The correlation is valid over the entire useful range of reduced temperatures from 0.2 to 1.0. The full temperature range has not been covered by previous corresponding states correlations. Average absolute deviations in predicted liquid volumes is one-quarter of 1% for 26 compounds. The correlation is also useful for calculating critical temperatures, pressures, and volumes when experimental critical data are lacking. The proposed method also provides a convenient means for calculating rapidly and accurately the statistical mechanical parameters used in the cell model correlation developed by Renon, Eckert, and Prausnitz.

Rates of sorption and diffusion of hydrocarbons in zeolites

Abstract: The kinetic patterns of sorption, desorption, and sorbate exchange have been studied for several C2-C5 hydrocarbons in synthetic zeolites of the mordenite, T and Y structures. The rate observations can best be represented by a model of sorption on interstitial sites in the solid, rather than by a model based on the analogy with macroporous sorbents. Two cases of interstitial diffusion have to be distinguished for this purpose. The number of vacant sites changes in time during the process of sorption, whereas it can remain constant if one sorbate is exchanged against another one. Rate measurements for both types of processes are reported and their interrelation is discussed.

Calculation of dispersion coefficients by means of moments

Abstract: The problem of evaluating the coefficient of dispersion in a general linear two-component chromatographic system is equivalent to a steady state source problem in multidimensional Euclidean space The equivalence of the two physical problems provides an intuitive insight into the contributions of different transport processes to dispersion For a wide class of systems the dispersion coefficient can be expressed as the maximum of a functional This can be utilized in the numerical evaluation of dispersion coefficients and in the application of perturbation techniques

Interfacial shear viscosity at fluid-fluid interfaces

Abstract: Fluid-fluid interfaces containing surface-active agents or macromolecules exhibit interfacial shear viscosity phenomena. The purpose of this paper is to investigate theoretically the dynamics of liquid-liquid and liquid-gas interfaces containing surfactants, and to establish the validity of the proposed model from shear flow data at uncontaminated interfaces. A theoretical analysis for the measurement of interfacial shear viscosity at liquid-liquid interfaces with an improved viscous traction surface viscometer is presented. The analysis takes into account the finite depths of the two liquids and permits interpretation of the experimental results in terms of interfacial shear viscosities at the liquid-gas interface in addition to the liquid-liquid interface. Results of the present analysis clearly show a strong coupling of interfacial and bulk fluid flows. Extensive measurements of the interfacial velocities at a xylene-water interface were made. A cetane-water interface was also studied. Interfacial flow data for uncontaminated systems were found to be in excellent agreement with theory.

Stretching of viscoelastic liquids

Abstract: Analyses of stretching of a viscoelastic liquid have been interpreted as showing that there is a maximum stretch rate to which the material can be subjected, and several physical phenomena have been explained on this basis. It is shown here theoretically and experimentally that the concept of a limiting stretch rate does not have general validity.

A thermodynamic consistency test for adsorption from binary liquid mixtures on solids

Abstract: A thermodynamic consistency test for adsorption from binary liquid mixtures is derived using the Gibbs equation for adsorption. Adsorption data for the liquid mixture pairs A-B, A-C, and B-C on the same adsorbent must be thermodynamically consistent. The consistency test is applied to experimental data for adsorption from the binary liquid mixtures benzene-cyclohexane, benzene-n-heptane and cyclohexane-n-heptane on silica gel at 30°C.