Victor K. La Mer

FLOCCULATION, SUBSIDENCE AND FILTRATION OF PHOSPHATE SLIMES. VI. A QUANTITATIVE THEORY OF FILTRATION OF FLOCCULATED SUSPENSIONS

Abstract A quantitative theory of filtration of suspensions flocculated with polymeric flocculants is developed. The theory, based upon a simple picture of the adsorption of the flocculant combined with considerations of floc geometry and the Kozeny-Carman permeability equation, explains the variations of filtration rate with flocculant concentration observed experimentally.

The energetics of flocculation and redispersion by polymers

Abstract The theory of polymer flocculation and of the filtration of colloidal dispersions flocculated by polymers has been extended to a molecular level. Maximum flocculation occurs at half surface coverage of the solid by adsorbed polymer. A Langmuir type isotherm describes the process of adsorption of individual polymer segments with surface sites. An energy profile is presented for the system of colloidal solid and polymer solution as the system undergoes change from dispersed to flocculated to redispersed.

Diffusional Boundary Value Problems Involving Moving Boundaries, Connected with the Growth of Colloidal Particles

A method is suggested for treating problems of diffusion which involve moving boundaries. This method is applicable when the flux of material through any surface in the diffusion field is considerably greater than the rate of change of concentration on that surface. The method is applied to two problems dealing with the growth of monodispersed aerosols and hydrosols.The solution of the first of these problems indicates that, in a naphthalene‐like aerosol system growing by means of the diffusion of vapor toward sinks (nuclei) which cannot support supersaturation, spontaneous nucleation will not occur if the number density of nuclei exceeds 100/cc.The solution of the second problem permits the reproduction from theory of several curves due to Zaiser and La Mer which depict the rate of growth of sulfur hydrosols, therefore lending support to the idea that the particles grow by means of a simple diffusion mechanism rather than by a surface catalyzed deposition. The critical supersaturation concentration for s...

The transport of water through monolayers of long-chain n-paraffinic alcohols

The importance of the chain length of the monolayer-forming molecule on evaporation resistance and spreading rate has been emphasized. Evaporation resistance-surface pressure isotherms show that n-hexane as the spreading solvent does not have a deleterious effect on the resistance; whereas benzene, since it is retained to some extent in the monolayer, reduces the resistance of a monolayer at all pressures. Kerosene, although retained at low pressures, is effectively squeezed out of the monolayer at high pressures. We have used resistance-pressure isotherms of high-purity materials to show more conclusively that the forces involved in the formation of a hole in a close-packed monolayer are primarily those of repulsion between the chains. Finally we have shown how the Columbia University quiescent evaporation resistance-surface pressure apparatus (Evaporimeter) is a valuable tool for specifying materials suitable for field tests in respect to many properties.

The kinetics of the formation and growth of monodispersed sulfur hydrosols

Abstract An investigation has been made of the kinetics of the formation and growth of monodispersed sulfur sols prepared by the action of dilute HCl (0.00075-0.006 M) on Na2S2O3 (0.0005-0.003 M). The study has been divided into three parts. I. The Homogeneous Reaction. The formation of molecularly dispersed sulfur begins as soon as the reactants are mixed. Ultraviolet absorption measurements with a Beckman quartz spectrophotometer at λ = 3000 A show that the concentration of dissolved sulfur reaches a constant value representing a limiting state of supersaturation, after which further formation of sulfur leads to condensation. Within the limits of experimental error the concentration of sulfur at the time, tB when the phase change occurs is unaffected by changing the concentrations of the reactants or by adding small amounts of salts. Furthermore, this time is reproducible and varies with the rate of formation of sulfur. It depends also upon the degree of supersaturation of sulfur, the solubility of sulfur in the medium, the nature of the nucleation process that occurs at the phase transition, and the wavelength of light used to detect the initiation of scattering. Since these variables were eliminated by using the same solvent and wavelength for all experiments, tB is a valid measure of the rate of the homogeneous reaction. The effect of changing the concentrations of the reactants showed that the rate of formation of sulfur is proportional to (T) 3 2 (H) 1 2 , where (T) and (H) are the total molar concentrations of thiosulfate and hydrogen ion. The fractional order and the shape of the curves for optical density as a function of time indicate an autocatalytic reaction, probably of the chain type. The reaction exhibits a positive Bronsted primary salt effect —e.g., the addition of lanthanum salts produces a marked acceleration. The rate-controlling step is, therefore, a reaction between negatively charged ionic species, either (S2O3= + HS2O3−) or (2HS2O3−). II. The Condensation Stage. This stage begins with the formation of nuclei capable of further growth, less than 2 min. before the appearance of colloidal sulfur is detected experimentally. The existence of a limiting state of supersaturation is in accord with the accepted theory for phase transitions. The degree of supersaturation that must be reached before condensation occurs is dependent to a critical extent on the rate of nucleus formation. Although, when the Tyndall beam first appears, the scattered light is bluish, its intensity is not proportional to γ 6 λ 4 and Rayleighs limiting law (for γ λ 10 ) cannot be applied to the determination of the sizes of particles because their radii are already 1 3 the wavelength of light. Attempts to detect the scattering at smaller radii failed because the number of particles is so small (106/cm.3). The particle number which is necessary to give perceptible scattering in this region is so large that rapid coagulation would occur according to Smoluchowskis law. Values of the radius were determined by applying the Mie theory to measurements of optical density as a function of time at λ = 4000 and 8000 A. At these wavelengths sulfur is transparent and has refractive indices for which calculated values of the scattering area coefficient K3 = 2.3 log (I0/I)/πγ2nl as a function of α = 2πγ/λ′ are available. In the range α = 1.2–3.0 the variation of Ks with α can be expressed by empirical linear relationships, thus permitting the determination of radii from 0.07 to 0.30μ. Since the variation of γ2 with time is non-linear, a steady state in the diffusion process by which dissolved sulfur is deposited on the surfaces of the particles is not set up in the early stage of growth. III. The Heterogeneous Stage. The overall rate of the chemical changes that occur during the growth of a sol has been found by titrations with iodine and alkali to be proportional to (T)2(H). The variation with time of the number and radii of the particles in suspension was determined by an application of the Mie theory to transmittance measurements. The occurrence of a maximum in the number vs. time curves is explained by ascribing increases in number to the formation of molecularly dispersed sulfur at a greater rate than it can diffuse to the growing particles already present. Decreases in number result from coagulation and settling. From the asymptotic linear variation of γ2 with time it is suggested that a steady state has been reached in which the rate of diffusion of dissolved sulfur to the particle surfaces remains constant. The monodispersity of a sol is strongly influenced by the rate of sulfur formation. Polydispersity in the early stages of particle growth is caused by the continued formation of new particles while older ones are growing, and by coagulation, and is, therefore, favored by high reactant concentrations. The deterioration of a monodispersed sol on aging is largely due to the settling out of the particles. An overestimate of the total amount of colloidal sulfur in these systems has been made by correcting the particle number for decreases due to coagulation and settling, and by assuming that growth continues on all particles whether they are in suspension or not. In spite of this, the difference between the amount of sulfite found and the estimated total colloidal sulfur is too great to be interpreted as the quantity of dissolved sulfur present. This indicates that the pentathionate which is the product of a side reaction takes up sulfur to give higher polythionates.

Filtration of colloidal dispersions flocculated by anionic and cationic polyelectrolytes

The state of flocculation produced by polyelectrolyte additions can be followed accurately by measurements of the improvement in the rate of subsequent filtration, which becomes a measure of size of flocs and the porosity of macroflocs forming the filter cake. This rate increases rapidly, as the eighth power of the concentration of polyelectrolyte, and reaches a sharp maximum whose value PM is a reproducible characteristic for each polymer-substrate system. Flocculation is dominated by the extent of adsorption of the polyelectrolyte which leads to a bridging mechanism between particles, and not by electrostatic interaction as required by the DLVO theory. The adsorption theory of Smellie and La Mer, modified by Healy and La Mer to take into account molecular parameters, gives an accurate description of the re-filtration rate in terms of Langmuirs θ, the fraction of the surface covered, and (1–θ) the fraction uncovered.The steady-state kinetics of flocculation, of deflocculation, and of repair of flocs, yields the Smoluchowski equation for rate of coagulation, but is modified by the factor [θ(1–θ)] to become the rate of primary flocculation. This factor is a quantitative measure of sensitization. The radius of the floc R depends on [θ2(1–θ2)] and the rate of filtration upon [θ4(1–θ)4], which is the theoretical basis for the experimental eighth power law. New data emphasizing cationics is presented and contrasted with that for anionics in respect to zeta potential, molecular weight, length of chain, and specific radicals affecting adsorption.

Flocculation, subsidence, and filtration of phosphate slimes: IV. Flocculation by gums, and polyelectrolytes and their influence on filtration rate

Abstract The efficiencies of a large number of gums and polyelectrolytes as flocculants for improving flocculation and filtration of phosphate slimes have been investigated. Such factors as the speed of rotation and the total number of rotations in the mixing of flocculants and slimes, and the methods of adding the flocculants are discussed. The method of preparing stock solutions of flocculants and the age of such stock solutions significantly affect the flocculating efficiency in some cases. All the flocculants tested produce an optimum (maximum) in flocculation and, hence, filtration rate within a very narrow increment of flocculant concentration. This behavior was previously observed with starches. The pertinent data for 12 commercial products (out of about !50 tested), found to be the most effective flocculants for phosphate slimes, are summarized.

The preparation and size distribution of some monodisperse emulsions

Abstract A number of emulsions have been prepared in which one of the important variables determining their behavior, namely, the size of the droplets, has been controlled. This control will permit more quantitative and meaningful researches in future studies of emulsions. The preparation of monodisperse emulsions of oil in water was accomplished by passing electrically charged, monodispersed aerosols exhibiting the higher order Tyndall spectra through a liquid medium containing an emulsifier. The aerosol became emulsified without appreciable change in size distribution as shown by measurements of the higher order Tyndall spectrum. This was confirmed by more precise determinations of size and number with the Coulter Counter, an electronic sizing instrument. The reliability of this counter was verified by measurements on 36 samples in the range of diameters 0.5 to 1.6 microns. Dilute monodisperse Dow polystyrene latices were used for calibration. The mechanism of the emulsification process of aerosols was studied. The rate of emulsification increased when the aerosol particles were charged electrically, but the rate did not depend significantly upon the radius of the particles nor upon the nature of the emulsifying agent. Monodisperse emulsions could not be prepared when the concentration of the emulsifying agent was below its critical micelle concentration. Emulsification took place mainly in the foam produced by bubbling the aerosol through the emulsifier solution and not by contact with the bulk solution. Contact with the foam-air interface was shown to be sufficient for emulsification to occur.

The effect of the spreading solvent on the properties of monolayers

Abstract The effects produced by benzene or hexane as spreading solvents upon the surface pressure-area isotherms of octadecanol and stearic acid were investigated. Diluting the spreading solution resulted in an increase in the area/molecule at π = 1 dyne/cm. This expansion was greater with hexane than with benzene. Monolayers of stearic acid expanded more than those of octadecanol upon adding benzene liquid or vapor to the surface. Benzene vapor was irreversibly adsorbed on a monolayer of stearic acid. Octadecanol monolayers expanded when the concentration of benzene in the subphase was increased. An expansion of the monolayer with age was noted. This effect was greater for octadecanol than stearic acid monolayers. Aging could be attributed to changes in the structure of the monolayer as well as to contamination. Expansions resulting from both aging and solvent effects were greater at low surface pressures. A model based on the relative rates of solvent evaporation and diffusion into the subphase during the spreading process is proposed. The surface concentrations of benzene evaluated from experimental data and the model are compared. The two values agree within a factor of three.

The Evaporation Resistances of Monolayers of Long-Chain Acids and Alcohols and Their Mixtures

Publisher Summary This chapter describes the evaporation resistances of monolayers of long-chain acids and alcohols and their mixtures. The ability of a monomolecular film to retard the evaporation of the water on which it is spread has been the subject of spasmodic interest in the laboratory for many years but has only recently been used in a practical way to conserve water in reservoirs. The evaporation rate is determined by measuring the rate of uptake of water by a desiccant suspended a few millimeters above the water surface. The specific evaporation resistance is a property of the monolayer alone: it does not depend on any apparatus constant, and it is expressed in absolute units (sec/cm). The formation of holes in the monolayer through which water molecules can escape is treated by transition state theory based on the Gibbs free energy of activation. For monolayers of two components, a mixture rule is deduced, which enables the evaporation resistance of an ideal mixture to be calculated from the resistances of the components and the composition. An analysis of the evaporation process indicates that the water molecules penetrate the monolayer in one step rather than in a series of small steps.