Unit Area Of Interface Research Articles

Diffusion controlled reactions at an interface

This paper analyzes diffusion controlled reactions between Brownian particles in d dimensions separated by a d−1-dimensional hyperplane. We calculate the rate coefficient k(t) defined by Ṅ=k(t)ρAρB, where Ṅ is the reaction rate per unit interface area, ρi is the number density of i far from the interface on the side containing i, and t is the reaction time. k(t) is expressed in terms of the particle diffusion coefficients Di and the distance of closest approach between the components before a reaction. The critical dimension dc at which reaction kinetics cross over from compact (d<dc) to noncompact (d>dc) behavior is reduced by the presence of an interface to dc =1 from dc =2 for reactions without an interface. Thus, for d>1, k(t) exhibits all the characteristics of noncompact reactions. For example, k(t) has a constant long time limit k. For noncompact cases with d>2 we find that when DA/DB≫1 the more mobile species dominates (k∝DA) while for d=2 the slow species enters logarithmically and k vanishes in the limit DB →0 [k∝DA/ln(DA/DB)]. The crossover case d=dc =1 is very different and exhibits some features of compact behavior; e.g., k(t) is quenched logarithmically at long times. In this case we find, as in the d=2 noncompact case, that k(t) vanishes in the limit DB/DA→0. This effect is entirely absent for reactions without an interface and results from the rate being limited by diffusion of the slow species to the interface.

Analysis of water entrainment into dispersed W/O emulsion drops.

The effects of operating conditions on mechanical water entrainment into W/O emulsion drops in a (W/O)/W emulsion system were studied in a stirred tank in the absence of permeation due to osmotic pressure. The water entrainment was influenced by surfactant concentration, water volume fraction in W/O emulsion, inner water drop size, salt concentration in the external water phase, and agitation speed in the stirred tank. There was a satisfactory correlation between the extent of water entrainment and the weight of surfactant per unit interfacial area. These observations suggested that water entrainment proceeded as a result of additional emulsification at the drop surface. This idea was confirmed by examining the water entrainment in an oil-water dispersion system where water entrainment occurred by ernulsification. The effects of the operating conditions on water entrainment in the oil-water dispersion system were quite similar to those in the (W/O)/W emulsion system. In addition, the volume of water entrained per unit surface area of dispersed oil drops was in fair agreement with that in the (W/O)/W emulsion system. These results supported the proposed mechanism of water entrainment.

Effect of the surface-active substance cetylpyridinium chloride on the electric light scattering of bentonite

The changes in the electric properties and the stability of an aqueous suspension of sodium bentonite on addition of the cationic surface-active substance cetylpyridinium chloride (CPC) is studied by electric light scattering. The CPC concentration varies from 10 −5 to 10 −3 mol l −1, and the suspension weight concentration is 5 · 10 −6 kg l −1. The dimensions of the bentonite particles are followed by electron microscopy and the decay of the electro-optic effect. The particle dimensions are greatest at the isoelectric point (10 −4 mol l −1 CPC), determined microelectrophoretically. The greater value of the electro-optic effect in the kHz range for suspensions to which CPC is added in comparison with untreated suspensions is explained by the increase of the particle dimensions, which leads to an increase in the particle electric polarizability. The electric polarizability per unit interfacial area of the particles decreases, which is related to CPC adsorption on the particles. The greater dispersion for suspensions with CPC at frequencies below 100 Hz, also manifest in large negative effects, is explained by the increase of the ratio of permanent dipole moment to induced dipole moment.

ＳｉＣとアルミニウムの間のぬれ性に及ぼすＶａおよびＶＩａ族元素の影響

The wettability of molten aluminum alloys, containing 5 percent of V, Nb, and Ta in Va group and Cr, Mo, and W in VIa group, to SiC was measured by the dipping method. Wetting of SiC in all the alloys occurs after a certain period. The period is shortened by alloying all elements of Va and VIa groups. These elements without Cr accelerate the wetting rate. EPMA analysis shows formation of (V2C + V) and TaC at the boundary in the alloys containing V and Ta, respectively. The reaction rate is expressed by an equation proportional to the number of nuclei for wetting per unit interfacial area and unwetted ratio of the interface (1-alpha). Activation energy for wetting approximately 330 kJ/mol is obtained through temperature dependence of wetting of Al-V alloy. 7 references.

A new type of stacking fault in zeolites: presence of a coincidence boundary (√13. √13R32.2° superstructure)perpendicular to the tunnel direction in zeolite L

Real-space imaging has revealed a tendency for zeolite-L to form well-defined coincidence boundaries by rotation of 32.2° of one part of a crystal with respect to another; the generated interface has a superlattice repeat of √ 13 times that of the original, and the number of continuous tunnels intersecting unit area of interface is ca. 8% of that in the unfaulted crystal.

Drop-Interface Coalescence Rate in Tertiary Amine Solvent Extraction

Abstract An important requirement for economical application of solvent extraction technology is rapid and efficient phase disengagement. However, much progress toward a clear fundamental understanding of the factors that affect phase disengagement rate will be needed before a logical approach to the problem will be possible. In this paper, we develop the conceptual framework for the study of drop-interface coalescence in collapsing liquid/liquid dispersions and present the details of the experimental setup employed in our initial work. The method for determining the drop-interface coalescence rate requires measurement of the average volume of drops (vf) adjacent to the interface, their number (n) per unit area of interface, and dispersed-phase throughput (Q) per unit area. We have employed recording videomicrography for measurement of vf and n, while Q is found from the changing position of the major interface as the dispersion band collapses (batch mode).

Quantitation of surface affinities of red blood cells in dextran solutions and plasma

Mutual affinities of red blood cell surfaces in dextran solutions and plasma have been determined experimentally. The approach was to use dual micropipet techniques to manipulate cells and spherical cell "fragments" into position for contact. After contact, the red cells encapsulated the fragments to an extent that depended on the affinity. Surface affinity is defined as the reduction in free energy per unit area of interface that is associated with formation of adhesive contact. The surface affinity was calculated with the use of a minimum free energy analysis and knowledge of the red cell membrane elastic properties. With this approach, surface affinities were measured for normal and neuraminidase-treated red cells in plasma and various solutions of dextran. The data presented are the first direct measurements of the affinity of a biological membrane for another surface in a well-defined system. The peak surface affinities of normal red blood cells were found to be 4.9 x 10(-3) erg/cm2 in D70, 2.2 x 10(-2) erg/cm2 in D-150, and 2.0 x 10(-3) erg/cm2 in plasma. Neuraminidase-treated cells had higher affinities than normal cells: at least 2.8 x 10(-2) erg/cm2 in D70 and 1.8 x 10(-3) erg/cm2 in D28, which does not aggregate normal red cells.

The kinetics of solubilization of nonpolar oils by nonionic surfactant solutions

A quantitative study of the rate of solubilization of nonpolar oils in aqueous surfactant solutions has been made using a new technique. The dissolution of a single microscopic oil droplet adhering to a thin fiber suspended in an aqueous surfactant solution is recorded photomicrographically and the solubilization rate (rate of volume change per unit interfacial area) is calculated from the shape of the droplet using previously published theory (B. J. Carroll, J. Colloid Interface Sci. 57, 488 (1976)), which in this case reduces to a simple approximate form. The new technique has been used to study solubilization kinetics in some well-characterized systems containing a high-purity nonionic surfactant. The effects of surfactant concentration, temperature, and oil type were studied. The rate of solubilization is proportional to the surfactant concentration above the CMC and depends on the oil polarity and molecular weight. The rate is strongly temperature dependent in the region of the nonionic cloud point: 15°K below the cloud point, the rate is extremely small relative to that at the cloud point. It is shown that in the case of highly insoluble oils the solubilization mechanism must involve the adsorption-desorption of micelles at the oil/water interface, rather than the diffusion of molecules of oil into the micelle via the aqueous phase. The experimental data are shown to be consistent with the slow stage of the process being the adsorption, not desorption, of the micelle at the interface. The magnitude of the measured rate constant is consistent with theory if dissociation of the micelle occurs prior to the adsorption step and an estimate of the relaxation time for demicellization is obtained. The temperature dependence of the rate in the cloud point region is discussed in terms of changes in the properties of the nonionic solution in this region.

On the problem of development of hierarchic models of gas-liquid reactors

It has been shown that in multicomponent absorption with first and zero order chemical reactions proceeding without resistance to mass transfer in the gas phase, the locally averaged diffusive fluxes through unit interfacial area are linear functions of locally averaged concentrations. This relation can be used for the development of hierarchic models of gas-liquid reactors.

Adhesion versus cohesion in liquid-liquid and solid-liquid dispersions

It is found experimentally that, in the absence of specific interactions or electrical effects at the interface, the more stable liquid-in-liquid films are those formed by the liquid of smaller surface tension, which surrounds and separates droplets of the liquid of larger surface tension. A thermodynamic theory postulates that the condition for stability of the film is that the work of adhesion per unit area of interface between the two liquids shall be larger than the specific surface free energy of the liquid of which the film is composed. The deflocculation or flocculation of a dispersed solid in a liquid medium is also shown to depend on the same relation between the work of adhesion and the specific surface free energy of the medium, or, in equivalent terms, on whether the solid particle is “wetted” or not “wetted” by the medium.

Wetting Front Instability in Layered Soils

AbstractPercolation of a one‐dimensional wetting front in homogeneous soil is known to be stable. On the other hand, in a layered soil whose upper layer is finer and less conductive than the coarser layer beneath, the wetting front becomes unstable and breaks into narrow wetting columns, or “fingers,” in which flow is three‐dimensional. The instability originates at the interface but takes some time to develop, hence the wetting fingers appear some distance below the interface. The fingers move downward at a velocity equal to the saturated conductivity divided by the saturated volumetric water content of the bottom layer. The fingers consist of a saturated inner core percolating downward surrounded by an unsaturated outer layer. Experimental results indicate that the width of the fingers is independent of the flow rate and of irregularities at the interface. The number of fingers per unit area of interface is directly proportional to the flow rate. Instability of the wetting front in layered soil following rain or irrigation makes it possible for smaller volumes of water to penetrate deeper than would have been possible had the wetting front remained stable.

Temperature Coefficient for Twin Boundary Free Energy in 304 Stainless Steel: An Electron Microscope Study

It has been recently shown that, as generally assumed, the coherent twin boundary free energy and the intrinsic stacking fault free energy in fee pure metals are approximately related by a factor of 2 at constant temperature, i. e.,In the case of pure metals, the temperature coefficient assumes a simple Gibbs form for a general interface (stacking fault or twin boundary):where S is the interfacial entropy per unit area of interface. It is noted in Eq. (2) that the temperature coefficient for an idealized pure metal is always negative. Thus, in the absence of interfacial adsorption of vacancies or impurities [assumed in Eq. (2)], the stacking fault and twin boundary free energies will increase with increasing temperature, and will be related by Eq. (1).In the case of multicomponent (alloy) systems, the temperature coefficient becomes a complex function of component entropy contributions, surface adsorption and desorption, and their temperature dependence:

Adhesion of viscoelastic materials to rigid substrates. III. Energy criterion for failure

AbstractMeasurements are described of the strength of a model adhesive joint subjected to (1) tensile rupture, with the interface containing a small unbonded region of varying size, and (2) pure shear deformation, in the form of a partly unbonded sheet. These, and previous measurements of resistance to peeling separation, are all shown to be consistent with an energy criterion for adhesive failure. The characteristic failure energy per unit area of interface has been determined for the model adhesive material as a function of the effective rate of detachment, over a wide range covering almost the entire spectrum of viscoelastic response. The values obtained are found to increase from levels only slightly higher than thermodynamic considerations would predict, i.e., 102−103 ergs/cm2, at low rates of crack propagation, up to a value of about 106 ergs/cm2 at high rates when the material responds in a glasslike manner. These results suggest that the failure energy has two components: the (reversible) work of adsorption and the (irreversible) work of deformation of the adhesive in effecting separation.

Noise from a Simplified Model of a Supersonic Turbulent Shear Layer

A layer of two-dimensional square “eddies” separates a main flow Uj from fluid at rest; the eddies move at the mean (supersonic) speed Uj/2. The initially plane interfaces will ripple slightly, developing Mach waves to balance internal and external pressures. The Mach wave pressure pattern (noise) is readily calculable. The sound power from unit area of interface comes out to be P = e(peak eddy velocity)4 [(Uj/2c)2 − 1]12/16 Uj. In an example (simulated round rocket jet), the effective area is taken as 6π (diam)2, Uj/c = 6, peak eddy velocity = 0.1 √ Uj. The efficiency (noise power/flow power) comes out to be 0.17%, which is of the order of measured values for rocket noise. [This study was supported by a grant from the Air Force Office of Scientific Research.]

A mathematical treatment of the effect of particle size distribution on mass transfer in dispersions

AbstractA mathematical model is proposed that takes into account interaction between drops or bubbles in a swarm as well as the effect of particle size distribution. The model is used to solve the equations for unsteady state mass transfer with and without chemical reaction when the drops or bubbles are suspended in a nonextraordinarily purified agitated fluid. Steady state diffusion to a family of moving drops with clean interface and without interaction and chemical reaction has been also analyzed. The model demonstrates the sort of error that may arise when one applies uniform drop size assumptions to drop populations. It is shown quantitatively that this error is usually small when one replaces the variable particle size by the mean. By using variables that can be determined and predicted, the equations presented permit the estimation of diffusion rate per unit area of interface, as well as the average concentration and the total average rate of mass transfer in the disperser under pseudo steady state conditions.

Adsorbed films of bovine serum albumin: tensions at air-water surfaces and paraffin-water interfaces.

Abstract Using the pendant-drop method, the interfacial tension between n-octadecane and aqueous solutions of bovine serum albumin reached constant values after about 30 min, and became independent of protein concentration above about 0.025%. At low ionic strength there is a minimum in the interfacial tension in the isoelectric region whereas at higher ionic strengths there is a tendency for a maximum to occur in this pH region. The addition of octadecylamine to the n-octadecane decreases considerably the interfacial tension against water both in the presence and absence of bovine serum albumin. The entropy change per unit area of interface goes through a sharp maximum with increasing concentration of bovine serum albumin. The compressibilities of the interfacial bovine serum albumin films as obtained from decreasing the size of the drop increases sharply at a film pressure of about 22 dynes/cm.

An Approximate Relation Between Surface Tension and Concentration for Regular Solutions

An equation for the variation of surface tension with concentration in regular solutions is derived using Hildebrand's model and calculating the work per unit interfacial area required to separate a body of liquid reversibly into two infinitely removed parts. Spherical symmetry in shape and molecular field of both components is assumed. Values of a factor of deviation from the geometric mean relationship for intermolecular attraction between unlike non-polar molecular species are calculated both from surface tension and vapor pressure data. Values of the factor calculated from these two independent sources for a number of systems are in reasonable agreement. The linearity of surface tension with volume fraction in ideal systems is predicted, in agreement with experiment.