Spherical Water Droplets Research Articles

Formation of Water-in-Carbon Dioxide Microemulsions with a Cationic Surfactant: A Small-Angle Neutron Scattering Study

The formation of water-in-carbon dioxide microemulsions with a cationic perfluoropolyether trimethylammonium acetate surfactant, PFPE−C(O)−NH−CH2−N+(CH3)3 CH3COO-, is reported over a range of temperatures (25−90 °C) and pressures (87.3−415 bar). Spherical droplets are observed by SANS with radii ranging from 16 to 36 Å for water-to-surfactant molar ratios (Wo) from 9.5 to 28. Porod analysis of the SANS data indicates an area of approximately 60 Å2/surfactant molecule at the water−CO2 interface, in reasonable agreement with the value of 72 Å2 determined from the change in the droplet radius with Wo. The CO2-phobic functionality between the surfactant headgroup and perfluoropolyether tail reduces CO2 penetration of the tails, resulting in a smaller area/surfactant than in the case of an anionic perfluoropolyether surfactant [Langmuir 1997, 13, 3934]. A relatively rigid film, with a mean film rigidity (2K + K̄) of approximately 1 kBT, along with the strong partitioning of the surfactant toward CO2 versus water, lead to the small, rigid, spherical water droplets in CO2.

Sublimation and vaporization of an ice aerosol particle in the form of thin cylinder by laser radiation

Formulae for heat and mass exchange from the surface of ice particles of different forms are derived. Destruction of plate, cylindrical and spherical particles in the sublimation regime, as well as the subsequent melting (cylinder, disk) and evaporation of the water droplet formed are investigated. The study was conducted for the parameters averaged over the particle volume: heat release intensity, temperature, evaporation efficiency, etc. Heating time, melting time, evaporation time, evaporation efficiency, temperature for particles in the form of thin long cylinder is presented versus the intensity of laser radiation at various temperatures and pressures of the surrounding air. The results are compared with the correspondent evaporation parameters of a supercooled spherical water droplet.

Effect of charge density fluctuations within a droplet on dielectric polarization of ionic microemulsions

A statistical model of the dielectric polarization of ionic water-in-oil microemulsions is proposed. The model makes it possible to describe the effect of temperature and dispersed phase content on the static dielectric permittivity behavior of the microemulsions at a region far below percolation. With the help of this model, the microemulsions formed with the surfactant, sodium bis(2-ethylhexyl) sulfosuccinate (AOT), have been analyzed. The studied systems are considered to consist of nanometer-sized spherical non-interacting water droplets of equal size with negatively charged head groups SO − 3, staying at the interface and positive counterions Na +, distributed in the electrical diffuse double layer of the droplet interior. It can be conjectured that two different mechanisms, that provide an increase of the static dielectric permittivity as a function of temperature, may take place. These may be attributed either to the aggregation of droplets or the temperature growth of polarizability of non-interacting and therefore non-aggregating droplets dispersed in oil. The results support the hypothesis that the experimental temperature behavior of dielectric polarization far below the percolation region is only due to the polarization of a single droplet and not to an aggregation. The droplet polarizability is proportional to the fluctuation mean-square dipole moment of a droplet. It is shown that this mean-square dipole moment and the corresponding value of the dielectric increment, depend upon the equilibrium distribution of counterions within a diffuse double layer. The density distribution of ions is determined by the degree of the dissociation of the ionic surfactant. The dissociation of the ionic surfactant in the system has been analyzed numerically. The relationship between the constant of dissociation and the experimental dielectric permittivity has been ascertained.

Fluctuation mechanism of the dielectric polarization of water-in-oil microemulsions with ionic surfactant

A statistical model is proposed to describe the dielectric polarization of ionic microemulsions at a region far below percolation in which the microemulsions consist of spherical single droplets with water in the central core surrounded by a layer of surfactant molecules. The model describes the effect of temperature and dispersed phase content on the behavior of the dielectric polarization of ionic water-in-oil microemulsions and explains the experimentally observed increase of the static dielectric permittivity as a function of temperature. The microemulsions formed with surfactant sodium bis(2-ethylhexyl) sulfosuccinate have been analyzed with the help of this model. The systems are considered to consist of nanometer-sized spherical noninteracting water droplets of equal size with negatively charged head groups, staying at the interface, and positive counterions, distributed in the electrical diffuse double layer of the droplet interior. It is shown that the droplet polarizability is proportional to the mean-square fluctuation dipole moment of the droplet. This mean-square dipole moment and the corresponding value of the dielectric increment depend on the equilibrium distribution of counterions within a diffuse double layer. The density distribution of ions is determined by the degree of the dissociation of the ionic surfactant. The relationship between the dielectric permittivity, the constant of dissociation of surfactant, the content of the dispersed phase, and the temperature has been ascertained.

Evaluation of the Accuracy of PMS Optical Array Probes

This paper considers the theory of diffraction image formation of spherical particles and peculiarities of particle sizing by discrete imaging probes. The diffraction images of spherical water droplets are approximated by Fresnel diffraction by an opaque disc. The approach developed in the paper is applicable to all types of array and matrix imaging probes. The analysis measurement accuracy is performed for the PMS Optical Array Prove (OAP)-2D-C and OAP-2Dgray probes. It is shown that a 25-μm resolution PMS OAP-2D-C probe can both oversize and undersize droplets smaller than approximately 100 μm in diameter, and oversize droplets larger than approximately 100 μm. The errors in droplet sizing increase with decreasing size. The discrete manner of particle image registration also leads to losses of particles with sizes smaller than 100 μm. For the ideal case with zero photodiode response time, these losses reach 70% for 25-μm droplets. A nonzero response time will increase these losses. These findings help explain discrepancies observed in the overlap region of the PMS FSSP and OAP droplet spectra. A variety of calculated digital images for PMS OAP-2D-C and OAP-2Dgray probes is presented. Different methods of particle image sizing are discussed. Several methods of size correction of individual droplets and droplet ensembles are suggested. Correction algorithms for these effects are derived, and distortion and correction retrieval matrices are calculated. Several examples of actual and measured size distributions are presented.

On the bicontinuous microstructure induced by a guest protein in a typical AOT microemulsion

The ternary microemulsion AOT/water/isoctane was investigated in the presence of the human serum albumin (HSA) protein as solubilized guest molecule by NMR relaxation and self-diffusion measurements. The analysis of the 23Na NMR relaxation rates of the counterions and the interpretation of the 1H relaxation and self-diffusion data of water in terms of the usual spherical water droplet model gave a strong and direct evidence for important modifications of the water-in-oil droplet microstructure in the presence of HSA. With decreasing the water/surfactant ( W S ) molar ratio, which implies a linear decrease of the water core, the system containing the protein shows a transition to a bicontinuous microstructure. Some protein residues are likely to contribute to the total interfacial area to retain the favored curvature of the AOT molecules located at the polar-apolar interface. At W S larger than 25, which corresponds to an average radius of the water core larger than 2.8 nm, the relaxation parameters and the self-diffusion coefficients are almost unaffected by the presence of HSA. Consequently, it can be suggested that HSA molecules are hosted in closed water domains, which are likely to assume an average spherical shape as well as the unfilled, AOT stabilised, water droplets.

Distinction of Coal Dust Particles from Liquid Droplets by Variations in Azimuthal Light Scattering

Abstract An experimental study was performed to determine the feasibility of optically distinguishing coal particles from water droplets for the purpose of reducing the mass concentration artifact from water sprays and steam reported for optical dust monitors. A single-particle multiangle optical detector was used to measure the scattering of monochromatic, circularly polarized light by mixtures of nonspherical bituminous coal dust particles and 0.5 μm dioctyl sebacate (DOS) droplets, which were used for modeling small, spherical water droplets. A total of 20 different mixtures with known coal number fractions ranging from 6 to 90 percent were measured by the detector using two data acquisition methods known as peak-detection and digital signal evaluation (DSE). Variability in azimuthal scattering by single particles, which is an indicator of the degree of sphericity, was used to discern the fraction of coal particles present in each aerosol mixture. Number concentrations of coal and DOS aerosols were mea...

Cirrus Infrared Parameters and Shortwave Reflectance Relations from Observations

Abstract A summary of experimental observations and analysis of cirrus from high-altitude aircraft remote sensing is presented. The vertical distribution of cirrus optical and infrared cross-section parameters and the relative effective emittance and visible reflectance are derived from nadir-viewing lidar and multispectral radiometer data for observations during the 1986 and 1991 FIRE cirrus experiments. Statistics on scattering and absorption cross sections in relation to altitude and temperature are given. The emittance and reflectance results are considered as a function of solar zenith angle. Comparative radiative transfer calculations based on the discrete-ordinate method were carried out for three representative cloud phase function models: a spherical water droplet, an ice column crystal cloud, and a Henyey-Greenstein function. The agreements between observations of the effective emittance and shortwave reflectance and the model calculations were a function of the solar zenith angle. At angles bet...

Structure and dynamics of water-in-oil microemulsions near the critical and percolation points

The three-component ionic microemulsion system consisting of AOT/water/ decane shows an interesting phase behavior in the vicinity of room temperature. The phase diagram in the temperature-volume fraction (of the dispersed phase) plane exhibits a lower consolute critical point at about 40°C and 8% volume fraction. A percolation line, starting from the vicinity of the critical point, cuts across the plane, extending to the high-volume fraction side at progressively lower temperatures. This phase behavior can be understood in terms of a system of polydispersed spherical water droplets, each coated by a monolayer of AOT, dispersed in a continuum of oil. These droplets interact with each other via a hard-core plus a short-range attractive interaction, the strength of which increases with temperature. We show that Baxter's sticky-sphere model can account quantitatively for the phase behavior, including the percolation line, provided that the stickiness parameter is a suitable function of temperature. We use the structure factors measured by small-angle neutron scattering below the critical temperature to determine this functional dependence. We also investigate the dynamics of droplets, below and approaching the critical and percolation points, by dynamic light scattering. Both theQ dependence of the first cumulant and the time evolution of the droplet density correlation function can be quantitatively calculated by assuming the existence of polydispersed fractal clusters formed by the microemulsion droplets due to attraction.

Further thoughts on Newton’s zero-order rainbow

A zero-order rainbow angle may be defined as the relative minimum angle of deviation of geometrical light rays transmitted without internal reflections through a transparent particle. If the incident rays are parallel and the particle is a sphere, such a minimum does not exist. But if the incident rays are not parallel or if the particle has an elliptical rather than circular cross section, an angle of minimum deviation, hence a zero-order rainbow, can occur. For a spherical water droplet, the zero-order rainbow will occur when a point source is placed less than a droplet radius away from its surface. If a column of water with an elliptical cross section is illuminated by a plane wave, a zero-order rainbow will occur if the length of the major axis of the cross section is more than twice the length of the minor axis.

Diffusion model for lightning radiative transfer

A one‐speed Boltzmann transport theory, with diffusion approximations, is applied to study the radiative transfer properties of lightning in optically thick thunderclouds. Near‐infrared (λ = 0.7774 μm) photons associated with a prominent oxygen emission triplet in the lighting spectrum are considered. Transient and spatially complex lightning radiation sources are placed inside a rectangular parallelepiped thundercloud geometry and the effects of multiple scattering are studied. The cloud is assumed to be composed of a homogeneous collection of identical spherical water droplets, each droplet a nearly conservative, anisotropic scatterer. Conceptually, we treat the thundercloud like a nuclear reactor, with photons replaced by neutrons, and utilize standard one‐speed neutron diffusion techniques common in nuclear reactor analyses. Valid analytic results for the intensity distribution (expanded in spherical harmonics) are obtained for regions sufficiently far from sources. Model estimates of the arrival‐time delay and pulse width broadening of lightning signals radiated from within the cloud are determined and the results are in good agreement with both experimental data and previous Monte Carlo estimates. Additional model studies of this kind will be used to study the general information content of cloud top lightning radiation signatures.

Structure and dynamics of dense water-in-oil microemulsions below percolation threshold

The three-component ionic microemulsion system consisting of AOT/water/decane shows an interesting phase behavior in the vicinity of room temperature. The phase diagram in the temperature-volume fraction (of the dispersed phase) plane exhibits a lower consolute critical point around 10% volume fraction and a percolation line, cutting across the plane starting from the vicinity of the critical point, extends to high volume fraction side, at progressively lower temperatures. This phase behavior can be understood in terms of a system of polydispersed spherical water droplets, each coated by a monolayer of AOT, dispersed in a continuum of oil. These droplets interact with each other via a hard-core plus a short-range attractive interaction, the strength of which increases with temperature. We show that Baxter's sticky sphere model can account for the phase behavior including the percolation line, quantitatively, provided that the stickiness parameter is a suitable function of temperature. We use the structure factors measured by small angle neutron scattering below the critical temperature to determine this functional dependence. We also investigate the dynamics of droplets below and approaching the percolation line by dynamic light scattering. Both the first cumulant and the droplet density time correlation function can be quantitatively calculated by assuming the existence of polydispersed fractal clusters form by the microemulsion droplets due to the attraction. Analysis of SANS data indicates that above the percolation line, the clustered droplets structure gradually transforms into an ordered bicontinuous structure

Structural studies of microemulsions stabilised by aerosol-OT

In this article we review structural studies of AOT-stabilised water-in-oil microemulsions. Nanometer-sized spherical droplets of water coated by a curved monolayer of surfactant are preferred over a wide range of pressure and temperature conditions, as well as in very different physical environments, for example a supercritical or a solid alkane. Within the one-phase region variation of pressure and temperature essentially serves to fine-tune the strength of the attractive interactions between droplets.

Non-exponential relaxation in dense microemulsions

Three-component mixtures of sodium di-2-ethyl-hexylsulfosuccinate (AOT), water and decane, having a fixed molar ratio of water to AOT equal to 40 but with different amount of decane, form one-phase microemulsions in the vicinity of room temperature. The microemulsion consists of spherical droplets of water, coated by mono-layers of AOT, dispersed in continuous medium of decane. The average radius of the droplets is about 85 Å with a polydispersity of 25%. By varying the relative amount of decane, the volume fraction of the doplets can be varied continuously from 10 to 70%, simulating gas and liquid phases of simple fluids. The phase diagram of this model microemulsion system, in the temperature-volume fraction ( T− φ)-plane, shows a lower miscibility gap at low φ with a lower consolute temperature of 40°C at a critical volume fraction of 10%. For φ > 40%, the isotropic, disordered microemulsions undergo a first order phase transformation to a lamellar structure upon heating to sufficiently high T. In addition, there is a percolation line cutting the one-phase region from low to high volume fractions starting near the consolute point. Extensive dynamic light scattering measurements have been used to study time-dependent droplet density correlation functions below and above the percolation temperatures, in both dilute and dense microemulsions. Evolution of the time correlation functions from an exponential to a stretched exponential decay, as the volume fraction and temperature are varied, is discussed in the light of the critical phenomenon, the percolation transition and a glass-like transition at volume fraction of 60%.

Scattering studies of microemulsions in low-density alkanes

Using small-angle neutron scattering and dynamic light scattering we have studied the structure and dynamics of water-in-oil microemulsion droplets stabilised by the surfactant Aerosol-OT in the low-density alkanes propane and n-butane. The phase stability, interdroplet structure and droplet diffusion coefficient are dependent on the alkane density. At densities of ca. 0.6 × 103 kg m–3 surfactant-coated, essentially monodisperse, randomly distributed, weakly interacting, spherical water droplets are present. At lower densities enhanced droplet–droplet attractions promote large, transient clusters of droplets. The intradroplet structure (i.e. droplet size) appears to be independent of alkane chain length and density.

Electro-optical and dielectric properties of oil continuous aerosol ot/water/isooctane micro-emulsions

A water in oil microemulsion is a thermodynamically stable, isotropic, transparent liquid dispersion of small spherical water droplets, surrounded by a layer of surfactant molecules, in a continuous oil phase [1]. In an electric field the droplets become spheroidal. Experimentally one finds for low volume fractions a negative Kerr effect for small droplets which becomes positive for larger radii [2]. We extended these measurements. Comparison with a formula for the Kerr constant which we derive shows good agreement. For larger volume fractions the droplets cluster. This follows rather convincingly if we compare our experimental values for the dielectric permittivity with the theoretical expression.

SANS studies of the microstructure of a three-componnent microemulsion

Small-angle neutron scattering measurements have been performed on a three-component microemulsion system consisting of water, hexane and didodecyl-dimethylammonium bromide. For a water-to-surfactant weight ratio of 0.95 and less than 5 wt% surfactant, these measurements are best fit by a model with a Gaussian size distribution of spherical water droplets in hexane. The average water core radius is determined to be about 2.9 nm. On addition of water while the same water-to-surfactant ratio is maintained, there is some evidence that the basic unit of the microstructure remains a sphere with the same radius. The interaction between the spheres is found to be attractive, and the spheres may be connected for volume fractions of water larger than 5%.

What Laboratory-Produced Plasma Structures Can Contribute to the Understanding of Cosmic Structures Both Large and Small

The tradition of the classical 1901 work by Birkeland [1] on aurora phenomena by laboratory terrella experiments was resumed by Alfvén [2], Cowling [3], Ferraro et al. [4], and by Bennett [5] in his terrella experiments. In 1954 [6] when experimenters accidentally produced in the laboratory structures later identified as diamagnetic vortex filaments, and in 1961 [7] when filaments, later identified as current-carrying paramagnetic plasma vortex structures (which are both electric motors and dynamos), were observed in the Z and theta-pinch experiments, this tradition was being further reestablished. It has been successfully argued [6], [8], [11], [20] that both of these types of vortices are force-free minimum-free-energy structures that spontaneously spring to life as readily as do thousands of spherical bubbles and water droplets during the splash of a breaking water wave. The Birkeland aurora filaments are a hybrid combination of these two basic types (paramagnetic and diamagnetic) of plasma vortices. It is to be expected that such structures on a cosmic scale play an important role in the cosmos, and indeed they do in the formation of galaxies, stars, binary stars, solar systems, solar prominences, solar flares, solar wind, comet tails, cosmic "strings" in the Crab nebula, string-like galactic clusters, expansion of the Universe, giant galactic jets, cosmic rays, sunspots, vortex rolls in sunspot penumbra, twinkling of radio stars by the density fluctuations in the ionosphere, turbulence at the interface between the solar wind and the earth's magnetosphere, etc.

Droplet evaporation by combined mechanisms in an ICF reactor

The heat transfer from dense steam plasma to a moving spherical water droplet has been computed using a self-similar solution for an optically thick boundary layer. Simultaneous radiation, vapor dissociation, convection, conduction and blowing were considered. The droplet evaporation rate has been computed for several pressures and temperatures and compares well with known rates at low temperature and atmospheric pressure. The results were incorporated into a model describing the cooling process of a stagnant steam fireball predicted for an ICF reactor.

The optical properties of water droplets in the infrared

Mie theory is used to calculate the extinction and scattering efficiencies and the mean cosine of scattering for spherical water droplets. Tables and graphs are presented of properties averaged over the black-body distribution at temperatures of 280K, 350K and 413K for a range of droplet radii between 0.5 and 20 mu m. The accuracy of using these wavelength-averaged quantities in the calculation of heat fluxes is found to be typically better than 5% for droplets with radius greater than 5 mu m. The effect of small systematic changes in the refractive index is examined: a change of a few per cent in the real part may produce changes of three to six times as much in scattering efficiencies. The values predicted by commonly used approximation formulae are compared with Mie theory values: agreement is found to be poor for small drops and around 10% for drops with radii greater than 7 mu m.