Showing papers on "Critical radius published in 2000"

Nucleation : basic theory with applications

Abstract: Thermodynamics of Nucleation: First-Order Phase Transitions Driving Force for Nucleation Work for Cluster Formation Nucleus Size and Nucleation Work Nucleation Theorem Properties of Clusters Equilibrium Cluster Size Distribution Density-Functional Approach. Kinetics of Nucleation: Master Equation Transition Frequencies Nucleation Rate Equilibrium Stationary Nucleation First Application of the Nucleation Theorem Nonstationary Nucleation Second Application of the Nucleation Theorem Nucleation at Variable Supersaturation. Factors affecting Nucleation: Seed size Line Energy Strain Energy Electric Field Carrier-Gas Pressure Solution Pressure Preexisting Clusters Active Centres. Applications: Overall Crystallization Crystal Growth Third Application of the Nucleation Theorem Induction Time Fourth Application of the Nucleation Theorem Metastabiltiy Limit Maximum Number of Supernuclei Size Distribution of Supernuclei Growth of Thin Films Lifetime of Amphiphile Bilayers. Appendices References Author index Subject Index.

Magnetorotational Instability in Protoplanetary Disks. II. Ionization State and Unstable Regions

Abstract: We investigate where magnetorotational instability operates in protoplanetary disks, which can cause angular momentum transport in the disks. We investigate the spatial distribution of various charged particles and the unstable regions for a variety of models for protoplanetary disks, taking into account the recombination of ions and electrons at grain surfaces, which is an important process in most parts of the disks. We find that for all the models there is an inner region that is magnetorotationally stable due to ohmic dissipation. This must make the accretion onto the central star nonsteady. For the model of the minimum-mass solar nebula, the critical radius, inside of which the disk is stable, is about 20 AU, and the mass accretion rate just outside the critical radius is 10-7-10-6 M☉ yr-1. The stable region is smaller in a disk of lower column density. Dust grains in protoplanetary disks may grow by mutual sticking and may sediment toward the midplane of the disks. We find that the stable region shrinks as the grain size increases or the sedimentation proceeds. Therefore, in the late evolutionary stages, protoplanetary disks can be magnetorotationally unstable even in the inner regions.

Transient pores in stretched vesicles: role of leak-out

Abstract: We have visualized macroscopic transient pores in mechanically stretched giant vesicles. They can be observed only if the vesicles are prepared in a viscous solution to slow down the leak-out of the internal liquid. We study here theoretically the full dynamics of growth (driven by surface tension) and closure (driven by line tension) of these large pores. We write two coupled equations of the time evolution of the radii r(t) of the hole and R(t) of the vesicle, which both act on the release of the membrane tension. We find four periods in the life of a transient pore: (I) exponential growth of the young pore; (II) stop of the growth at a maximum radius rm; (III) slow closure limited by the leak-out; (IV) fast closure below a critical radius, when leak-out becomes negligible. Ultimately the membrane is completely resealed. Notation d membrane thickness E surface stretching modulus K b Helfrich bending constant Q leak-out flux r pore radius r i pore radius at nucleation r c pore radius at zero tension r L characteristic radius of leak-out r m radius at maximum (II) r 23 pore radius at cross-over between (II) and (III) r 34 pore radius at cross-over between (III) and (IV) R vesicle radius R i initial vesicle radius R 0 vesicle radius at zero tension V L leak-out velocity V 3 slow closure velocity limited by leak-out (III) V 4 fast closure velocity at end (IV) η 2 lipid viscosity η s surface viscosity η 0 viscosity of solution σ surface tension σ 0 surface tension before pore opening τ rise time of pore growth (I) J line tension

Coupling between meniscus and smectic-A films: circular and catenoid profiles, induced stress, and dislocation dynamics

Abstract: In this paper we discuss the formation and shape of the meniscus between a free-standing film of a smectic-A phase and a wall (in practice the frame that supports the film). The wall may be flat or circular, and the system with or without a reservoir of particles. The formation of the meniscus is always an irreversible thermodynamic process, since it involves the creation of dislocations in the bulk (therefore it involves friction). The four basic shapes of meniscus discussed are the following: exponential, algebraic ${(x}^{3/2}),$ circular, and catenoid. Three principal regions of the whole meniscus must be distinguished: close to the wall with a high density of dislocations, away from the wall with medium density of dislocations, and far from the wall (i.e., close to the film) with a low density of dislocations (vicinal regime). The region with medium density of dislocations is observable using a microscope, and is determined by the competition between surface tension, energy of dislocations, and pressure difference set by the mass of the meniscus or by the reservoir. Its profile is circular as observed in recent experiments [J.-C. G\'eminard, R. Ho\l{}yst, and P. Oswald, Phys. Rev. Lett. 78, 1924 (1997)]. By contrast, the vicinal regime with low density of dislocations is never observable with an optical microscope. In the regime with a high density of dislocations, the reasons why the dislocations tend to gather by forming giant dislocations and rows of focal conics are discussed. Finally, we discuss the stability of a smectic film with respect to the formation of a dislocation loop. We show experimentally that the critical radius of the loop is proportional to the curvature radius of the meniscus in its circular part, in agreement with the theory. In addition, we show that the mobility of edge dislocations measured in thick films is in agreement with that found in bulk samples from a creep experiment. This result confirms again our model of the meniscus.

Calculated properties of field-induced aggregates in ferrofluids

Abstract: We have calculated the critical radius of aggregates in thin layers of ferrofluid, assuming a cylindrical aggregate shape, as a function of external field and plate separation. Results are obtained by minimizing the Helmholtz free energy, and can be used to predict aggregate radius and spacing. The model, with entropy included, provides reasonable predictions for the onset of the labyrinth pattern. These results show good agreement when compared with data from experiments on Fe3O4 kerosene-based ferrofluids and magnetorheological fluids.

A stable non-BPS configuration from intersecting branes and antibranes

Abstract: We describe a tachyon-free stable non-BPS brane configuration in type-IIA string theory. The configuration is an elliptic model involving rotated NS5-branes, D4-branes and anti-D4 branes, and is dual to a fractional brane-antibrane pair placed at a conifold singularity. This configuration exhibits an interesting behaviour as we vary the radius of the compact direction. Below a critical radius the D4 and anti-D4 branes are aligned, but as the radius increases above the critical value the potential between them develops a minimum away from zero. This signals a phase transition to a configuration with finitely separated branes.

Dewetting Revisited: New Asymptotics of the Film Stability Diagram and the Metastable Regime of Nucleation and Growth of Dry Zones

Abstract: Stability properties of a nonwetting film are discussed. Assuming a general form of the disjoining pressure, accurate asymptotic formulas for the upper thickness range of the film instability/metastability are derived. This analysis is applied to two particular cases: a nonionic liquid film with the (m, n) power form of the disjoining pressure and an ionic liquid film with an exponentially decaying electrostatic part of the disjoining pressure. The metastable regime of dewetting is considered, and an expression for the critical radius of a hole is derived. A new Fokker-Planck kinetic model of metastable dewetting, applicable at early stages of the process, is developed. It yields a relationship between the number of viable holes (per unit area and unit time) moving in steady-state regime to the supercritical part of the "embryo size space" and the equilibrium number of "critical" holes determined from thermodynamics. The dynamics of metastable dewetting is quantitatively described in terms of the surface fraction of holes in the film. Continuous dynamic models of the metastable dewetting applicable in the entire range of times have to include the thermal noise, as proposed by V. S. Mitlin (1994, Colloids Surf. A 89, 97). Copyright 2000 Academic Press.

Nucleation and early stage growth in phase-separating liquid mixtures under weak time-dependent supersaturation

Abstract: In the standard description of phase separation, quenching from an initial equilibrium state to a final metastable state in the two-phase region is usually assumed to be instantaneous. Such an artificial situation is nevertheless intrinsically at variance with experiments because the quench rate is finite due to the continuous changes in thermodynamic parameters between the initial and final states. We experimentally explore this issue in near-critical micellar phases of microemulsion with induced transient grating techniques, focusing our attention on the very early stage of droplet growth, where the influence of the time dependence of supersaturation is the strongest. The experiment makes use of laser-induced concentration variations to locally quench the mixture with two intersecting pump beams, whose interference pattern optically traps the nucleated droplets on fringes. Due to the slow mass diffusion kinetics of quenches in composition, the time-resolved reflectivity of a third probe beam on the resulting droplet grating allows us to determine the mean nucleation time and the mean quench depth at the beginning of the decay of the metastable state. By varying the amplitudes of the control parameters (beam power, beam radii), we are able to characterize the dynamic properties of nucleation onset during continuous quenching. The results are interpreted in the light of very simple scaling arguments. We show in particular that for a weak linear temporal variation of the supersaturation, where and are, respectively, the measured critical radius and nucleation time.

Spontaneous motion of droplets during the demixing transition in binary fluids

Abstract: The convective interaction between a pair of droplets coarsening during the demixing transition of a binary fluid is examined. The starting point is the model H equation for binary fluids, and the droplet sizes are considered to be large enough that thermal fluctuations are neglected. Droplet motion is induced by the convective coupling in the concentration equation, where there is a flux of concentration due to the fluid velocity, and a reciprocal effect in the momentum equation. The effect of the convective force density is separated into two parts—one due to the sharp concentration gradients at the droplet interface, and the other due to the variation in the matrix. It is shown that the dominant contribution to the fluid velocity field is due to the sharp concentration variation at the interface, and this is proportional to the square of the droplet flux at the surface. The surface flux is determined by solving the diffusion equation in the matrix between the droplets, and matching the solution to that in the interfacial region. The analysis indicates that there is an attractive interaction if the two droplets have radii larger or smaller than the critical radius, while the interaction is repulsive if the radius of one droplet is larger and the other smaller than the critical radius. The magnitude of the induced droplet velocity is estimated.

Optimization of the critical nuclear size for protein crystallization: a note.

Abstract: It was observed that for some proteins the best crystals for X-ray diffraction have been obtained at supersaturation ratios of ca 2.5–3 (in experiments without seeding). It was then noticed that under certain conditions specific to the protein such values are close to a local minimum of the critical radius for nucleation. A relation between the two observations is proposed.

A Thermodynamic Theory of Suspension I. Thermodynamic Theory

Abstract: The stability of a colloid has been treated in terms of repulsion by electric charge and attraction by cohesion of particles, but colloid particles are v-times larger in volume-size than the solvent molecules. v is as large as 103-6 and the molar energy of cohesion H/v is negligibly small compared with the electric repulsion energy Wel/v. Cohesion acts over the distance of 1—5 A or only at the contact point. H does not increase with v, contrary to the DLVO theory. The molar energy of sedimentation Wsed/v is taken as an influential factor for the stability of a colloid of large particles. It is calculated from Stokes law as Wsed/v = Δρ u2, where Δρ is the density difference and u is the stationary velocity of sedimentation equal to (Δρ/η)(2/9)gr2, where η, r, and g are viscosity of solvent, radius of particle, and acceleration constant of gravity, respectively. Sedimentation occurs when Wsed/v is equal to kT/3, i.e., the perpendicular component of the energy of Brownian motion. The critical radius rc is rc...

Kinetics of spontaneous precipitation of calcium sulfate dihydrate

Abstract: They have established a precise measuring-calculating system to determine the variation of concentration for all species in the super saturated solution of calcium sulfate dihydrate(CSD).Judging the relationship between critical time and supersaturation, They have calculated the free surface energy of CSD to be 21.5 mJ/m 2 in the experimental conditions.Based on the theory of thermodynamics, classic theory of precipitation kinetics and the value of free surface energy, they have also got some values in critical phase,such as critical radius of nucleus、number of particles in critical nucleus. The good linear relationship between index I d and time indicates that the process of CSD precipitation is mainly controlled by diffusion mechanism.

A Stable Non-BPS Configuration From Intersecting Branes and Antibranes

Abstract: We describe a tachyon-free stable non-BPS brane configuration in type IIA string theory. The configuration is an elliptic model involving rotated NS5 branes, D4 branes and anti-D4 branes, and is dual to a fractional brane-antibrane pair placed at a conifold singularity. This configuration exhibits an interesting behaviour as we vary the radius of the compact direction. Below a critical radius the D4 and anti-D4 branes are aligned, but as the radius increases above the critical value the potential between them develops a minimum away from zero. This signals a phase transition to a configuration with finitely separated branes.

The Spacetime Life of a Non-BPS D-particle

Abstract: We investigate the classical geometry generated by a stable non-BPS D-particle. We consider the boundary state of a stable non-BPS D-particle in the covariant formalism in the type IIB theory orbifolded by (-1)^{F_L} I_4. We calculate the scattering amplitude between two D-particles in the non-compact and compact orbifold and analyse the short and long distance behaviour. At short distances we find no force at order $v^2$ for any radius, and at the critical radius we find a BPS-like behaviour up to $v^4$ corrections for long and short distances. Projecting the boundary state on the massless states of the orbifold closed string spectrum we obtain the large distance behaviour of the classical solution describing this non-BPS D-particle in the non-compact and compact cases. By using the non-BPS D-particle as a probe of the background geometry of another non-BPS D-particle, we recover the no-force condition at the critical radius and the $v^2$ behaviour of the probe. Moreover, assuming that the no-force persists for the complete geometry we derive part of the classical solution for the non-BPS D-particle.

Critical radius in axial channeling

Abstract: When studying phenomena related to the channeling of charged particles it is of great importance to consider them as functions of the impact parameter. This point of view plays an important role to the interpretation of experimental results as well as to computer simulations. Thus the distance of minimum approach, for which channeling conditions still hold, either under axial or planar channeling is of importance. In the present work we use the Monte-Carlo method to investigate the correlation of the distance of minimum approach of axially channeled particles with the exit angle of those particles from the crystal. We calculated the distance of minimum approach for several incidence angles at different temperatures and for many crystal thickness. The results we obtained prove that the distance of minimum approach has two main properties. (a) It is independent of the crystal thickness and depends only slightly on the incidence angle (as long as the incidence angle does not exceed the Lindhard angle) and slightly decreases with increasing temperature. (b) It agrees with Lindhard’s theory predictions but at the same time it seems that some particles approach too close to the crystal axis without being dechanneled.

The effect of the concentration dependence of a diffusion coefficient on the stability of a growing spherical particle

Abstract: The influence of the concentration dependence of the diffusion coefficient on the stability of a spherical particle growing from a supersaturated solution was studied with the Mullins-Sekerka approximation. The critical radius of stability was found, and it was shown that its value may increase by a factor of more than 1.5 if the concentration dependence of the diffusion coefficient is taken into consideration.