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Using a simple mean field density functional theory (DFT), the authors investigate the structure and phase behavior of a model colloidal fluid composed of particles interacting via a pair potential which has a hard core of diameter σ, is attractive Yukawa at intermediate separations, and is repulsive Yukawa at large separations. The authors analyze the form of the asymptotic decay of the bulk fluid correlation functions, comparing results from DFT with those from the self-consistent Ornstein-Zernike approximation (SCOZA). In both theories the authors find rich crossover behavior, whereby the ultimate decay of correlation functions changes from monotonic to long wavelength damped oscillatory decay on crossing certain lines in the phase diagram or sometimes from oscillatory to oscillatory with a longer wavelength. For some choices of potential parameters the authors find, within the DFT, a λ line at which the fluid becomes unstable with respect to periodic density fluctuations. SCOZA fails to yield solutions for state points near such a λ line. The propensity towards clustering of particles, which is reflected by the presence of a long wavelength (>σ) slowly decaying oscillatory pair correlation function, and a structure factor that exhibits a very sharp maximum at small but nonzero wave numbers, is enhanced in states near the λ line. The authors present density profiles for the planar liquid-gas interface and for fluids adsorbed at a planar hard wall. The presence of a nearby λ transition gives rise to pronounced long wavelength oscillations in the one-body density profiles at both types of interface. [ABSTRACT FROM AUTHOR]

Using density functional theory we calculate the density profiles of a binary solvent adsorbed around a pair of big solute particles. All species interact via repulsive Gaussian potentials. The solvent exhibits fluid-fluid phase separation, and for thermodynamic states near to coexistence the big particles can be surrounded by a thick adsorbed “wetting” film of the coexisting solvent phase. On reducing the separation between the two big particles we find there can be a “bridging” transition as the wetting films join to form a fluid bridge. The effective (solvent mediated) potential between the two big particles becomes long ranged and strongly attractive in the bridged configuration. Within our mean-field treatment the bridging transition results in a discontinuity in the solvent mediated force. We demonstrate that accounting for the phenomenon of bridging requires the presence of a nonzero bridge function in the correlations between the solute particles when our model fluid is described within a full mixture theory based upon the Ornstein–Zernike equations. [ABSTRACT FROM AUTHOR]

We investigate the solvation of a hard spherical cavity, of radius R, immersed in a fluid for which the interparticle forces are short ranged. For thermodynamic states lying close to the liquid binodal, where the chemical potential deviation δμ≡μ-μco(T) is very small and positive, complete wetting by gas (drying) occurs and two regimes of interfacial behavior can be identified. These are characterized by the length scale Rc=2γgl∞/(Δρδμ), where γgl∞ is the planar gas–liquid surface tension and Δρ is the difference in coexisting densities at temperature T. For R>Rc, the interfacial free energy and the density profile of the fluid near the hard wall can be expanded in powers of the curvature R-1, in keeping with the analysis of Stillinger and Cotter [J. Chem. Phys. 55, 3449 (1971)]. In the other regime, R

We present an alternative derivation of the dynamical density functional theory for the one-body density profile of a classical fluid developed by Marconi and Tarazona [J. Chem. Phys. 110, 8032 (1999)]. Our derivation elucidates further some of the physical assumptions inherent in the theory and shows that it is not restricted to fluids composed of particles interacting solely via pair potentials; rather it applies to general, multibody interactions. The starting point for our derivation is the Smoluchowski equation and the theory is therefore one for Brownian particles and as such is applicable to colloidal fluids. In the second part of this paper we use the dynamical density functional theory to derive a theory for spinodal decomposition that is applicable at both early and intermediate times. For early stages of spinodal decomposition our nonlinear theory is equivalent to the (generalized) linear Cahn–Hilliard theory, but for later times it incorporates coupling between different Fourier components of the density fluctuations (modes) and therefore goes beyond Cahn–Hilliard theory. We describe the results of calculations for a model (Yukawa) fluid which show that the coupling leads to the growth of a second maximum in the density fluctuations, at a wave number larger than that of the main peak. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The density profile ρ(z) and Gibbs adsorption Γ of a near-critical fluid confined between two identical planar walls is studied by means of Monte Carlo simulation and by density functional theory for a Lennard-Jones fluid. By reducing the strength of wall–fluid interactions relative to fluid–fluid interactions we observe a crossover from behavior characteristic of the normal surface universality class, strong critical adsorption, to behavior characteristic of a “neutral” wall. The crossover is reminiscent of that which occurs near the ordinary surface transition in Ising films subject to vanishing surface fields. For the “neutral” wall ρ(z), away from the walls, is almost constant throughout the slit capillary and gives rise to a Γ that is constant along the critical isochore. The same “neutral” wall yields a line of capillary coexistence that is almost identical to the bulk coexistence line. In the crossover regime we observe features in ρ(z) similar to those found in the magnetization profile of the critical Ising film subject to weak surface fields, namely two smooth maxima, located away from the walls, which merge into a single maximum at midpoint as the strength of the wall–fluid interaction is reduced or as the distance between walls is decreased. We discuss similarities and differences between the surface critical behavior of fluids and of Ising magnets. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The thermodynamics of fluids confined between two adsorbing solid substrates (walls) is revisited. Attention is focused on the phase equilibria of an open system characterized by the variables μ (chemical potential), T (temperature), and H (wall separation). Clapeyron equations for the shape of lines of coexistence are derived and used to interpret the results of earlier calculations of two first-order transitions, namely capillary condensation of an undersaturated ‘‘gas’’ to ‘‘liquid’’ and prewetting (thick–thin film transition) at finite H. At such transitions the adsorption Γ and the solvation force f jump discontinuously. Criticality of a confined fluid is associated with the divergence of the derivatives (∂Γ/∂μ)T,H and (∂2Γ/∂μ2)T,H or equivalently, with the divergence of (∂f/∂H)T,μ and (∂2f/∂H2)T,μ. The presence of the additional field variable H, and its conjugate density f, implies that the phase equilibria of a confined fluid can be much richer than those of a bulk fluid or of a single interface (H=∞). By extending the formalism to multicomponent systems Clapeyron equations are derived for the coexistence of phases in confined fluid mixtures. An equation for the shift in chemical potential (or concentration) of the phase separation curve of a binary liquid mixture resulting from confinement at constant pressure and temperature is presented. This equation, which becomes exact for large separations H, is the appropriate analog for mixtures of the Kelvin equation used to describe capillary condensation in pure fluids; it can also be regarded as a generalization to nonzero concentrations of the Ostwald–Freundlich formula for the dependence of solubility on particle size. Our analysis provides a framework for interpreting recent solvation force measurements on phase-separating liquid... [ABSTRACT FROM AUTHOR]

By means of a density functional approach the phase equilibria of a simple fluid confined by two adsorbing walls have been investigated as a function of wall separation H and chemical potential μ for temperature T corresponding to both partial and complete wetting situations. For large values of H and small undersaturations Δμ ≡ μsat-μ, we recover the macroscopic formulas for the undersaturation at which a first- order phase transition (capillary condensation) from dilute ‘‘gas’’ to a dense ‘‘liquid’’ occurs in a single, infinitely long slit. For smaller H we compute the lines of coexistence between gas and liquid in the (Δμ, 1/H) plane at fixed values of T. The adsorption Γ(Δμ), at fixed T and H, is characterized by a loop. At the first order transition Γ jumps discontinuously by a finite amount; however metastable states exist and these could give rise to hysteresis of the adsorption isotherms obtained for the single slit. The loop disappears at a capillary critical point (Δμc, 1/Hc) at each T. For HΔμc, condensation can no longer occur and no metastable states are present. The location of the critical points is described and for a complete wetting situation we find that these lie outside the bulk two phase region. Our theory provides a simple explanation of phase transitions observed in earlier computer simulations and mean-field lattice gas calculations for confined fluids and suggests that measurements of the forces between plates, either by simulation or in real fluids, should provide rather direct information about capillary condensation and, possibly, capillary critical points. The relevance of our results for adsorption experiments on mesoporous solids is discussed briefly. [ABSTRACT FROM AUTHOR]

We examine the properties of perturbed spherically imploding shock waves in an ideal fluid through the collapse, bounce, and development into an outgoing shock wave. We find broad conservation of the size and shape of ingoing and outgoing perturbations when viewed at the same radius. The outgoing shock recovers the velocity of the unperturbed shock outside the strongly distorted core. The results are presented in the context of the robustness of the shock ignition approach to inertial fusion energy. [ABSTRACT FROM AUTHOR]

Using a simple density functional theory (DFT) the height of the free energy barrier for forming a droplet of the liquid phase from the metastable gas phase is determined for a model colloidal fluid exhibiting competing interactions. The pair potential has a hard core of diameter σ, is attractive Yukawa at intermediate separations, and is repulsive Yukawa at large separations. It is found that even a very weak long-range repulsive tail in the pair potential has a profound effect on nucleation: increasing the amplitude of the repulsive Yukawa tail reduces significantly the free energy barrier height and therefore increases the liquid droplet nucleation rate. The method introduced for calculating the droplet density profile and free energy employs a fictitious external potential to stabilize a liquid droplet of the desired size, i.e. with a given excess number of particles. For the critical droplet, corresponding to an extremum of the grand potential, this fictitious potential is everywhere zero. The decay of the droplet density profiles into the bulk gas is examined. For a range of nucleation state points the DFT predicts exponentially damped, long wavelength oscillatory decay for systems exhibiting long-range repulsion, contrasting sharply with the monotonic decay found when the pair potential has only an attractive Yukawa piece. The changes in nucleation properties found for small amplitudes of the repulsive Yukawa tail reflect the propensity of the fluid to form modulated structures such as clusters or stripes. [ABSTRACT FROM PUBLISHER]

The fluid flow characteristics near top dead centre (TDC) were numerically simulated for three different combustion chambers designed to generate squish flow and enhance turbulence generation in spark ignition engines. One of the combustion chambers was a plain bowl-in-piston type while the remaining two were different configurations of the squish-jet chamber, which has a unique geometry for forming jets that converge radially inwards as TDC is approached. The computational fluid dynamics (CFD) code KIVA-3V was used to produce the simulations and particular attention was given to mean velocities and turbulent fluctuations near TDC. The flow fields were measured experimentally (with particle image velocimetry (PIV) and laser Doppler velocimetry (LDV)) in a unique rapid-intake and compression machine, and compared with the output from the KIVA-3V code. The use of the rapid-intake and compression machine enabled the initial conditions to match exactly those in the KIVA-3V calculations, thus reducing uncertainty in the validation study. The study led to a greater understanding of the flow processes inside these complex combustion chambers and the results showed that squish-jet chambers tend to generate higher peak turbulence levels than do plain bowl-in-piston chambers, even though they may generate lower mean squish velocities. From this perspective, the KIVA code can be a useful tool for designing squish-jet combustion chambers. The study also showed that KIVA-3V predicted downstream squish jet velocities well. Nevertheless, the squish-jet velocities at the piston bowl rim were overestimated and the specific turbulent kinetic energy (k) and its dissipation (e) appear to have been overestimated during much of the compression period tested. [ABSTRACT FROM AUTHOR]

Fluid flow characteristics near top dead centre (TDC) were measured in three different combustion chambers designed to generate squish flow and to enhance turbulence generation in internal combustion engines. One of the combustion chambers was a plain bowl-in-piston type, whereas the remaining two were different configurations of the squishjet chamber, which has a unique geometry for forming jets that converge radially inwards as TDC is approached. Both particle image velocimetry (PIV) and laser Doppler velocimetry (LDV) were used to measure mean velocities and turbulent fluctuations near to TDC. To accurately and consistently set the initial and boundary conditions, the University of British Columbia Rapid Intake and Compression Machine (UBC-RICM) was used. The microscopic particles used for PIV and LDV seeding were introduced into the cylinder by a novel system developed to suit the momentary flow in the UBC-RICM. The experimental study led to a greater understanding of the flow processes inside these complex combustion chambers. The results also indicated that squish-jet chambers tend to generate higher levels of turbulence than plain bowl-in-piston chambers do, even though they may generate lower mean squish velocities. These results will also be used in a future study to assess the validity of squish flow predictions made by the computational fluid dynamic code, KIVA-3V. [ABSTRACT FROM AUTHOR]

Various manifestations of structural crossover in the properties of a binary mixture of hard-spheres are studied. For homogeneous mixtures that are sufficiently asymmetric, there is a crossover line in the phase diagram such that for thermodynamic states that lie on one side, the decay of the three bulk pair correlation functions is oscillatory with a common wavelength approximately equal to the diameter of the smaller spheres, and for states on the other side, the common wavelength is approximately the diameter of the bigger spheres. Using density functional theory it is shown that structural crossover manifests itself in the intermediate range decay of (i) the one-body density profiles of a hard-sphere mixture adsorbed at planar walls, (ii) the effective (depletion) potential between two big hard-spheres immersed in the same binary mixture, and (iii) the solvation force, or excess pressure, of the same mixture confined between two planar hard walls. The structural crossover line is determined exactly for a one-dimensional binary mixture of hard-rods and evidence is presented, based on density functional theory calculations and Monte-Carlo simulations, for structural crossover in homogeneous binary mixtures of hard-disks in two dimensions. By considering a multicomponent mixture of hard-spheres, with an appropriate bimodal distribution of diameters, it is argued that structural crossover should still occur in the presence of polydispersity and that these results could be relevant to colloidal mixtures where correlation functions can be measured using real-space techniques. [ABSTRACT FROM AUTHOR]

The screened Coulomb (Yukawa) restricted primitive model (Y RPM) of a binary fluid is treated within the one-pole generalized mean-spherical approximation (GMSA). Fluid phase behaviour and structure are compared with the corresponding results for the unscreened Coulombic RPM. Screening increases the critical density and temperature above the values for the RPM and decreases the width of the liquid-gas coexistence curves. The asymptotics of pairwise correlation functions and the genesis of disorder lines in the phase diagram are discussed. These lines are where the ultimate decay of total density or concentration (charge) correlations crosses over from monotonic to oscillatory. The location of the disorder lines is strongly dependent on the range of the Yukawa potentials. We show that very shortrange interionic potentials (Yukawa models) can give rise to correlation functions which are difficult to distinguish (at all interionic separations) from those obtained for the long-range Coulombic case for structurally equivalent thermodynamic states, reinforcing the idea that pronounced charge ordering is not unique to Coulombic interactions but can occur whenever the interaction potential between different species (AB) is strongly attractive and the potentials between identical species (AA and BB) are repulsive. Although the GMSA generally improves upon the MSA, we show that it leads to artificial peaks (not found in simulation) for correlations g(r)between identical ionic species at separations r close to ionic contract when the density is high and the temperature is low. This failing, which occurs for both the RPM and Y RPM, reflects the sensitivity of g(r) near contact to approximations.ii. [ABSTRACT FROM AUTHOR]

The Fisher-Widom (FW) line is the locus of points in the density-temperature (rho, T) plane where the longest range decay of the pairwise correlation function of a fluid crosses over from monotonic to damped oscillatory decay. The FW line for a hard-core potential with an attractive Yukawa tail is calculated using two integral equation theories, the random phase approximation and the mean spherical approximation. Although the pole structure of the structure factor in this fluid is similar to that determined for model fluids with finite ranged potentials, the FW line is shifted far from the critical point and intersects the liquid branch of the coexistence curve at a much lower reduced temperature T/Tc than is found for the square-well or truncated Lennard-Jones models. The dependence of the FW line on the choice of model and approximate theory is discussed. [ABSTRACT FROM AUTHOR]