Surface tension modifies the evolution of the Rayleigh-Taylor and the Richtmyer-Meshkov instabilities in fluids undergoing a constant acceleration or a shock, respectively. We analyze the general case of N fluids with arbitrary densities and surface tensions and derive the eigenvalue equation determining the growth rate of the perturbations. For N=2 we recover the classical case of two semi-infinite fluids and extend it to the case of two finite-thickness fluids between fixed boundaries. The N=3 case is studied in detail; we find universal modes that are independent of the thickness of the intermediate fluid, and we find how surface tension modifies Taylor’s modes for a single fluid with free boundaries. We also analyze in detail recent and future two- or three-fluid experiments. Representing a shock as an impulsive acceleration we find that post-shock oscillations have frequencies and amplitudes that depend on the wave number k, leading to a nontrivial evolution for the spectrum of perturbations. Finally, we study turbulence at the interface between two fluids with surface tension and present specific predictions for the turbulent energy ${\mathit{E}}_{\mathrm{turbulent}}$ as function of the surface tension ${\mathit{T}}^{\left(\mathit{s}\right)}$. We propose new experiments, physical and/or numerical, to test our predictions.

We consider the Reynolds-number dependence of various higher-order quantities evaluated at a single spatial point in an incompressible turbulent flow. In particular, we consider ${\mathit{A}}_{\mathit{p}}$=〈(∂u/∂x${)}^{\mathit{p}}$〉, which gives the moments of the velocity derivative distribution, and ${\mathit{B}}_{\mathit{n}}$=〈(${\mathrm{\partial }}^{\mathit{n}}$u/∂${\mathit{x}}^{\mathit{n}}$${)}^2$〉, which gives the 2nth moment of the energy spectrum E(k). We assume that multifractal scaling in the inertial range can be extrapolated down to the locally fluctuating Kolmogorov microscale η(α), and we average over the distribution of η(α) using the appropriate multifractal spectrum f(α). We show that the scaling of ${\mathit{A}}_{\mathit{p}}$ and ${\mathit{B}}_{\mathit{n}}$ is the same if n=p-1. For n=1 and p=2, this gives the known result that the average energy dissipation is constant. For n=2 and p=3, this determines the scaling of the velocity derivative skewness or of the mean-square second derivative. These should scale together according to the Navier-Stokes equations, and we recover this result from the scaling analysis. For n=3 and p=4, the velocity derivative flatness is related to the sixth moment of the energy spectrum. In the limit of large p, we obtain a new relation between the exponential tail of the probability distribution of ∂u/∂x, and the exponential tail of the energy spectrum E(k). We compare our results for the skewness and flatness of velocity derivatives to an earlier result of Meneveau and Sreenivasan [Nucl. Phys. B Proc. Suppl. 2, 49 (1987)], and we suggest that a multiscaling analysis of the Reynolds-number dependence of E(k) might lead to an improved degree of universality.

The upper bound is calculated for the average power output of an irreversible heat engine whose working fluid is viscous and not necessarily uniform in temperature. The calculation is done via the generalized formalism of finite-time thermodynamics. The working fluid of the heat engine is described by partial-differential equations containing parameters in the boundary conditions. With some restrictions on parameters, the estimated power coincides with the optimal power output for the classical lumped-parameter (uniform-T) irreversible Carnot engine.

The Newtonian mechanics of a many-particle system evolving in time under the influence of an external body potential, that is, an external potential that couples to the center of mass only, is examined. The lack of any other external fields allows the complete separation of the center-of-mass (or external-field-dependent) equations from the internal (or external-field-independent) dynamics. The complete solution of the center-of-mass motion then allows an analytical evaluation of the external body potential contributions to the thermophysical properties of the system. The phenomena of field-induced heating, Taylor-Aris hydrodynamic form for the diffusion tensor, and an analogous hydrodynamic form for the viscosity tensor are derived from microscopic principles. A brief and model-dependent description of equilibrium phenomena is also presented.

Domain boundaries (DB’s) in convection patterns are studied near the onset of convection within the framework of amplitude equations of the Newell-Whitehead-Segel type. It is demonstrated that DB’s of an arbitrary direction are possible between domains occupied by convection rolls with different orientations. Those DB’s are always immobile, and they perform perfect selection of the rolls’ wave numbers. In certain particular cases, exact solutions for DB’s of this type are found, and their stability against long-wave flexural perturbations is established. DB’s between the rolls and a hexagonal pattern in the slightly overcritical case, and between the hexagons and the conduction (quiescent) state in the slightly subcritical case, are investigated as well. In this case, the DB is, generally speaking, moving with a constant velocity. The exponentially weak effect of pinning of the moving DB by a small-scale underlying structure is studied. Formation of DB’s of the ‘‘quiescent-state–hexagon’’ and ‘‘roll-hexagon’’ types near a sidewall is also investigated. The special case of a DB between two systems of rolls, the angle between which is close to π/3 or 2π/3, is studied in detail. This DB is, as a matter of fact, a bound state of two DB’s of the ‘‘roll-hexagon’’ type. Finally, it is demonstrated that in one-dimensional patterns (rolls) a stationary DB is not possible. In this case, a dynamical problem of decay of a DB-like structure is solved.

The microwave absorption of certain water soluble polymers (polyethylene glycol, polyvinyl pyrrolidone, proteins, and DNA) in solution is composed of three parts: absorption in the free water, absorption in the substance, and absorption in the hydration layer. Ethanol, sucrose, glycerol, and sodium acetate, which form weak hydrogen bonds or have an ionic nature in aqueous solutions, also have microwave absorption signatures similar to polymers that form hydration layers. The frequency-dependent absorption of the free water and of the hydration layer water is described by a simple Debye relaxation model. The absorption per unit sample volume attributable to the hydration layer is solute concentration dependent, and a simple model is used to describe the dependence. The hydration-layer relaxation time was found to vary from substance to substance and with solute concentration. The relaxation time was also found to be independent of solute length.

Experiments on a system of two magnetic holes (nonmagnetic microspheres in ferrofluid) subject to a rotating magnetic field show various types of behavior depending on the driving frequency. For two spheres (holes) mechanically bound together the stable rotation mode at low frequencies is replaced above a critical frequency by a mode with alternating rotation directions. This is described by simple nonlinear equations, and simulations show good quantitative agreement with the experiments. For two free spheres not bound together one observes a transition to a mode in which the spheres undergo both angular and radial motion around the center of mass of the system. Depending on the frequency and the anisotropy of the rotating magnetic field the motion passes through a sequence of states with sphere rotation mode-locked to the driving frequency at different ratios in good qualitative agreement with simulations. Adding a constant magnetic field normal to the plane causes the minimum sphere separation to increase from contact to a finite value. At high frequencies the spheres are influenced by an effective magnetic potential, giving rise to a static particle separation proportional to the normal component of the field.

If a test particle in a fluid is subject to a scalar field from each molecule of the fluid, the total field experienced by the test particle from N fluid molecules is a random variable whose probability density is often denoted a potential distribution. We develop a general procedure for the calculation of the potential distribution at a real test particle (a molecule of the fluid), based on a generalized, complex pair distribution function. The procedure involves the generalization of integral-equation theory of classical fluids to encompass a system with a complex interaction potential. The mean-spherical approximation for the same problem is studied to motivate a generalized closure of the integral-equation formalism. With this single approximate ingredient, a closed, coupled pair of nonlinear integral equations is obtained and their numerical solution is outlined. For the Gaussian approximation, a simplified version of the same procedure can be used to compute the second moment of the distribution without invoking the Kirkwood superposition approximation. The general method is applied to the calculation of the potential distribution in a one-component plasma.

The main aim of this work is to give a theoretical interpretation for the ‘‘anomalous’’ liquid-structure factors of zinc and cadmium near freezing and for their variation with temperature, as contrasted with the ‘‘normal’’ behavior of a liquid metal such as potassium. Using an ab initio generalized nonlocal model pseudopotential and with two alternative exchange-correlation functions for electronic screening, we construct interionic pair potentials for the above metals. These are then used for liquid-structure calculations within two alternative integral-equation schemes of considerable refinement, namely the modified hypernetted-chain approach of Rosenfeld and Ashcroft [Phys. Rev. A 20, 1208 (1979)] and the hybridization of the hypernetted chain and the soft-core mean spherical approximations as proposed by Zerah and Hansen [J. Chem. Phys. 84, 2336 (1986)]. The comparison between the theoretical results for the temperature dependence of the liquid-structure factor of potassium and very recent neutron-diffraction data gives us confidence in the high reliability of the pseudopotential in the present integral-equation schemes. The same approach is then extended to investigate the liquid-structure factors for zinc and cadmium near their freezing temperature and at a few temperatures above freezing. We find that the asymmetric shape of the main peak in the structure factor of these elements near freezing can be understood in terms of the role of the medium- and long-range interaction parts in the pair potential. Our results also shed some light on the subtle changes of the liquid structure of these divalent metals with temperature, and specifically on the thermal influence in restoring the skewed shape of the main peak back to a normal symmetric shape at much higher temperatures.

We report the shear viscosity measurements carried out in a dilute collidal solution of monodisperse polystyrene particles as a function of the volume fraction of the dispersed phase and for different particles sizes in a completely deionized water suspension and in the presence of a small amount of salt (NaCl). The results are analyzed in the frame of a recent simple model, based on the theory of interaction between electrical double layers, that relates the rheological properties of the system to the interparticle potential. The comparison between the calculated high-frequency shear modulus and the viscosity data show better agreement. Therefore we can confirm the idea that in such systems the rheological behavior can be completely explained in terms of the interparticle potential energy of interaction.

A density-functional theory of nonuniform fluid mixtures—based on a generalization of the one-component weighted-density approximation—is both presented and applied to freezing transitions in binary mixtures of hard spheres. A necessary step in this application is the specification of the crystal structure of the solid phase. Several different structures have been considered, namely, a disordered-fcc structure, three common ordered structures—the CsCl, NaCl, and zinc-blende structures—and a ‘‘sublattice-melt’’ structure (modeling fast-ion conductors). In the case of the disordered-fcc structure, results are reported for the temperature-concentration phase diagram and for freezing parameters, including the coexisting fluid and solid packing fractions, the latent heat of transition, and the Lindemann ratios. Especially interesting is the dependence of these results on the hard-sphere diameter ratio α. In particular, as a function of α the phase diagram is predicted to evolve from a spindle type in the range 1>α>0.94, to an azeotropic type in the range 0.94>α>0.87, and finally to a eutectic type for α<0.87. In comparison with available simulation data, the predictions of the theory are in excellent agreement when normalized to account for small discrepancies in the one-component case, yet in qualitative disagreement with the predictions of earlier density-functional theories, based on different approximations.

Also investigated are the relative stabilities, as a function of α, of the different crystal structures in coexistence with a fluid of equal concentrations of smaller and larger spheres. In particular, in the range 1>α>0.76 the most stable structure is predicted to be disordered fcc. For α<0.76 the two components are found to be completely immiscible in the disordered-fcc solid and the most stable structure is then predicted to be a pure fcc solid composed entirely of larger spheres. The ordered CsCl and NaCl structures are predicted to be metastable (relative to the stable structures) in the ranges 0.86>α>0.63 and 0.63>α>0.05, respectively, the sublattice-melt structure metastable (relative to NaCl) in the range 0.60>α>0.15, and the zinc-blende structure always mechanically unstable. These results for the relative stabilities are again in considerable disagreement with predictions of earlier theories.

We report the results of a measurement of the shear viscosity as a function of the temperature and of the water volume fraction in a three-component sodium di(2-ethylhexyl)sulfosuccinate-decane-water microemulsion. The explored concentration range is 0≤φ≤0.73 and the packing fraction of the water-in-oil spherical droplets has been changed in order to obtain a very dense glass-forming liquid. Well-defined maxima in the relative viscosity have been observed at different concentrations and the corresponding temperature values decrease with increasing φ. The data are discussed considering the system as a colloidal one in which aggregation phenomena are present. In such a way, on the basis of a two-fluid model, we can consider two different contributions to the viscosity. One is directly connected to the repulsive interaction potential, while the second one is directly connected to the attractive interaction that contributes indirectly, through the formation of aggregates. The results are compatible with those previously obtained by light-scattering measurements that gives clear evidence of the presence of a large structural order at the glass transition.

We present a theoretical study of a fluid in a narrow planar capillary, including the effects of the periodic structure of the confining walls. A layering transition had been observed for the same model in a previous Monte Carlo simulation, but it is missing in our density-functional calculation. The transition is recovered with an approach based on the cluster variational method, which treats the free energy as a functional of the four-particle distribution function.

We study fast, salt-induced aggregation of polystyrene spheres by means of low-angle static light scattering covering two decades of scattered wave vector q. The measurements are taken at a fixed salt concentration, varying the monomer concentration from ${\mathit{c}}_0$=1×${10}^9$ to 5×${10}^{10}$ ${\mathrm{cm}}^{\mathrm{-}3}$. During each run, the fractal dimension ${\mathit{d}}_{\mathit{f}}$ of the clusters and the time evolution of the average radius 〈${\mathit{R}}_{\mathit{G}}$〉 and average mass 〈M${\mathrm{〉}}_{\mathit{w}}$ are determined. At larger concentrations we consistently find ${\mathit{d}}_{\mathit{f}}$=1.61±0.02, but, as the concentration is decreased, ${\mathit{d}}_{\mathit{f}}$ grows to 1.83±0.02. The value of ${\mathit{d}}_{\mathit{f}}$ is determined both from the asymptotic behavior of the scattered intensity I(q) and from the relation between the average mass and radius, I(0)∝${\mathit{R}}_{\mathit{G}\mathit{f}}^{\mathit{d}}$. Good agreement is found between the two sets of data. The earlier portions of the curves for ${\mathit{R}}_{\mathit{G}}$ as a function of time t are compatible with a power-law growth and collapse onto a master curve when the reduced time T=${\mathit{c}}_0$t is used. Noticeable deviations from power-law growth are, however, observed at later times. Finally, we show that for the lowest concentrations the reactions stop when the clusters attain a maximum diameter. We present arguments showing that reaction termination is due to sedimentation, the time required to diffuse across intercluster distance becoming longer than the settling time through the sample due to sedimentation.

The growth of ramified metallic deposits by electrodeposition from dilute salt solutions and in a high electric field has been considered in the geometry of a thin rectangular cell. The equations governing ion motion in the case of a dilute electrolyte have been solved numerically and analytically in a one-dimensional (1D) and a 2D approximation. It is found that ramified growth is a direct consequence of the creation of a space charge upon anion depletion in the vicinity of the cathode. The front of the ramified deposit is predicted to advance at a speed just equal to the velocity of the anions in the applied electric field. The presence of this space charge ahead of the growing front is associated with a potential drop δV. Resolution of the equations in the 2D case shows that the dense-parallel morphology of the deposit also results quite naturally from the existence of a space charge in the vicinity of the filament tips. The average filament spacing and sidebranch tilting angle can be directly related to the values of δV and of the applied electric field. The mechanism giving rise to the space charge will apply as well to any physical system involving electric conduction with two types of carriers, if one of them exhibits blocking-contact characteristics.

We have studied cellular shapes in directionally solidified ${\mathrm{CBr}}_4$-${\mathrm{Br}}_2$ and have shown that they follow a scaling law from the planar-cellular threshold ${\mathit{V}}_{\mathit{c}}$ up to about (8–9)${\mathit{V}}_{\mathit{c}}$: the shapes depend on the relative velocity ε=(V-${\mathit{V}}_{\mathit{c}}$)/${\mathit{V}}_{\mathit{c}}$, and not separately on the absolute velocity V or the temperature gradient G. A comparison with Saffman-Taylor profiles is found to be unsatisfactory. We then examined cellular widths and their variation along a given solidification front from threshold up to the appearance of dendrites. Again up to about (8–9)${\mathit{V}}_{\mathit{c}}$, the dispersion is comparable to experimental uncertainties but beyond that point the width of some cells begins to increase spectacularly. These abnormally wide cells change shape, and the widest ones become dendrites once the Péclet number reaches 2–3.

We report on the measurements of electron as well as ion mobility in neon gas at low temperature (close to the critical temperature) and up to very high density (N≊180×${10}^{20}$ ${\mathrm{cm}}^{\mathrm{-}3}$). We have found evidence of localized electron states at densities larger than (90–100)×${10}^{20}$ ${\mathrm{cm}}^{\mathrm{-}3}$. The transition from the region of quasifree states to that of coexisting quasifree and localized states takes place in a density range in fairly good agreement with the predictions of a simple bubble model. The mobility data of the quasifree electron are in disagreement with the actual multiple-scattering theory. The detailed calculation of the mean mobility in the high-density region where localization takes place is still an unsolved problem.

We present in this work refractivity measurements of very high accuracy and reliability in a helium pulsed plasma. The aim of this work is to determine the validity of the approximation based on the assumption that the contribution to the refractivity of the nonelectronic species is constant with wavelength. This approximation is used broadly to obtain the electronic density from refractivity at two wavelengths. Using this method, we have measured five wavelengths to determine this contribution.

A kinetic analysis of the nonlinear evolution of the free-electron-laser (FEL) instability is presented. The governing equations are the coupled Vlasov-Maxwell equations, which are investigated for a system consisting of a relativistic electron beam propagating through a helical wiggler magnetic field. Assuming that a single cavity mode of the electromagnetic field takes part in the lasing, a general nonlinear solution of the Vlasov equation is obtained in the resolvent formalism. Use of this solution in the wave equation provides a nonlinear description of the FEL. The saturation properties of the FEL are discussed by numerical and analytical solutions of this equation.

In this paper we discuss interaction of intense, subpicosecond laser pulses with plasmas. We propose a self-consistent analytical model of the anomalous and normal skin effects in plasmas with steplike density profile. The heat transport is described by classical Spitzer conductivity with new boundary conditions accounting for laser absorption in the thin skin layer. We obtain self-similar solutions for the heat-conduction problem, and the scaling laws for important plasma parameters are also discussed. Our predictions are consistent with the recent experimental results.