Attila R. Imre

Electrochemical determination of the fractal dimension of fractured surfaces

An electrochemical method, based on the analysis of the time dependence of the diffusional flux of molecular species to a surface, for accurately (⩽ ± 0.02) determining the fractal dimension of rough surfaces 2 ⩽ Df < 2.4) in the 1–100 μm size range is described. We discuss how this method can be used for the measurement of the fractal dimension of fractured steel surfaces prepared by the Charpy impact test.

Lattice Boltzmann methods for two-phase flow modeling

Abstract In this paper the most important properties of the lattice Boltzmann methods are reviewed with focus on two-phase flow modeling. The lattice methods are compared with the conventional computational fluid dynamics methods, their advantages and disadvantages are highlighted. Necessary improvements for practical applications are summarized.

Liquid-liquid demixing from solutions of polystyrene. 1. A review. 2. Improved correlation with solvent properties

Low pressure liquid–liquid demixing data for polystyrene dissolved in 76 different one‐component solvent systems are reviewed and correlated. The phase diagrams are discussed. With only one exception the molecular weight of each solvent is less than that of two polystyrene monomer units. A new relation is developed which quantitatively correlates the area of solubility lying between the UCS and LCS demixing curves in the (Tc, Mw−1/2) projection with solvent solubility parameters.

Thermodynamics of negative pressures in liquids

Nature uses negative pressures in the most resourceful and efficient ways. Yet, negative pressure states are still sometimes considered inaccessible by part of the scientific community. In this paper we show that any condensed phase can exist in absolute negative pressure regimes, while the same is not true for gas phases. We also demonstrate that such states are not merely possible but have, in spite of their metastability, been observed experimentally on numerous occasions. Moreover, physical properties of several substances and mixtures have already been determined in the stretched liquid phase at absolute negative pressures. Nevertheless, conceiving of and succeeding in an experiment that produces high tension in a liquid are rather difficult. Thus, equations of state and computer simulations are powerful tools for studying metastable liquids. By using a simple equation of state we show: how negative pressure regimes can be attained; the maximum intrinsic tension a liquid can sustain; and below which temperature a liquid can be found in this state. Experimental and theoretical work on liquids at negative pressures is reviewed. Furthermore, the similarities and differences between negative temperature and negative pressure states are demonstrated. Due to waters non-trivial behavior as well as its technological and scientific importance, it has been the most studied substance in metastable phenomena. We will thus devote particular attention to some of the rich features of its metastable phase diagram. Water belongs to a class of substances that presents density anomalies. We also show how the negative pressure region of the phase diagram proves to be paramount in understanding the unusual behavior of this class of substances.

Diffusion kinetics at fractal electrodes

Abstract Rough, porous or partially active electrodes are often modelled as fractals and the laws of electrode kinetics are derived accordingly. The theories dealing with diffusion-controlled currents towards fractal interfaces are surveyed and their applicability to real rough electrode surfaces is discussed.

Estimation of the liquid-vapor spinodal from interfacial properties obtained from molecular dynamics and lattice Boltzmann simulations

Interfacial pressure and density profiles are calculated from molecular dynamics and lattice Boltzmann simulations of a liquid film in equilibrium with its vapor. The set of local values of tangential pressure and density along an interface exhibits a van der Waals-type loop; starting from the stable vapor bulk phase one passes through metastable and unstable states to the stable liquid bulk phase. The minimum and maximum values of the profile of tangential pressure are related to the liquid and vapor spinodal states, respectively. The spinodal pressures turn out to be linearly related to the extreme values of the tangential pressure in the interface. The comparison with equations of state shows good agreement with the simulation results of the spinodals. In addition the properties of the metastable region are obtained. Based on this investigation a method is proposed for the estimation of the liquid spinodal from experimentally obtained interfacial properties. Estimations for water and helium are presented.

Liquid–liquid equilibria in polymer solutions at negative pressure

Properties of liquids under tension (i.e. at negative pressure) are discussed together with methods of producing negative pressure. That established, the pressure dependence of liquid–liquid demixing in certain polymer–solvent solutions, including demixing at negative pressure is described.

The relation of interface properties and bulk phase stability: molecular dynamics simulations of carbon dioxide.

The limit of metastability, the so-called spinodal, is calculated for pure carbon dioxide by molecular dynamics simulation. The determination of the spinodal is based on properties of the liquid vapor interface using a recently developed method. This method relates the tangential pressure component through the vapor-liquid interface to the van der Waals loop in the two-phase region of the phase diagram. By application of the thermodynamic stability criteria, the location of the spinodal can be determined. The spinodal determined in this way is called interface spinodal here. Furthermore, the simulation provides equation of state properties in the complete metastable region of the phase diagram. The performance of different correlation equations for the density and the pressure tensor profiles with respect to the estimation of the spinodal is compared. It has been found that the interface spinodal coincides with the thermodynamic mean field spinodal within some reasonable deviation. Finally the influence of the size of the simulation box on the spinodal properties is investigated showing that the temperature-density spinodal data are independent of the interface thickness. Additional simulations using a Lennard-Jones fluid confirm these results over a range of 1.5 orders of magnitude for the systems size. A further result is that interface systems require a very long simulation time in order to obtain reliable results.

Stability limits in binary fluids mixtures

The stability limits in binary fluid mixtures are investigated on the basis of the global phase diagram approach employing a model for the attracting hard-sphere fluid. In addition to the diffusion spinodals the mechanical spinodals are included. As a result one finds topologically different types of the diffusion spinodals while only one shape exists for the mechanical spinodals which are present in the region of liquid-vapor equilibria only. The diffusion spinodals represent the underlying properties of the phase behavior. The types of stable phase behavior therefore resemble that of the spinodal behavior. The different shapes of the spinodals can be important for nonequilibrium processes in nature and technology.

Fractal dimension of time-indexed paths

Abstract Measuring animal track or other trajectories (for example, the track of a flowing particle) by divider method to obtain the fractal dimension without knowing the chronology of the points of the path, one can obtain erroneous results. The importance of time-indexing of the track’s point will be demonstrated by a simply geometrical example. Neglecting these indices, the error can be high enough to mask relevant differences between various movement paths.