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Register a new userEquilibrium thermodynamic properties of two-component and two phase mixtures
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We present general calculations allowing to express the thermodynamical coefficients and thermophysical properties (compressibility, thermal coefficients and heat capacities) of a material composed of a mixture of two constituents or phases, regardless of the equations of state considered for each of the constituant or for the mixture. We consider mixtures under complete thermodynamical equilibrium, either with mass exchange between the two constituents (phase change), such as an oil and gas mixture (black-oil) and water-vapor system or with two immiscible phases, such as air and water mixtures (foam). Keywords Thermodynamic coefficient, Thermophysical properties, thermal coefficients, speed of sound, two phase systems, liquid vapor equilibrium
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The zero-temperature phase diagram of binary mixtures of particles interacting via a screened Coulomb pair potential is calculated as a function of composition and charge ratio. The potential energy obtained by a Lekner summation is minimized among a variety of candidate two-dimensional crystals. A wealth of different stable crystal structures is identified including $A,B,AB_2, A_2B, AB_4$ structures [$A$ $(B)$ particles correspond to large (small) charge.] Their elementary cells consist of triangular, square or rhombic lattices of the $A$ particles with a basis comprising various structures of $A$ and $B$ particles. For small charge asymmetry there are no intermediate crystals besides the pure $A$ and $B$ triangular crystals.
Classical MD data on the charge-charge dynamic structure factor of two-component plasmas (TCP) modeled in Phys. Rev. A 23, 2041 (1981) are analyzed using the sum rules and other exact relations. The convergent power moments of the imaginary part of the model system dielectric function are expressed in terms of its partial static structure factors, which are computed by the method of hypernetted chains using the Deutsch effective potential. High-frequency asymptotic behavior of the dielectric function is specified to include the effects of inverse bremsstrahlung. The agreement with the MD data is improved, and important statistical characteristics of the model TCP, such as the probability to find both electron and ion at one point, are determined.
We study the global influence of curvature on the free energy landscape of two-dimensional binary mixtures confined on closed surfaces. Starting from a generic effective free energy, constructed on the basis of symmetry considerations and conservation laws, we identify several model-independent phenomena, such as a curvature-dependent line tension and local shifts in the binodal concentrations. To shed light on the origin of the phenomenological parameters appearing in the effective free energy, we further construct a lattice-gas model of binary mixtures on non-trivial substrates, based on the curved-space generalization of the two-dimensional Ising model. This allows us to decompose the interaction between the local concentration of the mixture and the substrate curvature into four distinct contributions, as a result of which the phase diagram splits into critical sub-diagrams. The resulting free energy landscape can admit, as stable equilibria, strongly inhomogeneous mixed phases, which we refer to as antimixed states below the critical temperature. We corroborate our semi-analytical findings with phase-field numerical simulations on realistic curved lattices. Despite this work being primarily motivated by recent experimental observations of multi-component lipid vesicles supported by colloidal scaffolds, our results are applicable to any binary mixture confined on closed surfaces of arbitrary geometry.
Partial Quantum Nearest Neighbor Probability Density Functions (PQNNPDFs) are formulated for the purpose of determining the behavior of quantum mixed systems in equilibrium in a manner analogous to that provided for classical multi-component systems. Developments in partial quantum m-tuplet distribution functions, a generalization of the partial quantum radial distribution function, along with their relationship to PQNNPDFs, are briefly elucidated. The calculation of statistical thermodynamic properties of quantum mixtures is presented for arbitrary material systems. Application to the limiting case of dilute, weakly correlated quantum gas mixtures has been outlined and the second virial coefficient is derived. The case of dilute strongly degenerate mixtures is also addressed, providing an expression for the PQNNPDF applicable in this thermodynamic regime.
We present a new approach to simulating mixtures of gas and dust in smoothed particle hydrodynamics (SPH). We show how the two-fluid equations can be rewritten to describe a single-fluid mixture moving with the barycentric velocity, with each particle carrying a dust fraction. We show how this formulation can be implemented in SPH while preserving the conservation properties (i.e. conservation of mass of each phase, momentum and energy). We also show that the method solves two key issues with the two fluid approach: it avoids over-damping of the mixture when the drag is strong and prevents a problem with dust particles becoming trapped below the resolution of the gas. We also show how the general one-fluid formulation can be simplified in the limit of strong drag (i.e. small grains) to the usual SPH equations plus a diffusion equation for the evolution of the dust fraction that can be evolved explicitly and does not require any implicit timestepping. We present tests of the simplified formulation showing that it is accurate in the small grain/strong drag limit. We discuss some of the issues we have had to solve while developing this method and finally present a preliminary application to dust settling in protoplanetary discs.
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