On models of polydisperse sedimentation with particle-size-specific hindered-settling factors

Polydisperse suspensions consist of particles differing in size or density that are dispersed in a viscous fluid. During sedimentation, the different particle species segregate and create areas of different composition. Spatially one-dimensional mathematical models of this process can be expressed as strongly coupled, nonlinear systems of first-order conservation laws. The solution of this system is the vector of volume fractions of each species as a function of depth and time, which will in general be discontinuous. It is well known that this system is strictly hyperbolic provided that the Masliyah–Lockett–Bassoon (MLB) flux vector is chosen, the particles have the same density, and the hindered-settling factor (a multiplicative algebraic expression appearing in the flux vector) does not depend on the particle size but is the same for all species. It is the purpose of this paper to prove that this hyperbolicity result remains valid in a fairly general class of cases where the hindered-settling factor does depend on particle size. This includes the common power-law type hindered-settling factor in which the exponent, sometimes called Richardson–Zaki exponent, is determined individually for each species, and is a decreasing function of particle size. The importance of this paper is two-fold: it proves stability for a class of polydisperse suspensions that was not covered in previous work, and it offers a new analysis of real data.     

Etude de phases quaternaires Winsor IV. Diagrammes de phases et propriétés electriques

A comparative study of phase diagram features and electrical properties of Winsor IV phases (so-called microemulsions) led to define two types of quaternary systems involving water, a hydrocarbon, and an ionic surfactant/alcohol combination defined byk, the surfactant/alcohol mass ratio. Systems of the first type exhibit a Winsor IV domain consisting of two disjointed areas corresponding to water-in-oil (w/o) and oil-in-water (o/w) monophasic fluid transparent isotropic media. The w/o and o/w areas are separated by a composition zone over which exist viscous turbid long-range organized structures related to the o/w w/o phase inversion mechanism. In that case, over the w/o area, the low frequency electrical conductivity and permittivity undergo non-monotonous changes as the composition varies. From conductivity maxima and minima, it is possible to define in the general case two lines ₁ and ₂ separating three adjacent sub-areas to which can be assigned compositions representing pre-micellar entities, inverted swollen spherical micelles and micelles clusters. For systems of the second type, the w/o and o/w sub-areas merge so as to form a unique monophasic area, which implies that the w/o o/w phase inversion occurs through a progressive diffuse mechanism. In that case the conductivity exhibits much higher values than in the preceding situation, and its variations with composition allow to define two linesC _d andC _m partitioning the Winsor IV domain into three adjacent areas. AboveC _d , that is for low and medium water contents, the conductivity variations with water content follow equations derived from the Percolation and Effective Medium theories, which indicates that the w/o swollen spherical micelles are submitted to attractive interactions. Below C_m, i. e. in the water rich region, the conductivity decrease with water content results from the progressive dilution of the external aqueous phase of the o/w Winsor IV media. BetweenC _d andC _m , the Winsor IV media exhibit an anomalous conductive behaviour which suggests that they are neither w/o nor o/w systems. This region can be considered as the diffuse phase inversion zone over which the systems are in a hybrid state that could be depicted tentatively as resulting from the formation of equilibrium bicontinuous structures.

     

Exploiting structure in piecewise-linear homotopy algorithms for solving equations

We consider the recent algorithms for computing fixed points or zeros of continuous functions fromR ⁿ to itself that are based on tracing piecewise-linear paths in triangulations. We investigate the possible savings that arise when these fixed-point algorithms with their usual triangulations are applied to computing zeros of functionsf with special structure:f is either piecewise-linear in certain variables, separable, or has Jacobian with small bandwidth. Each of these structures leads to a property we call modularity; the algorithmic path within a simplex can be continued into an adjacent simplex without a function evaluation or linear programming pivot. Modularity also arises without any special structure onf from the linearity of the function that is deformed tof. In the case thatf is separable we show that the path generated by Kojima's algorithm with the homotopyH ² coincides with the path generated by the standard restart algorithm of Merrill when the usual triangulations are employed. The extra function evaluations and linear programming steps required by the standard algorithm can be avoided by exploiting modularity.This research was performed while the author was visiting the Mathematics Research Center, University of Wisconsin-Madison, and was sponsored by the United States Army under Contract No. DAAG-29-75-C-0024 and by the National Science Foundation under Grant No. ENG76-08749.     

Influence of tetraalkylammonium ions on structure of nonaqueous solvents

Summary The half-wave potentials of the redox system [Co(en)₃]³⁺/[Co(en)₃]²⁺ have been influenced by the tetraalkylamonium cation of the supporting electrolyte used. This was explained with the specific interactions (solvation) of the tetraalkylamonium ion with the nonaqueous solvent.

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Einfluß von Tetraalkylammoniumionen auf die Struktur nichtwäßriger Lösungsmittel (Kurze Mitt.)

Zusammenfassung Das Halbwellenpotential des Redoxsystems [Co(en)₃]³⁺/[Co(en)₃]²⁺ wird von Tetraalkylammonium-Ionen des Stützelektrolyten beeinflußt. Dies wird durch die spezifischen Wechselwirkungen (Solvatation) der Ionen mit dem nichtwäßrigen Lösungsmittel erklärt.

     

非水溶液盐效应的气液色谱研究——非电解质(烃、芳烃、氯代烃、酮)+盐(NaI、NaSCN、KSCN)+碳酸丙烯酯体系

由于碳酸丙烯酯(PC)具有较宽的液相区间(mp:224.0K,bp:514.9K)、较高的介电常数(64.92,298.15K)和较大的偶极矩(4.94D),它是一个在工业和科学研究中有广泛应用的非质子型极性溶剂。已有大量文献就PC溶液中电解质-PC、非电解质-PC和离子-离子间的相互作用情况作了报导。对于非电解质-电解质-PC三元系中溶质-溶剂间的相互作用情况还缺乏了解。本文希望通过测定非电解质溶质在PC的电解质溶液中的无限稀释活度系数γ_1~∞,对非水溶液中的溶质-溶剂作用情况有新的了解。气液色谱法(CLC)是测定无限稀释溶液活度系数的有效方法之一。作者曾利用GLC测定了一些烃、氯代烃、醇、酮在环丁砜电解质溶液中的无限稀释活度系数和盐效应常数.     

Symmetric homotopy construction

Homotopy continuation methods can be applied to compute all finite solutions to a given polynomial system. Computations will be performed more efficiently if the symmetric structure of the system can be exploited. This paper presents the construction of a symmetric homotopy. Using this homotopy, only the paths according to the generating solutions have to be traced during continuation.     

Branch-and-bound methods for solving systems of Lipschitzian equations and inequalities

In this note, we show how branch-and-bound methods previously proposed for solving broad classes of multiextremal global optimization problems can be applied for solving systems of Lipschitzian equations and inequalities over feasible sets defined by various types of constraints. Some computational results are given.This research was accomplished while the second author was a fellow of the Alexander von Humboldt Foundation at the University of Trier, Trier, West Germany.     

Decomposition of arborescent linear programs

We apply what we call sequential projection to reformulate certain linear programs as recursive optimization problems. We then apply the standard idea of approximating the return function at each stage of the recursion by using inner (or outer) linearization, and iteratively refining the approximation until the original linear program has been solved. The contribution of the paper lies in its unification of existing decomposition approaches and in showing that they can be generalized to apply to what we call arborescent linear programs.     

An advanced implementation of the Dantzig—Wolfe decomposition algorithm for linear programming

Since the original work of Dantzig and Wolfe in 1960, the idea of decomposition has persisted as an attractive approach to large-scale linear programming. However, empirical experience reported in the literature over the years has not been encouraging enough to stimulate practical application. Recent experiments indicate that much improvement is possible through advanced implementations and careful selection of computational strategies. This paper describes such an effort based on state-of-the-art, modular linear programming software (IBM's MPSX/370).