Diffusion effects on the interfacial tension of immiscible polymer blends

Most methods of measuring the interfacial tension between two immiscible polymers are based on the analysis of the shape that a drop of one polymer immersed in the other one exhibits under the action of flow or gravity. In such a situation, the small, yet nonzero mutual solubility between the two polymers acts toward mass transfer between the drop and the surrounding fluid. In this work, diffusion effects on the interfacial tension of the pair polyisobutylene/polydimethylsiloxane have been investigated by drop deformation under shear flow. When the drop was made of polyisobutylene, drop size decreased with time due to diffusion. Drop shrinkage was associated with a significant increase in interfacial tension, until an apparent plateau value was reached. The effect was attributed to a selective migration of molecular weights, which would act to enrich the drop with higher molar mass material. To support such an interpretation, drop viscosity was evaluated by drop shape analysis and it was actually found to increase with time. In some cases, the ratio between drop and continuous phase viscosity became higher than the critical value for drop breakup in shear flow. Upon inverting the phases (i.e., when the drop was made of polydimethylsiloxane), no significant transient effects were observed. In the light of these results, the problem of what are the correct values of interfacial tension and viscosity ratio for a polymer blend of a certain composition will also be discussed. Received: 25 January 1999 Accepted: 24 May 1999     

Diffusion of hydrocarbons in confined media: Translational and rotational motion

Diffusion of monatomic guest species within confined media has been understood to a good degree due to investigations carried out during the past decade and a half. Most guest species that are of industrial relevance are actually polyatomics such as, for example, hydrocarbons in zeolites. We attempt to investigate the influence of non-spherical nature of guest species on diffusion. Recent molecular dynamics (MD) simulations of motion of methane in NaCaA and NaY, benzene in NaY and one-dimensional channels AlPO₄−5, VPI−5 and carbon nanotube indicate interesting insights into the influence of the host on rotational degrees of freedom and orientational properties. It is shown that benzene in one-dimensional channels where the levitation parameter is near unity exhibits translational motion opposite to what is expected on the basis of molecular anisotropy. Rotational motion of benzene also possesses rotational diffusivities aroundC ₆ and C₂axes opposite to what is expected on the basis of molecular geometry. Methane shows orientational preference for 2+ 2 or 1 + 3 depending on the magnitude of the levitation parameter.     

Wetting and evaporation behaviors of molten Mg on partially oxidized SiC substrates

The wetting and evaporation behaviors of molten Mg drops on pressureless-sintered SiC surfaces were studied in a flowing Ar atmosphere at 973-1173 K by an improved sessile drop method. The initial contact angles are between 83° and 76°, only mildly depending on temperature. The formation of a ridge at the triple junction as a result of reaction between molten Mg and the SiO₂ film on the SiC surface pins the triple line and leads to a constant contact diameter mode during the entire evaporation process. Moreover, the diffusion coefficients of the Mg vapor at different temperatures were evaluated based on a simple model.     

Long range effect of ion irradiation on diffusion

Argon ion irradiation enhanced diffusion between Cu and Ni was found beyond the radiation effect zone in classical theory. The enhanced diffusion effect attenuates along with the distance between the diffusion zone and the radiated surface. An interpretation based on irradiation induced discrete breathers was employed as a possible mechanism.     

Threshold control of mutual insurance with limited commitment

We study the optimal premium policy of mutual insurance when the charged premium cannot be higher than a preset rate. We provide a complete solution to the problem and use numerical simulations to illustrate how the optimal premium policy responds to changes of outside factors. The results are useful for mutual insurance firms to design premium policies and can be used to test the behavior of these firms in empirical studies.     

A note on the central limit theorem for bipower variation of general functions

In this paper we present a central limit theorem for general functions of the increments of Brownian semimartingales. This provides a natural extension of the results derived in [O.E. Barndorff-Nielsen, S.E. Graversen, J. Jacod, M. Podolskij, N. Shephard, A central limit theorem for realised power and bipower variations of continuous semimartingales, in: From Stochastic Analysis to Mathematical Finance, Festschrift for Albert Shiryaev, Springer, 2006], where the central limit theorem was shown for even functions. We prove an infeasible central limit theorem for general functions and state some assumptions under which a feasible version of our results can be obtained. Finally, we present some examples from the literature to which our theory can be applied.     

Taylor–least-squares finite element for two-dimensional advection-dominated unsteady advection–diffusion problems

A new finite element method, the Taylor–least-squares, is proposed to approximate the advection-dominated unsteady advection–diffusion equation. The new scheme is a direct generalization of the Taylor–Galerkin and least-squares finite element methods. Higher-order spatial derivatives in the new formulation necessitate higher-degree polynomials. Hermite cubic shape functions are used. Extensive comparisons with other methods in one dimension proved that the new scheme is a step forward in modelling this difficult problem. The method offers straightforward generalizations to higher dimensions without losing the accuracy demonstrated in one dimension, i.e. the method preserves the important property of the Taylor–Galerkin scheme of being free of numerical crosswind diffusion. Several numerical experiments were made in two dimensions and excellent results were obtained from the representative experiments.     

Global dynamics behaviors for a nonautonomous Lotka–Volterra almost periodic dispersal system with delays

A nonautonomous Lotka–Volterra dispersal system with continuous delays and discrete delays is considered. By using a comparison theorem and delay differential equation basic theory, we obtain sufficient conditions for the permanence of the population in every patch. By constructing a suitable Lyapunov functional, we prove that the system is globally asymptotically stable under some appropriate conditions. Using almost periodic functional hull theory, we get sufficient conditions for the existence, uniqueness and globally asymptotical stability for an almost periodic solution. This implies that the population in every patch exhibits stable almost periodic fluctuation. Furthermore, the results show that the permanence and global stability of system, and the existence and uniqueness of a positive almost periodic solution, depend on the delay; then we call it “profitless”.