Effect of interfacial tension on propagating polymerization fronts

This paper is devoted to the investigation of polymerization fronts converting a liquid monomer into a liquid polymer. We assume that the monomer and the polymer are immiscible and study the influence of the interfacial tension on the front stability. The mathematical model consists of the reaction-diffusion equations coupled with the Navier-Stokes equations through the convection terms. The jump conditions at the interface take into account the interfacial tension. Simple physical arguments show that the same temperature distribution could not lead to Marangoni instability for a nonreacting system. We fulfill a linear stability analysis and show that interaction of the chemical reaction and of the interfacial tension can lead to an instability that has another mechanism: the heat produced by the reaction decreases the interfacial tension and initiates the liquid motion. It brings more monomer to the reaction zone and increases even more the heat production. This feedback mechanism can lead to the instability if the frontal Marangoni number exceeds a critical value. (c) 2000 American Institute of Physics.     

Numerical modeling of the local relaxation kinetics of the KrF laser

A multilevel mathematical model of the local kinetics of a laser medium of initial composition He-Kr-F₂ is constructed by analyzing the relaxation mechanisms of a plasma produced when an electron beam enters a dense gas. A working program is written for solving with a BÉSM-6 computer the corresponding system of balance equations for the populations and temperatures. Some results of demonstration computations are cited. Ways and prospects of improving the model are discussed.Translated from Trudy Ordena Lenina Fizicheskogo Instituta im. P. N. Lebedeva AN SSSR, Vol. 145, pp. 131–159, 1984.     

Computer-aided molecular modeling of polymers. III. enthalpy of polymerization as a measure of stability

A formalism of computational chemistry methods is presented to estimate the stability of vinyl polymers. This approach takes into account changes in electronic energy upon polymerization using quantum mechanical methods and contributions of the conformational energetics of the polymerized state using a molecular mechanics force field. A work term, ΔV, based upon the molecular volume difference between the monomer and the reactant, is shown to be negligible. For 10 structurally diverse vinyl polymers, the sum of the electronic and conformational energy differences between reactant and monomer states, AEp, has a high linear correlation with corresponding measured enthalpies of polymerization, ΔHp. The linear regression least square fit is ΔHp = 0.89 AEp-13.39. Errors due to possible contributions to AHp not included in the formalism reported here are probably small and/or relatively constant over the set of polymers studied. If this were not the case, a linear correlation between AHp and AEp, with a slope near 1, would not be observed. Most likely the intercept of-13.39 kcal/mol is due to the choice of the quantum mechanical method used, MNDO. Overall, the formalism presented here seems a reliable means of predicting relative polymerization stability, in advance of synthesis, for a structurally congeneric set of polymers.     

The non-linear stability of front solutions for parabolic partial differential equations

For the Ginzburg-Landau equation and similar reaction-diffusion equations on the line, we show convergence ofcomplex perturbations of front solutions towards the front solutions, by exhibiting a coercive functional.     

Existence and stability of propagating fronts for an autocatalytic reaction-diffusion system

We study a one-dimensional reaction-diffusion system which describes an isothermal autocatalytic chemical reaction involving both a quadratic (A + B → 2B) and a cubic (A + 2B → 3B) autocatalysis. The parameters of this system are in the ratio D = D_B/D_A of the diffusion constants of the reactant A and the autocatalyst B, and the relative activity k of the cubic reaction. First, for all values of D > 0 and k ≥ 0, we prove the existence of a family of propagating fronts (or travelling waves) describing the advance of the reaction. In particular, in the quadratic case k = 0, we recover the results of Billingham and Needham [Phil. Trans. R. Soc. London A 334 (1991) 1–24]. Then, if D is close to 1 and k is sufficiently small, we prove using energy functionals that these propagating fronts are stable against small perturbations in exponentially weighted Sobolev spaces. This extends part of the results that are known for the scalar equation to which our system reduces when D = 1.     

Existence and stability of steady fronts in bistable coupled map lattices

We prove the existence and we study the stability of the kinklike fixed points in a simple coupled map lattice (CML) for which the local dynamics has two stable fixed points. The condition for the existence allows us to define a critical value of the coupling parameter where a (multi) generalized saddle-node bifurcation occurs and destroys these solutions. An extension of the results to other CMLs in the same class is also displayed. Finally, we emphasize the property of spatial chaos for small coupling.     

The existence of dendritic fronts

In this paper, we study a fourth order semilinear parabolic equation on the infinite real line. We show that in a certain parameter range, this equation has propagating front solutions (solutions tending to 0 at + and advancing to the right with a speedc) which leave behind them aperiodic pattern in the laboratory frame. This is thus an example of spontaneous pattern formation.     

Population kinetics in turbulent plasmas: The role of non-Markovian fluctuations

A novel approach to the modeling of atomic populations in turbulent plasmas is applied to ionization-recombination balance calculations. Fluctuations of the fluid parameters are retained using a time-dependent statistical approach, suitable for cases where the turbulence characteristic times are of the same order as or smaller than the typical atomic relaxation times. We show that the populations are sensitive to the shape of the autocorrelation function of the fluctuations. An illustration is proposed through an ideal two-level system forced by non-Markovian temperature fluctuations.     

ITER CB超导电缆力学性能数值模拟研究

国际热核试验堆(International Thermonuclear Experimental Reactor,简称ITER)的校正场线圈(Correction Coil,简称CC)采用校正母线(Corrector Busbar,简称CB)连接磁体线圈和电流引线,以传递整个磁体系统所需的电流。CB导体采用的主要是管内电缆导体(Cable-in-Conduit Conductor,简称CICC),而CICC导体的主要结构是由超导线与铜线经过多级绞制而成的超导电缆。利用数值模拟方法给出了CB超导电缆力学模型,并分析了CB超导电缆中超导线的应分布。     

Numerical modeling of fiber grating

The numerical simulation of light wave transmission and reflection in fiber grating is presented. The simulation is based on three-dimensional finite difference time domain algorithm. A method that can make the faint reflected wave distinct and legible is also proposed. With this method, we exhibit light wave reflection and radiation in fiber grating and tilted fiber grating, respectively, in numerical simulation.     

The role of unequal diffusivities in ignition and extinction fronts in strained mixing layers

We have studied flame propagation in a strained mixing layer formed between a fuel stream and an oxidizer stream, which can have different initial temperatures. Allowing the Lewis numbers to deviate from unity, the problem is first formulated within the framework of a thermo-diffusive model and a single irreversible reaction. A compact formulation is then derived in the limit of large activation energy, and solved analytically for high values of the Damköhler number. Simple expressions describing the flame shape and its propagation velocity are obtained. In particular, it is found that the Lewis numbers affect the propagation of the triple flame in a way similar to that obtained in the studies of stretched premixed flames. For example, the flame curvature determined by the transverse enthalpy gradients in the frozen mixing layer leads to flame-front velocities which grow with decreasing values of the Lewis numbers.

The analytical results are complemented by a numerical study which focuses on preferential-diffusion effects on triple flames. The results cover, for different values of the fuel Lewis number, a wide range of values of the Damköhler number leading to propagation speeds which vary from positive values down to large negative values     

Exponential stability of large-amplitude traveling fronts for quasi-linear relaxation systems with diffusion

This paper is concerned with the stability of traveling front solutions for 2×2 quasi-linear relaxation systems with small diffusion rate. By applying geometric singular perturbation method, special Evans function estimates, detailed spectral analysis and C₀ semigroup theories, we prove that all the non-degenerate waves for semi-linear relaxation systems are locally exponentially stable in some exponentially weighted spaces. We also obtain the linear exponential stability of the non-degenerate waves for quasi-linear relaxation systems, where the wave strengths can be large.     

Non-linear scission/recombination kinetics of living polymerization

Living polymers are formed by reversible association of primary units (unimers). Generally the chain statistical weight involves a factor σ < 1 suppressing short chains in comparison with free unimers. Living polymerization is a sharp thermodynamic transition for σ ≪ 1 which is typically the case. We show that this sharpness has an important effect on the kinetics of living polymerization (one-dimensional association). The kinetic model involves i) the unimer activation step (a transition to an assembly-competent state); ii) the scission/recombination processes providing growth of polymer chains and relaxation of their length distribution. Analyzing the polymerization with no chains but unimers at t = 0 , with initial concentration of unimers M ≳ M ^* (M^* is the critical polymerization concentration), we determine the time evolution of the chain length distribution and find that: 1) for M ^* ≪ M ≪ M ^*/σ the kinetics is characterized by 5 distinct time stages demarcated by 4 characteristic times t₁, t₂, t₃ and t^*; 2) there are transient regimes (t ₁ ≲ t ≲ t ₃) when the molecular-weight distribution is strongly non-exponential; 3) the chain scissions are negligible at times shorter than t₂. The chain growth is auto-accelerated for t ₁ ≲ t ≲ t ₂ : the cut-off chain length (= polymerization degree 〈n〉_w N ₁ ∝ t ² in this regime. 4) For t ₂ < t < t ₃ the length distribution is characterized by essentially 2 non-linear modes; the shorter cut-off length N₁ is decreasing with time in this regime, while the length scale N₂ of the second mode is increasing. (5) The terminal relaxation time of the polymer length distribution, t^*, shows a sharp maximum in the vicinity of M^*; the effective exponent is as high as ∼ σ^-1/3 just above M^*.     

A spiral wave front beacon for underwater navigation: basic concept and modeling

A spiral wave front source produces an acoustic field that has a phase that is proportional to the azimuthal angle about the source. The concept of a spiral wave front beacon is developed by combining this source with a reference source that has a phase that is constant with the angle. The phase difference between these sources contains information about the receiver's azimuthal angle relative to the beacon and can be used for underwater navigation. To produce the spiral wave front, two sources are considered: a "physical-spiral" source, which produces the appropriate phase by physically deforming the active element of the source into a spiral, and a "phased-spiral" source, which uses an array of active elements, each driven with the appropriate phase, to produce the spiral wave front. Using finite element techniques, the fields produced by these sources are examined in the context of the spiral wave front beacon, and the advantages of each source are discussed.     

Numerical modeling of transport barrier formation

In diverse media the characteristics of mass and heat transfer may undergo spontaneous and abrupt changes in time and space. This can lead to the formation of regions with strongly reduced transport, so called transport barriers (TB). The presence of interfaces between regions with qualitatively and quantitatively different transport characteristics impose severe requirements to methods and numerical schemes used by solving of transport equations. In particular the assumptions made in standard methods about the solution behavior by representing its derivatives fail in points where the transport changes abruptly. The situation is complicated further by the fact that neither the formation time nor the positions of interfaces are known a priori. A numerical approach, operating reliably under such conditions, is proposed. It is based on the introduction of a new dependent variable related to the variation after one time step of the original one integrated over the volume. In the vicinity of any grid knot the resulting differential equation is approximated by a second order ordinary differential equation with constant coefficients. Exact analytical solutions of these equations are conjugated between knots by demanding the continuity of the total solution and its first derivative. As an example the heat transfer in media with heat conductivity decreasing abruptly when the temperature e-folding length exceeds a critical value is considered. The formation of TB both at a heating power above the critical level and caused with radiation energy losses non-linearly dependent on the temperature is modeled.     

Numerical modeling of low-pressure RF plasmas

A particle-in-cell simulation is used to model the plasma generated in a parallel plate RF reactor at low pressure. Nonperiodic boundary conditions are used, and the electric field and particle motion are obtained by finite-difference methods leading to the self-consistent creation of sheaths on the boundaries. Model cross sections are used to describe collisions between particles. Ionization is included, and the plasma is maintained by fast electrons generated in the RF sheaths. Most of the power dissipation is due to the acceleration of ions in the time-average sheath fields. At high applied voltage, the power dissipation is described well by the power law P∝V^5/2. Simple scaling laws for the density and plasma potential are obtained. The effect of ion mass and charge-exchange colisions on the ion energy spectrum collected by the electrodes is examined. The ion loss rate drops in the presence of charge-exchange collisions, and this leads to an increase in the density. The collisions also markedly alter the ion energy distribution function     

Numerical modeling of magnetic drug targeting

A special focused magnet, designed for the use in the magnetic targeted drug delivery system, was constructed. The theoretical calculation of the adhesion condition for a magnetic fluid drop in magnetic field with obtained design showed that the constructed focused magnet generates a sufficient magnetic force for the capture of a magnetic drop on the vessel wall and can be used 1.5–2 cm deeper in an organism compared with the prism permanent magnet, which can enable non-invasivity of the magnetic drug targeting procedure. The maximal values for magnetic field and gradient of magnetic field are 0.38 T and 101 T/m, respectively.     

Stabilization of the front of polymerization of composite materials in a plug-flow reactor

The polymerization of composite materials in a plug-flow reactor is studied based on the theory of combustion. A two-temperature mathematical model of the self-sustained exothermic polymerization front in a monomer-filler mixture is developed with consideration given to the basic macrokinetic characteristics of the process, exothermicity of the chemical reaction, and heat transfer. The structure of the fields of temperature and concentrations of the reactants in the front is studied. The influence of special heat-transfer elements, preheating the feedstock supplied into the reactor, on the dynamics of the polymerization process and on the stabilization of the polymerization front is examined.     

The effects of fluid motion on oscillatory and chaotic fronts

We study oscillatory and chaotic reaction fronts described by the Kuramoto-Sivashinsky equation coupled to different types of fluid motion. We first apply a Poiseuille flow on the fronts inside a two-dimensional slab. We show regions of period doubling transition to chaos for different values of the average speed of Poiseuille flow. We also analyze the effects of a convective flow due to a Rayleigh-Taylor instability. Here the front is a thin interface separating two fluids of different densities inside a two-dimensional vertical slab. Convection is caused by buoyancy forces across the front as the lighter fluid is under a heavier fluid. We first obtain oscillatory and chaotic solutions arising from instabilities intrinsic to the front. Then, we determine the changes on the solutions due to fluid motion.