Stability of convective patterns in reaction fronts: a comparison of three models

Autocatalytic reaction fronts generate density gradients that may lead to convection. Fronts propagating in vertical tubes can be flat, axisymmetric, or nonaxisymmetric, depending on the diameter of the tube. In this paper, we study the transitions to convection as well as the stability of different types of fronts. We analyze the stability of the convective reaction fronts using three different models for front propagation. We use a model based on a reaction-diffusion-advection equation coupled to the Navier-Stokes equations to account for fluid flow. A second model replaces the reaction-diffusion equation with a thin front approximation where the front speed depends on the front curvature. We also introduce a new low-dimensional model based on a finite mode truncation. This model allows a complete analysis of all stable and unstable fronts.     

Surface tension driven flow on a thin reaction front

Surface tension driven convection affects the propagation of chemical reaction fronts in liquids. The changes in surface tension across the front generate this type of convection. The resulting fluid motion increases the speed and changes the shape of fronts as observed in the iodate-arsenous acid reaction. We calculate these effects using a thin front approximation, where the reaction front is modeled by an abrupt discontinuity between reacted and unreacted substances. We analyze the propagation of reaction fronts of small curvature. In this case the front propagation equation becomes the deterministic Kardar-Parisi-Zhang (KPZ) equation with the addition of fluid flow. These results are compared to calculations based on a set of reaction-diffusion-convection equations.     

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.     

The effect of convection on a propagating front with a liquid product: Comparison of theory and experiments

This work is devoted to the investigation of propagating polymerization fronts converting a liquid monomer into a liquid polymer. We consider a simplified mathematical model which consists of the heat equation and equation for the depth of conversion for one-step chemical reaction and of the Navier-Stokes equations under the Boussinesq approximation. We fulfill the linear stability analysis of the stationary propagating front and find conditions of convective and thermal instabilities. We show that convection can occur not only for ascending fronts but also for descending fronts. Though in the latter case the exothermic chemical reaction heats the cold monomer from above, the instability appears and can be explained by the interaction of chemical reaction with hydrodynamics. Hydrodynamics changes also conditions of the thermal instability. The front propagating upwards becomes less stable than without convection, the front propagating downwards more stable. The theoretical results are compared with experiments. The experimentally measured stability boundary for polymerization of benzyl acrylate in dimethyl formamide is well approximated by the theoretical stability boundary. (c) 1998 American Institute of Physics.     

Global Solutions to a Reactive Boussinesq System with Front Data on an Infinite Domain

We prove the existence of global solutions to a coupled system of Navier–Stokes, and reaction-diffusion equations (for temperature and mass fraction) with prescribed front data on an infinite vertical strip or tube. This system models a one-step exothermic chemical reaction. The heat release induced volume expansion is accounted for via the Boussinesq approximation. The solutions are time dependent moving fronts in the presence of fluid convection. In the general setting, the fronts are subject to intensive Rayleigh-Taylor and thermal-diffusive instabilities. Various physical quantities, such as fluid velocity, temperature, and front speed, can grow in time. We show that the growth is at most for large time t by constructing a nonlinear functional on the temperature and mass fraction components. These results hold for arbitrary order reactions in two space dimensions and for quadratic and cubic reactions in three space dimensions. In the absence of any thermal-diffusive instability (unit Lewis number), and with weak fluid coupling, we construct a class of fronts moving through shear flows. Although the front speeds may oscillate in time, we show that they are uniformly bounded for large t. The front equation shows the generic time-dependent nature of the front speeds and the straining effect of the flow field. Received: 15 January 1996 / Accepted: 2 September 1997     

Double-diffusive cellular fingering in the horizontally propagating fronts of the chlorite-tetrathionate reaction

Horizontally propagating chemical fronts have been studied in the acid-catalyzed chlorite-tetrathionate reaction. Unusual cellular fingers develop in a relatively thin solution layer. Double-diffusive convection is among the driving forces in the pattern formation arising from the addition of a polyelectrolyte which immobilizes and reversibly removes the autocatalyst hydrogen ion in a controlled manner and drastically slows down the front. Convection therefore becomes significant in the thin horizontal solution layer. To corroborate our results we have measured the solution densities and viscosities, and determined the diffusion coefficients by PFGSE .     

竖直圆管中超临界压力CO2对流换热实验研究

本文对超临界压力CO2在竖直加热圆管内的对流换热进行了实验研究,比较了不同流向、不同热流密度等对流动和换热的影响。实验结果表明,管内径为2mm时,在低进口Re条件下,由于浮升力影响导致层流向湍流提前转变, 对流换热增强;与向上流动相比,向下流动更易由层流转变为湍流;向下流动的换热要强于向上流动,表明浮升力对换热有很大影响。对于管内径为0．27 mm的微细圆管,当进口Re高于104时,浮升力的影响可以忽略,对流换热系数的变化完全由物性的变化尤其是cp的变化导致。     

细圆管内超临界二氧化碳对流换热的实验研究

本文对超临界压力二氧化碳在内径为1 mm的竖直细圆管中的对流换热进行了实验研究.分析了流体的热流密度、进口温度、质量流量以及流动方向对超临界压力二氧化碳对流换热的影响.实验研究发现,热流密度、进口温度、质量流量以及浮升力对细圆管内对流换热的影响很大,对流换热系数在准临界温度附近存在峰值.在加热的前半段向上流动的对流换热强于向下流动,在加热的后半段则相反.随着热流密度与质量流量比值的不断增加,向上流动与向下流动对流换热强弱转换的交点不断向流体进口方向推移,并且向上流动的壁面温度出现峰值,发生换热恶化,而向下流动则没有出现换热恶化.     

Dynamics of A + B --> C reaction fronts in the presence of buoyancy-driven convection

The dynamics of A+B-->C fronts in horizontal solution layers can be influenced by buoyancy-driven convection as soon as the densities of A, B, and C are not all identical. Such convective motions can lead to front propagation even in the case of equal diffusion coefficients and initial concentration of reactants for which reaction-diffusion (RD) scalings predict a nonmoving front. We show theoretically that the dynamics in the presence of convection can in that case be predicted solely on the basis of the knowledge of the one-dimensional RD density profile across the front.     

Dynamics of Front Driven by Convection Field in Bistable Media

The front dynamics driven by a convection field in a model of FitzHugh-Nagumo type is studied both analytieMly and numerically. Saddle-node bifurcation induced by the convection field is found by using a singular perturbation analysis of front solutions. Convection field accelerates the B1och front propagating opposite the direction of convection field, but inhibits the Bloch front propagating along the direction of convection field. In addition convection field drives Ising front to travel opposite the direction of convection field.     

A hybrid level set method for modelling detonation and combustion problems in complex geometries

We present an accurate and fast wave tracking method that uses parametric representations of tracked fronts, combined with modifications of level set methods that use narrow bands. Our strategy generates accurate computations of the front curvature and other geometric properties of the front. We introduce data structures that can store discrete representations of the location of the moving fronts and boundaries, as well as the corresponding level set fields, that are designed to reduce computational overhead and memory storage. We present an algorithm we call stack sweeping to efficiently sort and store data that is used to represent orientable fronts. Our implementation features two reciprocal procedures, a forward ‘front parameterization’ that constructs a parameterization of a front given a level set field and a backward ‘field construction’ that constructs an approximation of the signed normal distance to the front, given a parameterized representation of the front. These reciprocal procedures are used to achieve and maintain high spatial accuracy. Close to the front, precise computation of the normal distance is carried out by requiring that displacement vectors from grid points to the front be along a normal direction. For front curves in two dimensions, a cubic interpolation scheme is used, and G ¹ surface parameterization based on triangular patches is used for the three-dimensional implementation to compute the distances from grid points near the front. To demonstrate this new, high accuracy method we present validations and show examples of combustion-like applications that include detonation shock dynamics, material interface motions in a compressible multi-material simulation and the Stephan problem associated with dendrite solidification.     

Influence of heat losses on nonlinear fingering dynamics of exothermic autocatalytic fronts

Across traveling exothermic autocatalytic fronts, a density jump can be observed due to changes in composition and temperature. These density changes are prone to induce buoyancy-driven convection around the front when the propagation takes place in absence of gel within the gravity field. Most recent experiments devoted to studying such reaction-diffusion-convection dynamics are performed in Hele-Shaw cells, two glass plates separated by a thin gap width and filled by the chemical solutions. We investigate here the influence of heat losses through the walls of such cells on the nonlinear fingering dynamics of exothermic autocatalytic fronts propagating in vertical Hele-Shaw cells. We show that these heat losses increase tip splittings and modify the properties of the flow field. A comparison of the differences between the dynamics in reactors with respectively insulating and conducting walls is performed as a function of the Lewis number Le, the Newton cooling coefficient α quantifying the amplitude of heat losses and the width of the system. We find that tip splitting is enhanced for intermediate values of α while coarsening towards one single finger dominates for insulated systems or large values of α leading to situations equivalent to isothermal ones.     

超临界CO2在烧结多孔圆管中换热的实验研究

本文对超临界压力二氧化碳在烧结多孔介质的竖直圆管中的对流换热进行了实验研究。分析了入口温度超过准临界温度、颗粒直径为0．2-0．28 mm的多孔圆管中,压力、流量、热流密度以及流动方向对超临界二氧化碳对流换热的影响。结果表明,准临界点附近剧烈变物性的影响使得超临界二氧化碳在多孔结构中的对流换热非常复杂。对流换热随着温度远离准临界温度和热流密度的增加不断减弱;流量对对流换热的影响比较复杂。在准临界温度附近,浮升力对换热有一定的影响。     

曲率相关的爆轰波在非结构四边形网格上的数值方法

假设爆轰波阵面的法向速度是曲率的线性函数,在非结构四边形网格上采用水平集方法模拟爆轰波阵面的运动过程.水平集方程的曲率无关项采用正格式离散,曲率项采用伽辽金等参有限元方法空间离散,时间离散采用半隐格式.在笛卡儿网格和随机网格上,含曲率的水平集方程的离散格式为强一阶精度,重新初始化方程的离散格式精度为近似一阶精度.曲率收缩的不光滑界面和多个爆轰波阵面相互作用的算例说明格式可有效地模拟爆轰波与曲率相关的运动.     

毛细管内液氮的自然对流换热数值计算分析

主要探讨了毛细管管径以及倾角对其内的加热丝与液氮的换热效果的影响。应用FLUENT软件对0、30、60、90倾角下管径为1.2mm和2.0mm的毛细管内的加热丝与液氮的换热情况进行了三维数值模拟,得到了管内液氮的速度、温度以及加热丝的温度分布情况。数值计算结果与实验结果吻合的比较好。计算结果表明倾角为30°和60°的换热效果最好,大管径下的换热情况要比小管径的换热效果好。     

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.     

Poiseuille advection of chemical reaction fronts

Poiseuille flow between parallel plates alters the shapes and velocities of chemical reaction fronts. In the narrow-gap limit, the cubic reaction-diffusion-advection equation predicts a front-velocity correction equal to the gap-averaged fluid velocity epsilon. In the singular wide-gap limit, the correction equals the midgap fluid velocity 3epsilon/2 when the flow is in the direction of propagation of the reaction front, and equals zero for adverse flow of any amplitude for which the front has a midgap cusp. Stationary fronts are possible only for adverse flow and finite gaps. Experiments are suggested.     

Experimental evidence of thermal vibrational convection in a nonuniformly heated fluid in a reduced gravity environment

We report experimental evidence of convection caused by translational vibration of nonuniformly heated fluid in low gravity. The theory of vibrational convection in weightlessness is well developed but direct experimental proof has been missing. An innovative point of the experiment is the observation of a temperature field in the front and side views of the cubic cell. In addition, particle tracing is employed. The evolution of this field is studied systematically in a wide range of frequencies and amplitudes. The flow structures reported in previous numerical studies are confirmed. The transition from four-vortex flow to the pattern with three vortices is observed in the transient state.     

Dynamic transition in the structure of an energetic crystal during chemical reactions at shock front prior to detonation

Mechanical stimuli in energetic materials initiate chemical reactions at shock fronts prior to detonation. Shock sensitivity measurements provide widely varying results, and quantum-mechanical calculations are unable to handle systems large enough to describe shock structure. Recent developments in reactive force-field molecular dynamics (ReaxFF-MD) combined with advances in parallel computing have paved the way to accurately simulate reaction pathways along with the structure of shock fronts. Our multimillion-atom ReaxFF-MD simulations of l,3,5-trinitro-l,3,5-triazine (RDX) reveal that detonation is preceded by a transition from a diffuse shock front with well-ordered molecular dipoles behind it to a disordered dipole distribution behind a sharp front.     

Linear stability of planar solidification fronts

We review, extend and modify the classical linear stability theory of planar solidification fronts in Langer's moving symmetric model. Using a new integral equation for the front position, we compute an exact linear stability equation and solve it exactly for an important special case. The classical theory is seen to be the long-time limit of the exact solution. Finally, we show how to treat a general planar front, using a short-time approximation. Our conclusions generalize those of previous analyses, by treating initial temperature field perturbations and the resulting transient growth phenomena.