On inhibiting runaway in catalytic reactors

We consider the problem of heat and mass transfer in porous catalyst pellets. Both the steady and time dependent operating characteristics are studied. Accurate approximate equations are derived from the basic governing equations of motion. A nonlinear stability analysis is employed to account for the observation that under certain conditions reactions on catalyst pellets can pass transiently stably into a region which would correspond to instability in the steady state. One consequence of our analysis is a possible control mechanism which inhibits temperature runaway by extending the stable operating characteristics desirable in modern reactors

On the Birth of Isolas

Isolas are isolated, closed curves of solution branches of nonlinear problems. They have been observed to occur in the buckling of elastic shells, the equilibrium states of chemical reactors and other problems. In this paper we present a theory to describe analytically the structure of a class of isolas. Specifically, we consider isolas that shrink to a point as a parameter τ of the problem, approaches a critical value τ_0. The point is referred to as an isola center. Equations that characterize the isola centers are given. Then solutions are constructed in a neighborhood of the isola centers by perturbation expansions in a small parameter ε that is proportional to (τ-τo), with a appropriately determined. The theory is applied to a chemical reactor problem

Filtration Combustion in Smoldering and SHS

Smolder waves and SHS (self-propagating high-temperature synthesis) waves are both examples of filtration combustion waves propagating in porous media. Smoldering combustion is important for the study of fire safety. Smoldering itself can cause damage, its products are toxic and it can also lead to the more dangerous gas phase combustion which corresponds to faster propagation at higher temperatures. In SHS , a porous solid sample, consisting of a finely ground powder mixture of reactants, is ignited at one end. A high temperature thermal wave, having a frontal structure, then propagates through the sample converting reactants to products. The SHS technology appears to enjoy a number of advantages over the conventional technology, in which the sample is placed in a furnace and "baked" until it is "well done". The advantages include shorter synthesis times, greater economy, in that the internal energy of the reactions is employed rather than the costly external energy of the furnace, purer products, simpler equipment and no intrinsic limitation on the size of the sample to be synthesized as exists in the conventional technology. When delivery of reactants through the pores to the reaction site is an important aspect of the combustion process, it is referred to as filtration combustion. The two types of filtration combustion have a similar mathematical formulation, describing the ignition, propagation and extinction of combustion waves in porous media. The goal in each case, however, is different. In smoldering the desired goal is to prevent propagation, whereas in SHS the goal is to ensure propagation of the combustion wave, leading to the synthesis of desired products. In addition, the scales in the two areas of application differ. Smoldering generally occurs at lower temperatures and propagation velocities than in SHS nevertheless, the two applications have much in common so that what is learned fit make application can be used to advantage in the other. In porous media, melting often occurs ahead of the propagating combustion wave. In certain cases there is so much melting that the porous solid structure is destroyed, e.g., by melting and a suspension arises, consisting of a liquid bath containing solid particles and/or gas bubbles. The resulting combustion wave is referred to as a liquid flame. We have considered a number of problems involving filtration combustion. Here, we describe four such studies: (A) rapid buoyant filtration combustion waves; (B) diffusion driven combustion waves; (C) rapidly propagating liquid flames in gravitational fields; and (D) gas-phase influence on liquid flames in gravitational fields

Argonne National Laboratory Reports

The deformation of a thin elastic plate which is initially wrinkled when the plate is subjected to a constant compressive end thrust is considered. The singularly perturbed bifurcation theory of Reiss and Matkowsky is used. It is found that the initial deformation (imperfection) of the plate leads to solutions which explain the experimentally observed decrease in the buckling load from that predicted by bifurcation theory and the smooth transition to a buckled solution

Argonne National Laboratory Reports

A previously developed perturbation method is used to obtain a new class of periodic motions for the nonlinear vibrations of rectangular, elastic plates. The dynamic von Karman plate theory is used in the analysis. The new solutions arise by secondary bifurcation from the periodic solutions that bifurcate from the natural frequencies of free vibrations of the linearized plate theory. The new motions are a linear combination of two modes of the linearized theory

Argonne National Laboratory Reports

Facilitated transport is a process, whereby the diffusion of a solute across a membrane is chemically enhanced. In this report an analysis is given of a facilitated transport system involving a volatile species A which reacts with a nonvolatile carrier species B to form the nonvolatile product AB

Argonne National Laboratory Reports

In this report it is shown that a burner placed in a combustible fluid can have a stabilizing effect on a plane flame. A mathematical model is derived in which the flame is modeled as a surface of discontinuity in the flow field. Jump conditions for the fluid variables, as well as an expression for the flame speed, are obtained from an asymptotic analysis of the detailed structure of the flame. The model is applied to investigate the linear stability of a plane flame. Stable behavior is shown to exist for certain regimes of the parameters: Lewis number, burner strength, heat release and inflow velocity