Paul L. Chambré

On the Solution of the Poisson‐Boltzmann Equation with Application to the Theory of Thermal Explosions

The theory of thermal explosions originally proposed by Frank‐Kamenetzky has been the subject of a number of investigations. The critical condition of inflammability requires the solution of the nonlinear Poisson‐Boltzmann differential equation. For the case of a reaction vessel of cylindrical or spherical shape the solution was obtained by previous investigators by numerical integration of the equation. It is shown, however, in the following that the solutions can be obtained in terms of known functions.

On the Diffusion of a Chemically Reactive Species in a Laminar Boundary Layer Flow

A chemically reactive species is emitted from the surface of a body located in a hydrodynamic flow field. It diffuses into the fluid where it undergoes a simple isothermal, homogeneous transformation. The analysis given enables one to trace the reaction history of this component in a laminar boundary layer flow which develops over the surface of a body.For illustration the development of a first‐order reaction in the neighborhood of a flat plate is calculated. Two reaction types are considered. In one case the reactant is destroyed; in the other, it is generated. The reaction histories show a number of interesting features which are discussed in some detail.

On Chemical Surface Reactions in Laminar Boundary Layer Flows

The progress of an isothermal chemical reaction on a catalytic surface, which is located in a laminar hydrodynamic flow field of large Reynolds number, is analyzed. Past analytical investigations have been restricted primarily to chemical reactions in fully velocity developed flow fields subject frequently to one or both of the following approximations. (i) The actual velocity distribution is replaced by a flow of uniform velocity. (ii) The concentrations of the reactants on the catalytic surface are prescribed subject to certain hypotheses concerning the rate controlling mechanism.In this investigation the principal aim has been to calculate the actual surface concentration in a laminar boundary layer flow without unduly sacrificing the hydrodynamic features or introducing unnecessary assumptions about the effective over‐all reaction mechanism. The method presented, which is related to an analysis of convective heat transfer from a nonisothermal surface, is applicable to arbitrary catalytic reaction mech...

Nonlinear Heat Transfer Problem

A study has been made of the time‐dependent heat conduction in a semi‐infinite medium subject to a boundary condition which can involve the temperature in a nonlinear manner. A formulation for the determination of the surface temperature, which is often of greatest physical interest, leads to a nonlinear Volterra integral equation. A simple iterative solution method, with an accuracy suitable for many practical purposes is presented. As an example, the problem of the time‐dependent surface temperature of a body receiving heat according to the Stefan‐Boltzmann law is treated. The analysis is also applicable to physical adsorption or chemisorption processes which occur at the boundary.

On chemical surface reactions in hydrodynamic flows

A general basis for the formulation of flow problems involving chemical reactions on solid surfaces is laid. The analysis allows one to trace a reaction history of arbitrary complexity in a general class of boundary layer type flow fields which cover both external as well as internal flows under isothermal and non-isothermal conditions.

Analytic Studies of Colloid Transport in Fractured Porous Media

We analyze the interactive migration of radioactive colloids and solute in fractured rock. Two possible interactions between radionuclides as colloids and as solute are considered: solute sorption on nonradioactive colloids to form pseudocolloids, and dissolution of radioactive colloids. Previous studies have discussed the formation and transport of colloids in porous media, including removal of colloids by filtration and sedimentation. Colloids can migrate faster than solute because of weaker sorption on stationary solids and because of hydrochromatography of colloid particles in flow channels. However, the migration of colloids and pseudocolloids can be retarded by the interaction of colloids with solute, and the migration of solute in local equilibrium with colloids can be more rapid than if colloids were not present. Here we present a new quantative analysis to predict the interactive migration of colloids and solute in porous and fractured media. 4 figs.

On the time-dependent lévêque problem☆

Abstract The classical steady state Leveque problem is generalized to include the time dependence. Exact analytical solutions are presented for the surface heat flux due to a time step in the surface temperature and for the case of the surface temperature due to a time step in the wall heat flux. The initial and final time behavior of the solution is explored analytically and this is supplemented by a numerical evaluation for the entire time span in the case of a step in the surface temperature.

On the Ignition of a Moving Combustible Gas Stream

The ignition phenomenon in a chemically reactive gas flowing about a heated body is discussed. Specifically the conditions at the forward stagnation point of the object are analyzed. A condition is formulated which relates the critical surface temperature for ignition with those parameters which control the heat and mass transport and the reaction kinetic mechanism.

Relationship Among Performance of Geologic Repositories, Canister-Array Configuration, and Radionuclide Mass in Waste

Abstract The relationship among the repository performance, the canister-array configuration, and the radionuclide mass in waste has been investigated by developing a radionuclide-transport model, where multiple waste canisters and their spatial configuration are taken into account. A mathematical analysis and numerical results show that the radionuclide concentration in the groundwater leaving the canister array increases with the number of canisters included in a water stream parallel to the array axis, but not necessarily in a linear manner. The dependency on the number of canisters is determined mainly by canister-array configuration to the water flow and by model assumptions for transport between multiple canisters. Reduction in the initial mass loading in the waste can potentially have significant effects on the repository performance. The way the mass-reduction effects on the repository performance appear is related to the canister-array configuration. Thus, designs for a repository and a partitioning-transmutation system should be done in a coupled manner.

Considerations of Autocatalytic Criticality of Fissile Materials in Geologic Respositories

Potential routes to autocatalytic criticality in geologic repositories are systematically assessed. If highly enriched uranium (HEU) or {sup 239}Pu are transported and deposited in concentrations similar to natural uranium ore, in principle, criticality can occur. For some hypothesized critical configurations, removal of a small fraction of pore water provides a positive feedback mechanism that can lead to supercriticality. Rock heating and homogenization for these configurations can also significantly increase reactivity. At Yucca Mountain, it is highly unlikely that these configurations can occur; plutonium transport would occur primarily as colloids and deposit over short distances. HEU solute can move large distances in the Yucca Mountain setting; its ability to precipitate into critical configurations is unlikely because of a lack of active reducing agents. Appropriate engineering of the waste form and the repository can reduce any remaining probability of criticality.