Mark Nelson's Research Interests

My main research interests are in combustion theory (AMS Classification: 80A25 Combustion; 80A30 Chemical kinetics; 80A32 Chemically reacting flows; 92E20 Classical flows, reactions, etc.). The mainstay of my work is the application of bifurcation theory, continuation methods and dynamical systems methodology.

My current research interests are:

1. The combustion of polymeric materials and their fire-retarded modifications. (1990-Present)
2. Catalytic combustion. (1997-Present)
3. Microwave heating of porous solids. (1998-Present)
4. Flammability limits of simple chemical reactions. (1999-present)

I am particularly interested in problems involving a strong interaction with experimentalists and which involve an understanding of physical chemistry, especially those involving chemical kinetics.

The Combustion of Polymeric Materials

Polymeric materials are widely used in buildings and construction applications and there is considerable interest in reducing their fire hazard. The combustion of solid polymers is a complicated process involving physical phenomena that are only partially understood. Simple mathematical models are being developed in order to gain an insight into the combustion characteristics of such materials.

• The development of mathematical models for fire engineering tests that are commonly used to investigate flammability; in particular, thermal analysis, radiative ignition tests (specifically the cone calorimeter), the limiting oxygen index test and the extinction oxygen index test.
• The development of conceptually simple models using accepted fire-engineering approximations, such as thermal pyrolysis and critical mass flux models;
• The development of more complicated models, involving the coupling of gas-phase and solid-phase processes, to investigate under what conditions the approximations mentioned above are valid.
• I have shown shown that thermoplastic combustion is either sustaining or non-sustaining, in the absence of an external irradiance, depending upon if the steady-state diagram is, or is not, physically disjoint. The design of materials which are represented by non physically disjoint steady-state diagrams is of considerable practicle interest. I am therefore interested in how physically-disjoint diagrams can be destroyed by the addition of a suitable fire-retardant.
• To what extent can materials performance in a medium scale test be predicted from its performance in a smaller scale test? This is an important industrial problem in the design and synthesis of new fire-retardant systems.
• The existence/non-existence of physically disjoint steady-state diagrams has strong implications for relative flammability ranking of materials depending upon if the ignition source is applied throughout the test or if it is applied for a subsection of the test.
• Investigating the effect that different classes of additive have in different tests.
• The action of solid-phase active additives;
• The action of char-promoting additives;
• The action of intumescent fire-retardants;
• The action of gas-phase active additives.
• The critical assembly problem for porous materials: if a material that is exposed to a hot environment is moved to a cooler environment will it ignite? This work links into the theme of self-sustaining combustion and covers a number of fire hazard situations that are of considerable importance.
• Given a material, what kind of additive optimises performance for a given fire engineering test?

The areas of interest described above are for test-methods which are `spatially uniform' in the sense that the source term is applied uniformally across one side of the test-sample. Test methods involving non-uniform source terms are also common, e.g. tests employing wooden cribs as the ignition source. Models for such experiments involve non-local reaction-diffusion equations. The mathematical behaviour of such systems has been little investigated. One of my long-term research goals is to investigate such models.

In practice many polymeric materials are semi-transparent and therefore polymer combustion models need to be combined with microwave heating models.

My collaborators in the area of polymer combustion are:

Catalytic Combustion

A catalyst is a substance that increases the rate at which a chemical system approaches equilibrium, without being consumed in the process. Catalytic materials are classified as being either homogeneous catalysts, if the catalyst and reactants are present in the same phase, or heterogeneous catalysts, if they are not. The industrial applications of heterogeneous catalysts includes energy conversion and the production of hydrocarbon feedstocks, the petroleum industry, the petrochemical industry, the heavy inorganic chemicals industry, the fine chemicals industry and atmospheric pollution control. A well known application of catalytic combustion is that of a catalytic converter, used for exhaust emission control.

In the most general case reaction systems involving a catalytic agent on a solid support and housed in a stirred vessel involve interactions between the homogeneous and heterogeneous reactions. Depending upon the application these may, or may not, be a desirable feature. Thus the modelling of these systems is made on three levels: (i) consideration of the homogeneous reaction alone, (ii) consideration of the solid catalyst alone, and (iii) examination of the behaviour of the reactor and catalyst material together.

My aims in catalytic combustion are:

• To examine the competition between adsorption-desorption processes and the catalytic reaction.
• To examine the effect of coupling between homogeneous gas-phase combustion and heterogeneously catalysed (surface-gas) combustion at high temperatures.
• To investigate deactivation of the catalyst by a poison.

These processes are being investigated within the framework of a continuously stirred tank reactor. We believe that this is the first model to include all three fundamental steps (adsorption, desorption and reaction) as non-isothermal processes. The resulting spatially-uniform models are then investigated by using the techniques of bifurcation theory, continuation methods and dynamical systems theory.

An early result of this work is that we have shown that reactor efficiency can be increased by a factor of 10³ by fine-tuning the initial conditions.

My collaborators in the area of catalytic combustion are:

Microwave Heating of Porous Solids

The process of heating porous solid materials by microwave heating is widely used in the agricultural industry. In this study, the microwave power absorption term is modelled as the product of an exponential temperature function with a function that decays exponentially with distance. The latter describes the penetration of the material by the microwaves and represents the simplest possible spatial dependence which has some accepted physical basis but which enables the heating aspects of the problem to be isolated from the electric and magnetic fields. The resulting models also apply to the ignition of combustible materials (including powders, solid fuels and explosives) by means of laser radiation.

The driving force behind this work Dr. X.D. Chen's experimental research group in biochemical and food engineering. We are currently investigating

• Thermal explosions due to heating in the absence of chemical reaction.
  • The phenomena of multiplicity in class-A geometries is being investigated.
  • Both infinite and finite biot numbers have been considered.
• The possibility of initiating high-temperature reactions at low temperatures using microwave heating.

My collaborators in the area of catalytic combustion are:

Flammability limits of simple chemical reactions

Although the reaction of hydrogen and oxygen to produce water is extremely energetically favourable, for some reaction mixtures and temperatures the reaction is almost immeasurably slow. A repeat of the experiment, with the ambient temperature increased by only a few kelvin or the pressure varied slightly, can show a completely different response with the reactant consumed rapidly (in milliseconds) as the mixture ignites. Such behaviour gives rise to the concept of a flammability limit.

Different types of flammable behaviour have been reported experimentally in continuously stirred tank reactors: simple oscillatory ignition, multi-stage ignition, complex ignitions, oscillatory cool flames, steady glow etc. The aim of this work is to identify the flammability limits of simple chemical reaction schemes. To this end we are working with idealised schemes (oxidative Sal'nikov schemes and the Rychly flame-chemistry scheme for gas-phase active fire retardants) and a reduced kinetic model for the hydrogen-chlorine reaction.

A goal of this work is to explore the use of continuously-stirred tank reactors in investigating the flammability of gases produced by the decomposition of polymers. A long-term goal is to investigate the interaction between heterogeneously catalysed and homogeneous combustion reactions.

My collaborators in the investigation of ``flammability limits of simple chemical reactions'' are