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Full-Text Articles in Physics
Semi-Analytical Solutions For A Gray-Scott Reaction-Diffusion Cell With An Applied Electric Field, Tim Marchant
Semi-Analytical Solutions For A Gray-Scott Reaction-Diffusion Cell With An Applied Electric Field, Tim Marchant
Tim Marchant
An ionic version of the Gray–Scott chemical reaction scheme is considered in a reaction–diffusion cell, with an applied electric field, which causes migration of the reactant and autocatalyst in a preferred direction. The Galerkin method is used to reduce the governing partial differential equations to an approximate model consisting of ordinary differential equations. This is accomplished by approximating the spatial structure of the reactant and autocatalyst concentrations. Bifurcation analysis of the semi-analytical model is performed by using singularity theory to analyse the static multiplicity and a stability analysis to determine the dynamic multiplicity. The application of the electric field causes …
Self-Heating In Compost Piles Due To Biological Effects, Tim Marchant
Self-Heating In Compost Piles Due To Biological Effects, Tim Marchant
Tim Marchant
The increase in temperature in compost piles/landfill sites due to micro-organisms undergoing exothermic reactions is modelled. A simplified model is considered in which only biological self-heating is present. The heat release rate due to biological activity is modelled by a function which is a monotonic increasing function of temperature over the range 0⩽T⩽a, whilst for T⩾a it is a monotone decreasing function of temperature. This functional dependence represents the fact that micro-organisms die or become dormant at high temperatures. The bifurcation behaviour is investigated for 1-d slab and 2-d rectangular slab geometries. In both cases there are two generic steady-state …
Semi-Analytical Solutions For One - And Two-Dimensional Pellet Problems., Tim Marchant
Semi-Analytical Solutions For One - And Two-Dimensional Pellet Problems., Tim Marchant
Tim Marchant
The problem of heat and mass transfer within a porous catalytic pellet in which an irreversible first–order exothermic reaction occurs is a much–studied problem in chemical–reactor engineering. The system is described by two coupled reaction–diffusion equations for the temperature and the degree of reactant conversion. The Galerkin method is used to obtain a semi–analytical model for the pellet problem with both one– and two–dimensional slab geometries. This involves approximating the spatial structure of the temperature and reactant–conversion profiles in the pellet using trial functions. The semi–analytical model is obtained by averaging the governing partial differential equations. As the Arrhenius law …
Cubic Autocatalysis With Michaelis - Menten Kinetics: Semi-Analytical Solutions For The Reaction - Diffusion Cell, Tim Marchant
Cubic Autocatalysis With Michaelis - Menten Kinetics: Semi-Analytical Solutions For The Reaction - Diffusion Cell, Tim Marchant
Tim Marchant
Cubic-autocatalysis with Michaelis–Menten decay is considered in a one-dimensional reaction–diffusion cell. The boundaries of the reactor allow diffusion into the cell from external reservoirs, which contain fixed concentrations of the reactant and catalyst. The Galerkin method is used to obtain a semi-analytical model consisting of ordinary differential equations. This involves using trial functions to approximate the spatial structure of the reactant and autocatalyst concentrations in the reactor. The semi-analytical model is then obtained from the governing partial differential equations by averaging. The semi-analytical model allows steady-state concentration profiles and bifurcation diagrams to be obtained as the solution to sets of …
Cubic Autocatalytic Reaction-Diffusion Equations: Semi-Analytical Solutions, Prof. Tim Marchant
Cubic Autocatalytic Reaction-Diffusion Equations: Semi-Analytical Solutions, Prof. Tim Marchant
Tim Marchant
The Gray-Scott model of cubic-autocatalysis with linear decay is coupled with diffusion and considered in a one-dimensional reactor (a reaction-diffusion cell). The boundaries of the reactor are permeable, so diffusion occurs from external reservoirs that contain fixed concentrations of the reactant and catalyst. The Galerkin method is used to approximate the spatial structure of the reactant and autocatalyst concentrations in the reactor. Ordinary differential equations are then obtained as an approximation to the governing partial differential equations. The ordinary differential equations are then analysed to obtain semi-analytical results for the reaction-diffusion cell. Steady-state concentration profiles and bifurcation diagrams are obtained …
Semi-Analytical Solutions For Continuous-Flow Microwave Reactors, Prof. Tim Marchant
Semi-Analytical Solutions For Continuous-Flow Microwave Reactors, Prof. Tim Marchant
Tim Marchant
A prototype chemical reaction is examined in both one and two-dimensional continuous-flow microwave reactors, which are unstirred so the effects of diffusion are important. The reaction rate obeys the Arrhenius law and the thermal absorptivity of the reactor contents is assumed to be both temperature- and concentration-dependent. The governing equations consist of coupled reaction-diffusion equations for the temperature and reactant concentration, plus a Helmholtz equation describing the electric-field amplitude in the reactor. The Galerkin method is used to develop a semi-analytical microwave reactor model, which consists of ordinary differential equations. A stability analysis is performed on the semi-analytical model. This …