Natural convection effects on thermal ignition in a porous medium. II. Lumped thermal model-I

In this paper, we examine the disappearance of criticality, ignition locus and bifurcation diagrams of temperature against Rayleigh number of a one-dimensional diffusion-convection-reaction model with the assumption of infinite thermal conductivity and zero species diffusivity. The predictions of this model are compared with those of the Semenov model to determine the impact of the species diffusion term. It is shown that for large values of the Rayleigh number (R* ≫ 1), the ignition locus may be expressed in a parametric form B Ls = t /ln t + t /( t - 1) (1 < t ≼ 3.4955), ψ / R * = ( B Ls ) 2 (( t - 1)/ t ) exp{ - B Ls + B Ls / t } ln t , where B is the heat of reaction parameter, ψ is the Semenov number and Ls is a (modified) Lewis number. Criticality is found to disappear at B Ls = 4.194. When these results are compared with those of the Semenov model, it is found that neglecting the species diffusion term gives conservative approximations to the ignition locus, and criticality boundary. It is found that the lumped thermal model-I has five different types of bifurcation diagrams of temperature against Rayleigh number (single­-valued, isola, inverse S , mushroom, inverse S + isola). These diagrams are qualitatively identical to the bifurcation diagrams of temperature against flow rate for the forced convection problem under the assumption of infinite thermal conductivity and zero species diffusivity.

Convective-diffusive-reactive Taylor dispersion processes in particulate multiphase systems

Convective-diffusive transport of a chemically reactive solute is studied analytically for a general model of a multiphase system composed of ordered or disordered particles of arbitrary shapes and sizes. Use of spatially periodic boundary conditions permits analysis of particulate multiphase systems of effectively infinite size. Solute transport occurs in both the continuous and discontinuous bulk phases, as well as within and across the interfacial phase boundaries separating them. Additionally, the solute is allowed to undergo generally inhomogeneous first-order irreversible chemical reactions occurring in both the continuous and discontinuous volumetric phases, as well as within the interfacial surface phase. Our object is that of globally describing the solute transport and reaction processes at a macro- or Darcy-scale level, wherein the resulting, coarse-grained particulate system is viewed as a continuum possessing homogeneous material transport and reactive properties. At this level the asymptotic long-time solute macrotransport process is shown to be governed by three Darcy-scale phenomenological coefficients: the mean solute velocity vector ͞U *, dispersivity dyadic ͞D *, and apparent volumetric reactivity coefficient ͞K *. A variant of a Taylor-Aris method-of-moments scheme (Brenner & Adler 1982), modified to include solute disappearance via chemical reactions, is used to express these three macroscale phenomenological coefficients in terms of the given microscale phenomenological data and geometry. The general solution technique, illustrated here for a simple, ordered geometrical realization of a two-phase system, reveals the competitive influences of the respective volumetric/surface-excess transport and reaction processes, as well as the solute adsorptivity, upon the three macroscale transport coefficients.

Computer simulation studies of anisotropic systems. XVIII. Re-entrant phase separation in nematogenic mixtures of cylindrical and spherical particles

Addition of a solute composed of quasi-spherical molecules to a nematic liquid crystal is known to depress the nematic–isotropic transition temperature. A biphasic régime, consisting of coexisting nematic and isotropic phases, is also created at the transition. A molecular field theory of such mixtures, developed by Humphries and Luckhurst, predicts, in addition, the appearance of a re-entrant biphasic region following the nematic phase for a narrow range of compositions. This unusual re-entrant phase separation has not been observed for real nematogenic mixtures, presumably because the system freezes before the re-entrant phases can be formed. Here we report the observation of this biphasic régime for a model nematogenic mixture, formed from cylindrical and spherical particles, which was studied using the Monte Carlo technique of computer simulation. The particles are confined to the sites of a simple cubic lattice but still retain their rotational freedom; in consequence the mixture is unable to freeze in the conventional sense. The temperature variation of the heat capacity and the solute–solute radial distribution function reveal the predicted transition to the re-entrant biphasic régime. The internal energy and the second-rank orientational order parameter were also determined as a function of temperature. The predictions of the Humphries–Luckhurst theory are found to be in good qualitative accord with the results of the simulation.

Minimizers and gradient flows for singularly perturbed bi-stable potentials with a Dirichlet condition

Minimizers and gradient flows are studied for the functional ∫ Ω W(u) + ϵ 2 ∣∇ u ∣ 2 d x , Ω ⊆ R n , ϵ > 0, where u satisfies a Dirichlet condition u = h ϵ on ∂ Ω . Here W is taken to be a double-well potential with minimum value zero attained at u = a and u = b . Questions of existence and structure of minimizers for small ϵ are resolved through the identification of a limiting variational problem, the so-called Γ-limit. A formal asymptotic solution is then constructed for the gradient flow ∂ t u ϵ = 2 ϵ ∆ u ϵ — ϵ -1 W' ( u ϵ ), u ϵ ( x , 0) = g ( x ), u ϵ ( x, t ) = h ϵ on ∂ Ω , valid when ϵ is small. Using multiple timescales we show that fronts rapidly develop and then propagate with normal velocity ϵk , where k is mean curvature. At the intersection of a front with ∂ Ω , the Dirichlet condition is shown to imply a contact angle condition for the front. This asymptotically correct evolution process represents gradient flow for the Γ-limit.

High strain-rate shear response of polycarbonate and polymethyl methacrylate

The high strain rate response of polycarbonate (PC) and polymethyl methacrylate (PMMA) are measured using a split Hopkinson torsion bar for shear strain rates Ẏ from 500 s -1 to 2200 s -1 , and temperatures in the range —100°C to 200°C. The yield and fracture behaviours are compared with previous data and existing theories for Ẏ < I s -1 . We find that PC yields in accordance with the Eyring theory of viscous flow, for temperatures between the beta transition temperature T β ≈ — 100°C and the glass transition temperature T g = 147°C. At lower temperatures, T < T β , backbone chain motion becomes frozen and the shear yield stress is greater than the Eyring prediction. Strain softening is an essential feature of yield of PC at all strain rates employed. Poly methyl methacrylate fractures before yield in the high strain rate tests for T < 80°C, which is close to the glass transition temperature T g 120°C. It is found that the fracture stress for both materials obeys a thermal activation rate theory of Eyring type. Fracture is thought to be nucleation controlled, and is due to the initiation and break down of a craze at the fracture stress τ f . Examination of the fracture surfaces reveals that failure is by the nucleation and propagation of inclined mode I microcracks which link to form a stepped fracture surface. This reveals that failure is by tensile cracking and not by a thermal instability in the material. The process of shear localization is fundamentally different from that shown by steel and titanium alloys.

Finite deformation of flexible composites

This paper examines the nonlinear elastic behaviour of flexible composites under finite deformation. The constitutive relations have been derived based on a strain-energy density which, in a fourth-order polynomial form, is assumed to be a function of the lagrangian strain components referring to the initial principal material coordinates. The constitutive equations thus obtained are verified by the following experiments: (1) off-axis tension and simple shear for unidirectional composites, and (2) uniaxial tension for flexible composites with wavy fibres. Good agreement has been found between the theory and experiments.

A theoretical analysis of electrochemical arc machining

Electrochemical arc machining (ECAM) involves the removal of metal from an anodically polarized workpiece by both erosion arising from discharges produced in an aqueous electrolyte and electrolytic dissolution. A theoretical model is derived for the process and analysed for two specific applications, fine-hole drilling and the finishing of components by smoothing of their initially rough surfaces. In the second of these examples, a perturbation procedure for obtaining approximate solutions is used; the model so developed encorporates the effects of current density on current efficiency which are known from experimental electrochemical machining (ECM) studies to influence the rate and mode of smoothing. For fine-hole drilling by ECAM, the analysis predicts that the interelectrode gap width increases with the applied voltage and inversely with the square root of the mechanically driven anode. In the case of smoothing, ECAM is found to remove the surface irregularities at a much faster rate and with lower loss of stock metal than ECM alone, when electrolytes such as sodium chloride solution yielding 100% current efficiency are used for the latter process. The analysis shows that an electrolyte solution with a current density-dependent current efficiency is needed if parent metal loss by ECM is to approach that of ECAM, and even then, machining by the latter is still much faster. Attention is drawn to experimental evidence in support of these predictions of ECAM behaviour. Finally, results from the model are used to verify the practical use of ECM for rapid finishing of the surfaces of components left rough by electrodischarge machining.

Examination of electrocatalysis in the anodic O 2 evolution reaction at Pt through evaluation of the adsorption behaviour of kinetically involved intermediate states

In regular heterogeneous catalytic reactions, evaluation of the adsorption behaviour of the ephemeral intermediates that participate kinetically in the main reaction pathway is often inaccessible experimentally. In electrocatalysis, on the other hand, electrochemical transient methods can provide such information. In the present paper, potential-relaxation transients are used to derive information on the electroactive, kinetically significant adsorbed intermediate states that are involved in the anodic O 2 evolution reaction (OER) at Pt electrodes. By means of such transients, digitally recorded over 5–6 decades of time from microseconds to seconds, the adsorption capacitance of the intermediate states in the reaction is evaluated as a function of potential over a range corresponding to appreciable current densities for O 2 evolution. Anodic O 2 evolution takes place at Pt, as at all other metal anodes, on an oxide film. A well-defined state of such a film must be established by a pre-conditioning programme to make meaningful and reproducible kinetic studies on the OER. The state of the oxide film is conveniently characterized by means of cyclic-voltammetry. The intermediate surface states in the reaction can be two or more oxidation states of Pt atoms in the oxide and OH or O species at the oxide’s surface. Two distinct types of adsorption behaviour are distinguished for potentials above and below ca . 1.85 V against the reversible H 2 electrode (RHE), and are related to the observed kinetics of the OER.

Receptivity of boundary layers: asymptotic theory and experiment

The sources of disturbance (vibrators, small jets, vortices, sound waves) in a boundary layer are considered, emphasizing their ability to provoke the onset of eigenoscillations with exponentially growing amplitude. Harmonic sources give rise to the Tollmien–Schlichting waves, whereas impulsive sources excite wave packets. General requirements are stated for the temporal and spatial characteristics of the signals emitted by the devices causing disturbance, as well as for obstacles met by signals when propagating. To scale the frequencies and wavenumbers in terms of the Reynolds number taking on indefinitely large values, the asymptotic theory of an interacting boundary layer with the triple-deck structure is used. The conclusions from the asymptotic analysis are in line with the results of measurements in wind tunnels when the Reynolds numbers were moderate.

Analysis of chemical kinetic systems over the entire parameter space. III. A wet combustion system

A simple generalization of Semenov thermal explosion theory is studied here; one exothermic reaction taking place at the same time as a second one involving water as a reactant. Evaporation and condensation are also considered. The resulting two ordinary differential equations containing three parameters are treated by recently developed methods outlined in the first paper of this series. This model is a simple representation of the combustion of wet cellulosic materials such as bagasse, cotton and sawdust. The theory predicts an amazing variety of behaviour arising in association with the degenerate singularities that occur. These include degeneracies up to and including the quartic fold, H3 2 bifurcation and degenerate double zero eigenvalue points.