Silvestro Crescitelli

The rigid-rod model for nematic polymers: An analysis of the shear flow problem

The rigid-rod model is capable of predicting several rheological features of rodlike polymers in the nematic phase. The model is formulated in terms of a nonlinear partial differential equation that describes the evolution of an orientational distribution function. The morphological properties and the rheological response of the sample can be determined once the distribution function is known. In this article the rigid-rod model is thoroughly analyzed with tools typical of bifurcation analysis for the case of shear flows. New flow regimes, both stationary and periodic, are found and illustrated. The detailed description of the model bifurcation structure allows some considerations about up to date closure approximations.

Effect of a novel physical pretreatment process on the drying kinetics of seedless grapes

In this paper an alternative physical method for enhancing the drying rate of seedless grapes is proposed. It consists of the superficial abrasion of the grape peel using an inert abrasive material. The effectiveness of this novel process was compared to that of the traditional ethyl oleate dipping process by analysing not only their respective drying times, but also the peel surfaces by scanning electron microscopy. Moreover, the drying kinetics of the above two treatments was reconstructed by using a mathematical model in which the grape pretreatment used was assumed to affect the water diffusivity in the grape peel, but not in the grape pulp. Even though the abrasion method was found to be as effective as the traditional method and gave rise to a darker final product, which is less attractive to consumers, it would allow grape pretreatment thus avoiding the use of chemical additives, and permit safer raisins to be produced.

Numerical model of ignition processes of polymeric materials including gas-phase absorption of radiation

Abstract A one-dimensional unsteady mathematical model of solid fuel ignition is presented. The solid fuel is heated by an external radiative heat source. Some radiation is absorbed in depth by the solid fuel and some by the decomposition products in the gas phase. Solid fuel degradation occurs according to a zero-order Arrhenius pyrolysis reaction and gas-phase combustion according to a second-order Arrhenius reaction. Gas-phase heat and mass transfer and solid phase heat transfer are described by differential balance equations that are coupled through the boundary conditions at the interface. The solution is computed numerically by an implicit finite difference method. PMMA radiative ignition is simulated by varying the intensity of the radiative heat flux and predictions show quite good agreement with experiments. The ignition process oceurs in the gas phase in a premixed fashion, rapidly followed by the transition to a diffusion flame. As the radiative heat flux is increased, higher surface temperatures and pyrolysis mass fluxes are reached, ignition occurs closer and closer to the fuel surface, and ignition delay times decrease. Gas-phase absorption of radiation plays a fundamental role in the predicted ignition phenomenon and ignition delay times. In particular, with realistic data and no absorption of radiation in the gas phase, ignition does not occur at all. Finally, a parametric study is performed in order to analyze the dependence of the predicted ignition phenomenon on key parameters used to model degradation and combustion processes, such as preexponential factors and activation energies of the reactions.

Bifurcation analysis of a molecular model for nematic polymers in shear flows

Abstract It is well known that the rigid rod model for the dynamics of nematic polymers can be formulated in terms of a non-linear partial differential equation for the orientational distribution function, the so-called Smoluchowski Equation, and the rheological predictions are then obtained by integrating this equation numerically. The integration requires cumber-some numerical schemes even for very simple flow fields, and thus techniques which reduce the complexity of the problem by transforming the partial differential to a set of a few ordinary differential equations are attractive. In these approximations, the bifurcation structure of the original model should be maintained, however. In this work, we have determined for the first time the bifurcation structure of the Smoluchowski Equation; the rigid rod model is exhaustively studied for the case of a shear flow.

Symmetry properties and bifurcation analysis of a class of periodically forced chemical reactors

Abstract In this work, we discuss how periodic forcing may induce symmetry properties into mathematical models of chemical reactors. We define a class of reactors subjected to discontinuous periodic forcing, and show that all the reactors belonging to this class have spatio-temporal symmetry. This symmetry and its influence on the possible bifurcation scenarios are discussed. The bifurcation analysis is carried out with suitable discrete systems that exploit a property of the Poincare map. In fact, it is shown that the spatio-temporal symmetry induced by the forcing makes the Poincare map of the continuous system an iterate of another map. On this basis, a technique to implement parameter continuation methods is proposed. With such a technique, it is also possible to characterize symmetric and nonsymmetric regimes and unstable limit sets otherwise undetected with “bruteforce” approaches. Examples for reverseflow reactors and networks of n -reactors with periodically switched feed and discharge positions are presented.

A mathematical model of mass transfer in spherical geometry:plum (Prunus domestica) drying

Abstract In this paper the analytical solution of a mathematical model of mass transfer in spherical geometry is presented for boundary conditions useful for simulating drying processes of fruit with near spherical stones. This model is applied to analyse the efficiency of a new pre-treatment for a prune drying processes. The new proposed physical abrasion pre-treatment increases the plum drying rate at 60 °C. The mathematical model here presented allows a complete comparison of the experimental results obtained with this pre-treatment and with traditional ones. In particular the greater efficiency of the new physical pre-treatment appears to be due to the enhancement of the water diffusivity in the plum skin. The dipping pre-treatment with ethyl oleate gives an enhancement of the diffusivity in the skin too, but it have lower efficiency and implies many problems due to the use of chemical additives.

The rigid rod model for nematic polymers: Testing closure approximations with bifurcation analysis

The rigid rod model has been proven successful in predicting the rheological response of rodlike polymers in the nematic phase. The model can be reduced to constitutive equations written in terms of a set of first‐order ordinary differential equations, provided that a mathematical approximation required to close the problem is introduced. These constitutive equations are attractive as they are suitable for fast numerical processing. The required closure approximation, however, may have profound effects on the capabilities of the constitutive equation to retain the features of the original model. A method based on the bifurcation analysis is proposed as an effective test of constitutive equations. As an example, the bifurcation analysis of a particular constitutive equation is presented, and the results are compared with the bifurcation pattern of the exact model.

Predictions Of The Dependence On The Opposed Flow Characteristics Of The Flame Spread Rate Over Thick Solid Fuel

A theoretical model is developed of the effect on the spread of flames over the surface of a thick solid combustible, of the velocity and oxygen concentration of a gas flow opposing the direction of the spread. In the analysis the transient, reactive, gas phase balance equations of energy and species coupled at the interface to the solid phase energy equation are solved numerically to predict the flame spread rate and flame structure dependence on the characteristics of the flow. The calculations for P~~~A agree with previous experimental results predicting a spread rate that, for a fixed oxygen concentration, first increases, reaches a maximum and then decreases as the flow velocity is increased. The analysis shows that this behavior is the result of the interaction of two controlling mechanisms: a flame to fuel heat transfer mechanism that dominates at low flow velocities and/or high oxygen concentrations, and a gas phase chemical kinetics mechanism that dominates at high velocities and/or low oxygen concentrations.

Influence of Solid Phase Thermal Properties on Flame Spread over Polymers

Abstract To determine the influence of solid phase thermal properties on the laminar flame spread over polymer sheets, several experiments were carried out to measure the spreading velocity of polymethyl met-acrylate (PMMA) and polystyrene (PS) samples modified by the addition of copper wires, metallic foils and metallic and inert powders. A mild but not negligible influence of the thermal diffusivity on the spread rate was detected.

Coal dust explosions in a spherical bomb

Abstract Results of coal dust explosion experiments obtained by means of the Barknecht-Siwek 20 litre sphere are presented and discussed. Several coal dusts have been tested at ambient conditions. The oxygen mass fraction and the initial pressure have been varied to test their influence. The data collected lead to an extension of the hazard limits for coal dusts with respect to data in the current literature. The maximum explosion overpressure depends linearly on the partial pressure of atmospheric oxygen. The ‘optimum’ dust concentration depends linearly on the oxygen concentration in the suspending atmosphere. This has led to a useful non-dimensional representation of the results: in the new variables, maximum explosion overpressure data for a coal dust at various values of the initial oxygen partial pressure are correlated by a single curve for all tests in which most of the oxygen is consumed. Differences in the maximum explosion overpressure exhibited by different coals could not be related to chemical parameters due to the prevailing effect of non-adiabatic explosions in this apparatus at such low rates of pressure rise. The maximum rate of pressure rise has been found generally to increase with the standard volatile matter content and with the hydrogen content in the coal.