Fractional pennes' bioheat equation: theoretical and numerical studies

In this work we provide a new mathematical model for the Pennes’ bioheat equation, assuming a fractional time derivative of single order. Alternative versions of the bioheat equation are studied and discussed, to take into account the temperature-dependent variability in the tissue perfusion, and both finite and infinite speed of heat propagation. The proposed bioheat model is solved numerically using an implicit finite difference scheme that we prove to be convergent and stable. The numerical method proposed can be applied to general reaction diffusion equations, with a variable diffusion coefficient. The results obtained with the single order fractional model, are compared with the original models that use classical derivatives.

Comparison of different numerical methods for the solution of the time-fractional reaction-diffusion equation with variable diffusion coefficient

In this work we perform a comparison of two different numerical schemes for the solution of the time-fractional diffusion equation with variable diffusion coefficient and a nonlinear source term. The two methods are the implicit numerical scheme presented in [M.L. Morgado, M. Rebelo, Numerical approximation of distributed order reaction- diffusion equations, Journal of Computational and Applied Mathematics 275 (2015) 216-227] that is adapted to our type of equation, and a colocation method where Chebyshev polynomials are used to reduce the fractional differential equation to a system of ordinary differential equations

Fractional bioheat equation

In this work we develop a new mathematical model for the Pennes’ bioheat equation assuming a fractional time derivative of single order. A numerical method for the solu- tion of such equations is proposed, and, the suitability of the new model for modelling real physical problems is studied and discussed

Safety classification using GIS in decision-making process to define priority road interventions

Given the current economic situation of the Portuguese municipalities, it is necessary to identify the priority investments in order to achieve a more efficient financial management. The classification of the road network of the municipality according to the occurrence of traffic accidents is fundamental to set priorities for road interventions. This paper presents a model for road network classification based on traffic accidents integrated in a geographic information system. Its practical application was developed through a case study in the municipality of Barcelos. An equation was defined to obtain a road safety index through the combination of the following indicators: severity, property damage only and accident costs. In addition to the road network classification, the application of the model allows to analyze the spatial coverage of accidents in order to determine the centrality and dispersion of the locations with the highest incidence of road accidents. This analysis can be further refined according to the nature of the accidents namely in collision, runoff and pedestrian crashes.

Probing dispersion and re-agglomeration phenomena upon melt-mixing of polymer-functionalized graphite nanoplates

A one-step melt-mixing method is proposed to study dispersion and re-agglomeration phenomena of the as-received and functionalized graphite nanoplates in polypropylene melts. Graphite nanoplates were chemically modified via 1,3-dipolar cycloaddition of an azomethine ylide and then grafted with polypropylene-graft-maleic anhydride. The effect of surface functionalization on the dispersion kinetics, nanoparticle re-agglomeration and interface bonding with the polymer is investigated. Nanocomposites with 2 or 10 wt% of as-received and functionalized graphite nanoplates were prepared in a small-scale prototype mixer coupled to a capillary rheometer. Samples were collected along the flow axis and characterized by optical microscopy, scanning electron microscopy and electrical conductivity measurements. The as-received graphite nanoplates tend to re-agglomerate upon stress relaxation of the polymer melt. The covalent attachment of a polymer to the nanoparticle surface enhances the stability of dispersion, delaying the re-agglomeration. Surface modification also improves interfacial interactions and the resulting composites presented improved electrical conductivity.

Dispersion and re-agglomeration of graphite nanoplates in polypropylene melts under controlled flow conditions

The kinetics of GnP dispersion in polypropylene melt was studied using a prototype small scale modular extensional mixer. Its modular nature enabled the sequential application of a mixing step, melt relaxation, and a second mixing step. The latter could reproduce the flow conditions on the first mixing step, or generate milder flow conditions. The effect of these sequences of flow constraints upon GnP dispersion along the mixer length was studied for composites with 2 and 10 wt.% GnP. The samples collected along the first mixing zone showed a gradual decrease of number and size of GnP agglomerates, at a rate that was independent of the flow conditions imposed to the melt, but dependent on composition. The relaxation zone induced GnP re-agglomeration, and the application of a second mixing step caused variable dispersion results that were largely dependent on the hydrodynamic stresses generated.

Dispersion of graphite nanoplates during melt mixing

Artigo publicado a convite da Society for Polymer Engineers

Dispersion of fillers in viscoelastic polymer matrices using Eulerian-Lagrangian approaches

Understanding the behavior of c omplex composite materials using mixing procedures is fundamental in several industrial processes. For instance, polymer composites are usually manufactured using dispersion of fillers in polymer melt matrices. The success of the filler dispersion depends both on the complex flow patterns generated and on the polymer melt rheological behavior. Consequently, the availability of a numerical tool that allow to model both fluid and particle would be very useful to increase the process insight. Nowadays there ar e computational tools that allow modeling the behavior of filled systems, taking into account both the behavior of the fluid (Computational Rheology) and the particles (Discrete Element Method). One example is the DPMFoam solver of the OpenFOAM ® framework where the averaged volume fraction momentum and mass conservation equations are used to describe the fluid (continuous phase) rheology, and the Newton’s second law of motion is used to compute the particles (discrete phase) movement. In this work the refer red solver is extended to take into account the elasticity of the polymer melts for the continuous phase. The solver capabilities will be illustrated by studying the effect of the fluid rheology on the filler dispersion, taking into account different fluid types (generalized Newtonian or viscoelastic) and particles volume fraction and size. The results obtained are used to evaluate the relevance of considering the fluid complex rheology for the prediction of the composites morphology

Understanding the dispersion of fillers in polymer matrices

Understanding the mixing process of complex composite materials is fundamental in several industrial processes. For instance, the dispersion of fillers in polymer melt matrices is commonly employed to manufacture polymer composites, using a twin-screw extruder. The effectiveness of the filler dispersion depends not only on the complex flow patterns generated, but also on the polymer melt rheological behavior. Therefore, the availability of a numerical tool able to predict mixing, taking into account both fluid and particles phases would be very useful to increase the process insight, and thus provide useful guidelines for its optimization. In this work, a new Eulerian-Lagrangian numerical solver is developed OpenFOAM® computational library, and used to better understand the mechanisms determining the dispersion of fillers in polymer matrices. Particular attention will be given to the effect of the rheological model used to represent the fluid behavior, on the level of dispersion obtained. For the Eulerian phase the averaged volume fraction governing equations (conservation of mass and linear momentum) are used to describe the fluid behavior. In the case of the Lagrangian phase, Newton’s second law of motion is used to compute the particles trajectories and velocity. To study the effect of fluid behavior on the filler dispersion, several systems are modeled considering different fluid types (generalized Newtonian or viscoelastic) and particles volume fraction and size. The results obtained are used to correlate the fluid and particle characteristics on the effectiveness of mixing and morphology obtained.

Microstructure and mechanical properties of carbon nanotube reinforced cementitious composites developed using a novel dispersion technique

The authors also acknowledge Centre for Textile Science and Technology (University of Minho) and FIBRENAMICS PLATFORMfor providing required conditions for this research. Sincere thanks are also due to Mr. Pedro Samuel Leite and Mr. Carlos Jesus for their kind help in sample preparation and testing.

Nanocomposites: the contribution of multiscale modelling to improve the dispersion levels

Tese de Doutoramento em Ciência e Engenharia de Polímeros e Compósitos