L. L. Ferrás

University of Porto | UP

Polymer processing techniques are crucial to the production of polymer components. Our objective with this Reprint is to provide cutting-edge research papers that contribute to the numerical, theoretical, and experimental knowledge regarding polymer physics.

Optimal control problems (OCPs) are essentials in various domains such as science, engineering, and industry, requiring the optimisation of control variables for dynamic systems, along with the corresponding state variables, that minimise a given performance index. Traditional methods for solving OCPs often rely on numerical techniques and can be c...

Hydropower Plants are a very important renewable energy resource. However optimizing their management is difficult. In this work we propose a neural network to predict the water inflow per hour and day for the Miranda Hydropower Plant in the Araguari lake, Brazil.

Neural Fractional Differential Equations (Neural FDEs) represent a neural network architecture specifically designed to fit the solution of a fractional differential equation to given data. This architecture combines an analytical component, represented by a fractional derivative, with a neural network component, forming an initial value problem. D...

Electrokinetic flows driven by electro-osmotic forces are especially relevant in micro and nano-devices, presenting specific applications in medicine, biochemistry, and miniaturized industrial processes. In this work, we integrate analytical solutions with numerical methodologies to explore the fluid dynamics of viscoelastic electro-osmotic/pressur...

Traditional computer vision techniques aim to extract meaningful information from images but often depend on manual feature engineering, making it difficult to handle complex real-world scenarios. Fractional calculus (FC), which extends derivatives to non-integer orders, provides a flexible way to model systems with memory effects and long-term dep...

Neural Fractional Differential Equations (Neural FDE) represent a neural network architecture specifically designed to fit the solution of a fractional differential equation to given data. This architecture combines an analytical component, represented by a fractional derivative, with a neural network component, forming an initial value problem. Du...

Fractional Differential Equations (FDEs) are vital for modeling complex systems in science and engineering due to their ability to capture non-local and memory-dependent behaviors through non-integer order differentiation and integration. This feature is crucial for systems where responses are influenced by historical interactions. Inspired by Neur...

Traditional computer vision techniques aim to extract meaningful information from images but often depend on manual feature engineering, making it difficult to handle complex real-world scenarios. Fractional Calculus (FC), which extends derivatives to non-integer orders, provides a flexible way to model systems with memory effects and long-term dep...

Neural Ordinary Differential Equations (Neural ODEs) are continuous-depth models that use an ordinary differential equation (ODE) to capture the dynamics of data. Due to their modelling capabilities several works on applications and novel architectures using Neural ODEs can be found in the literature. In this work, we call for the attention to the...

Neural Ordinary Differential Equations (Neural ODEs) have gained popularity for modelling real-world systems, thanks to their ability to fit ODEs to data. However, numerous systems in science and engineering often exhibit intricate memory behaviours, being classical ODEs inadequate for such tasks due to their inability to handle strong and complex...

Due to their dynamic properties such as irregular sampling rate and high-frequency sampling, Continuous Time Series (CTS) are found in many applications. Since CTS with irregular sampling rate are difficult to model with standard Recurrent Neural Networks (RNNs), RNNs have been generalised to have continuous-time hidden dynamics defined by a Neural...

Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise representation of processes characterised by non-local and memory-dependent behaviours. This property is useful...

The significance of polymer processing techniques cannot be overstated in the production of polymer components [...]

Hydropower plants play a pivotal role in advancing clean and sustainable energy production, contributing significantly to the global transition towards renewable energy sources. However, hydropower plants are currently perceived both positively as sources of renewable energy and negatively as disruptors of ecosystems. In this work, we highlight the...

Real-world systems are often formulated as constrained optimization problems. Techniques to incorporate constraints into Neural Networks (NN), such as Neural Ordinary Differential Equations (Neural ODEs), have been used. However, these introduce hyperparameters that require manual tuning through trial and error, raising doubts about the successful...

In this work, we present a generalisation of the Maxwell integral model by developing a new relaxation modulus based on the Mittag-Leffler function. The new model provides a better fit to linear experimental data compared to a classical 2-mode Maxwell model. The model is improved to become frame invariant and several analytical solutions are derive...

This work presents a comprehensive numerical implementation of a viscoelastic thixotropic model known as the modified-Bautista–Manero (MBM) model (a model widely used to characterize the rheological behavior of wormlike micellar solutions). This implementation is integrated into the OpenFOAM computational fluid dynamics software, specifically using...

The annular flow of complex viscoelastic fluids, described by the generalised Phan-Thien–Tanner model, is studied. This model considers the Mittag-Leffler function instead of the usual linear or exponential functions of the trace of the stress tensor, and includes two new parameters that provide additional fitting flexibility. We derive a semi-anal...

In multiphase flows, accurately modeling the interaction between the liquid phase of complex fluids and a porous medium of solid spheres poses a fundamental challenge. The dynamics of moderately dense non-colloidal suspensions constituted by static random arrays of monodisperse spherical particles in non-linear viscoelastic fluids is studied numeri...

Hydropower plants are crucial for stable renewable energy and serve as vital water sources for sustainable agriculture. However, it is essential to assess the current water management practices associated with hydropower plant management software. A key concern is the potential conflict between electricity generation and agricultural water needs. P...

Neural ODEs have been used to model natural systems due to their ability to handle irregularly sampled data and make predictions throughout the whole time domain. In general, natural systems follow strict rules that are known. Therefore, a NN modeling them would ideally operate strictly according to the governing laws. However, due to the black-box...

In this work, we incorporate a thixotropic-viscoelastic model into the widely used Computational Fluid Dynamics (CFD) software OpenFOAM, along with the rheoTool library. The model we implement is known as the Modified-Bautista-Manero (MBM), and effectively describes the rheological behavior of worm-like micellar solutions in extensional flows. We p...

This work introduces a novel numerical method designed to address three-dimensional unsteady free surface flows incorporating integral viscoelastic constitutive equations, specifically the K–BKZ–PSM (Kaye–Bernstein, Kearsley, Zapas–Papanastasiou, Scriven, Macosko) model. The new proposed methodology employs a second-order finite difference approach...

This work introduces a novel numerical method designed to address three-dimensional unsteady free surface flows incorporating integral viscoelastic constitutive equations, specifically, the K-BKZ-PSM (Kaye–Bernstein, Kearsley, Zapas - Papanastasiou, Scriven, Macosko) model. The new proposed methodology employs a second-order finite difference appro...

The continuous dynamics of natural systems has been effectively modelled using Neural Ordinary Differential Equations (Neural ODEs). However, for accurate and meaningful predictions, it is crucial that the models follow the underlying rules or laws that govern these systems. In this work, we propose a self-adaptive penalty algorithm for Neural ODEs...

Due to their dynamic properties such as irregular sampling rate and high-frequency sampling, Continuous Time Series (CTS) are found in many applications. Since CTS with irregular sampling rate are difficult to model with standard Recurrent Neural Networks (RNNs), RNNs have been generalised to have continuous-time hidden dynamics defined by a Neural...

This work introduces Neural Chronos Ordinary Differential Equations (Neural CODE), a deep neural network architecture that fits a continuous-time ODE dynamics for predicting the chronology of a system both forward and backward in time. To train the model, we solve the ODE as an initial value problem and a final value problem, similar to Neural ODEs...

Neural Ordinary Differential Equations (ODEs) have been used extensively to model physical systems because they represent a continuous-time function that can make predictions over the entire time domain. However, most of the time, the parameters of these physical systems are subject to strict laws/constraints. But there is no guarantee that the Neu...

Conventional methods that are commonly used for the preparation of microbubble delivery systems include sonication, high-shear emulsification, and membrane emulsification. However, these methods present significant disadvantages, namely, poor control over the particle size and distribution. To date, engineering core-shell microparticles remains a c...

This work presents a comparison between the PTT-X (extended Phan-Thien and Tanner (PTT)) and the generalised PTT (gPTT) viscoelastic models. The PTT-X model was derived based on a combination of Reptation and Network theories, allowing in this way a microstructural justification for the kernel function. The gPTT model is based on the Network theory...

The focus of this work is the numerical study of stable and pulsatory flame burst in an undulating geometry, using premixed hydrogen and air (with an equivalence ratio of 1.0). This work extends other works in the literature by considering a linear temperature profile along the wall. This allows an analysis of the flow dynamics without forcing the...

This work reports on an evaluation of the computational fluid dynamics–discrete element method (CFD-DEM) numerical approach to study the behavior of polymer-filled suspensions in a parallel-plate rheometer. For this purpose, an open-source CFD-DEM solver is used to model the behavior of such suspensions considering different particle volume fractio...

Viscoelastic materials are abundant in nature and present in our daily lives [...]

In this work, we present a generalised viscoelastic model using distributed‐order derivatives. The model consists of two distributed‐order elements (distributed springpots) connected in series, as in the Maxwell model. The new model generalises the fractional viscoelastic model presented by Schiessel and Blumen and allows for a more broad and accur...

Polymer processing techniques are of paramount importance in the manufacture of polymer parts [...]

In this work we present a generalised viscoelastic model using distributed-order derivatives. The model consists of two distributed-order elements (distributed springpots) connected in series, as in the Maxwell model. The new model generalises the fractional viscoelastic model presented in [H. Schiessel, A. Blumen, Hierarchical analogues to fractio...

In this work, a stable and convergent numerical scheme on non-uniform time meshes is proposed, for the solution of distributed-order diffusion equations. A set of numerical results illustrates that the use of particular non-uniform time meshes provides more accurate results than the use of a uniform mesh, in the case of non-smooth solutions.Keyword...

Taking into account the regularity properties of the solutions of fractional differential equations, we develop a numerical method which is able to deal, with the same accuracy, with both smooth and nonsmooth solutions of systems of fractional ordinary differential equations of the Caputo-type. We provide the error analysis of the numerical method...

In this work, we present a numerical study on the development length (the length from the channel inlet required for the velocity to reach 99% of its fully-developed value) of a pressure-driven viscoelastic fluid flow (between parallel plates) modelled by the generalised Phan–Thien and Tanner (gPTT) constitutive equation. The governing equations ar...

In this work we perform a numerical study on the flow around the hulls of competition kayaks with the aim of predicting accurate drag forces. The numerical simulations were first performed using the Wigley hull geometry, a typical validation case for flows around marine vessels. The total drag force and wave profiles of the hull were determined for...

Numerical simulations of fluid flows can produce a huge amount of data and inadvertently important flow structures can be ignored, if a thorough analysis is not performed. The identification of these flow structures, mainly in transient situations, is a complex task, since such structures change in time and can move along the domain. With the decom...

Abstract: The impact of the optimization algorithms Adam, RMSprop, L-BFGS, and SGD with momentum on the solution of the Fractional Laplacian Equation (FLE) by physics-informed neural networks is investigated considering two different analytical solutions, one smooth and the other non-smooth. The influence of the optimization approach, the smoothnes...

Abstract: This study involves a review of existing object detection methods as well as the development of a Deep Learning model that can detect swimming pools from satellite pictures. The model was trained on a Kaggle-customized dataset and then evaluated on a newly created dataset containing aerial images. Several metrics are used to evaluate the...

Abstract: When studying complex viscoelastic fluids, the exponential form of the original Phan-Thien and Tanner (PTT) model is frequently used. A generalized version of the PTT model was recently proposed, which employs the Mittag-Leffler function to generate a new function of the trace of the stress tensor. We propose two optimization problems for...

This work presents a study of the different existing object detection algorithms and the implementation of a Deep Learning model capable of detecting swimming pools from satellite images. In order to obtain the best results for this particular task, the RetinaNet algorithm was chosen. The model was trained using a customised dataset from Kaggle and...

The exponential form of the original Phan-Thien and Tanner (PTT) model is often used to study complex viscoelastic fluids. Recently, a generalised version of the PTT model, that uses the Mittag-Leffler function to compute a new function of the trace of the stress tensor, was proposed. This new model adds one or two additional fitting parameters tha...

This work presents a numerical method for the solution of two coupled distributed-order fractional differential equations, that appear in the pure tangential flow of fluids modelled by the Distributed-Order Viscoelastic Model. We prove the solvability of the method, and, perform numerical simulations of relaxation tests.

This work presents a viscoelastic model based on distributed-order derivatives. The model generalises the fractional springpot element by considering an integral kernel that captures the continuous contribution of all elements with fractional order α ∈ (0, 1). We derive some properties of the model and perform numerical simulations considering simp...

In this work, stable and convergent numerical schemes on nonuniform time meshes are proposed, for the solution of distributed-order diffusion equations. The stability and convergence of the numerical methods are proven, and a set of numerical results illustrate that the use of particular nonuniform time meshes provides more accurate results than th...

This work presents a detailed numerical investigation on the required development length (L=L/B) in laminar Newtonian fluid flow in microchannels with rectangular cross section and different aspect ratios (AR). The advent of new microfluidic technologies shifted the practical Reynolds numbers (Re) to the range of unitary (and even lower) orders of...

This work presents new semi-analytical solutions for the combined fully developed electro-osmotic pressure-driven flow in microchannels of viscoelastic fluids, described by the generalised Phan-Thien–Tanner model (gPTT) recently proposed by Ferrás et al. (Journal of Non-Newtonian Fluid Mechanics, 269:88–99, 2019). This generalised version of the PT...

Portuguese legislation states the compulsory reporting of the addition of amenities, such as swimming pools, to the Portuguese tax authority. The purpose is to update the property tax value, to be charged annually to the owner of each real estate. According to MarketWatch, this decade will bring a global rise to the number of swimming pools due to...

This work combines experimental and numerical (computational fluid dynamics) data to better understand the kinetics of the dispersion of graphite nanoplates in a polypropylene melt, using a mixing device that consists of a series of stacked rings with an equal outer diameter and alternating larger and smaller inner diameters, thereby creating a ser...

Melt mixing is a convenient method to prepare polymer nanocomposites, but the extent of the dispersion of the solid filler reached is often limited, and may compromise the anticipated performance of these materials during service. Since the efficiency of extensional flows on dispersion is now well recognized, several mixers were designed with the a...

Purpose The purpose of this paper is to develop new boundary conditions for simulating the injection molding process of polymer melts. Design/methodology/approach The boundary conditions are derived and implemented to simulate real-life air vents (used to allow the air escape from the mold). The simulations are performed in the computational libr...

This Special Issue aims to gather new developments on the different areas of viscous and Viscoelastic fluid flows, ranging from mathematical modeling to experimental work. All researchers working in these areas are encouraged to submit their works. All submissions will be subject to a rapid and thorough review. Keywords: viscoelasticity mathemati...

In this work, we present a systematic numerical investigation of the 1:4 planar expansion creeping flow under the influence of slip boundary conditions for Newtonian and viscoelastic fluids, the latter modeled by the simplified Phan–Thien–Tanner constitutive model. The linear and nonlinear Navier slip laws were considered with the dimensionless sli...

This work presents analytical and numerical studies for pure Couette and combined Poiseuille-Couette flows under slip. The fluid behaviour is described by the recently proposed viscoelastic model, known as the generalised simplified Phan-Thien-Tanner constitutive equation, that considers the Mittag-Leffler function instead of the classical linear and ex...

This work presents new analytical and semi-analytical solutions for the pure Couette and Poiseuille-Couette flows, described by the recently proposed (Ferrás et al., A Generalised Phan-Thien-Tanner Model, JNNFM 2019) viscoelastic model, known as the generalised Phan-Thien-Tanner constitutive equation. This generalised version considers the Mittag-L...

In this work we propose a novel generalised form of the Phan-Thien and Tanner (PTT) model by considering a new functional form of the nonlinear expression characterizing the destruction of physical network junctions and entanglements. This new function of the trace of the stress tensor is given by the generalized Mittag-Leffler function, and contai...

Considering the regularity properties of the solutions of fractional differential equations, we develop a numerical method which is able to deal, with the same accuracy, with both smooth and non-smooth solutions of systems of fractional ordinary differential equations of the Caputo-type. We provide the error analysis of the numerical method and we il...

In this work we present a new numerical method for the solution of the distributed order time-fractional diffusion equation. The method is based on the approximation of the solution by a double Chebyshev truncated series, and the subsequent collocation of the resulting discretised system of equations at suitable collocation points. An error analysis...

In this work we present new numerical methods for the solution of fractional differential equations of single and distributed order that find application in the different fields of physics and engineering. We start by showing the relationship between fractional derivatives and processes like anomalous diffusion and viscoelasticity, and, we then dev...

In this work we present a hybrid numerical scheme for the solution of systems of fractional differential equations arising in several fields of engineering. The numerical scheme can deal with both smooth and non-smooth solutions, and, the idea behind the hybrid method is that of approximating the solution as a linear combination of non-polynomial f...

This work presents a simple procedure for balancing the flow in extrusion dies. The method consists in using different temperatures on the different sides of the extrusion die surface, in this way altering the local viscosity of the polymer melt, and thus the melt flow distribution. The design methodology follows a numerical trial-and-error procedu...

This work reports the developments made in improving the numerical stability of the viscoelastic solvers available in the open-source finite volume computational library \(OpenFOAM^{\textregistered }\). For this purpose, we modify the usual both-side diffusion (BSD) technique, using a new approach to discretize the explicit diffusion operator. Calc...

This paper reports the implementation of slip boundary conditions in the open-source computational library OpenFOAM. The linear and nonlinear Navier slip laws, which are newly implemented in this paper, can be used both for Newtonian and viscoelastic constitutive models. For the former case, the Couette assumption near the wall is employed, and for...

Multiphase flows are relevant in several industrial processes mainly because they are present in the production of a large diversity of products. Hence, the availability of accurate numerical modeling tools, able to cope with this type of flows, is of major significance to provide detailed information about the system characteristics, in order to g...