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On simulation of soft matter and flow interactions in biomass processing applications
Abstract
In this research, we extend our studies of the extraction process from diverse plant materials, introducing advancements to our previous models. Our framework considers dynamic elements by taking into account the motion of the particles, departing from the statical particle assumption in prior articles. Several methods such as moving geometries or modified equations for a system with moving particles in Lagrangian coordinates are introduced to boost the precision of our simulations, taking into account the complex dynamics of the solvent and its interaction with the plant material. Expanding beyond our focus on supercritical carbon dioxide (scCO2), our research is addressing some different applications. Besides the traditional solvent-based extractions, we consider potential applications in filtration, wood industry processes, etc. This allows our model to adapt to diverse industrial contexts with varied extraction mediums. Our coupled system of equations contains fluid dynamics equations for solvent flow, reaction-advection-diffusion equations for solute, and equations governing remaining solute concentration in biomass. The exchange of active material between solid and fluid is modelled by the Langmuir law. Applying finite volume techniques and implemented in the Octave/Matlab environment, our model captures the temporal evolution of two and three dimensional solute distribution and solvent velocity field. This modular framework facilitates the integration of tailor-made laws to represent diverse plant materials, ensuring versatility across applications. Through our simulations, we present the analysis of our modified model’s performance and discuss its advantages and limitations. This research is a slight step forward in understanding and optimising extraction processes, offering valuable insights for industries involved in functional foods, nutraceuticals, pharmaceuticals, cosmetics, filtration, and wood processing.
The paper concerns mathematical modeling of natural medical products processing. Fick's Laws are forming the core of our understanding of diffusion in solids, liquids, and gases. The drying models mainly Fick's Laws based are described in detail. The drying process of medical plants is relatively well studied. The extraction studies are not so well developed. The paper gives some insight in mathematical modeling for extraction. Phenomenological models of the extraction process consist of mass balance equations for solute in solid phase and in fluid phase. By integration of these differential equations time-dependent concentration profiles in both phases are obtained and the extraction curve is calculated from fluid-phase concentration at the extractor outlet. Phase equilibrium depends on extraction pressure and temperature and on the composition of solute, solvent, and matrix. Unfortunately, all these studies are yet very far from the ability to produce the practical recommendations for medical plants processing.
Ideally, in an attempt to reduce laboratory expenses, one would like to make
predictions of a complex particulate flow's behavior by numerical
simulations, with the primary goal being to minimize time-consuming
trial and error experiments. The recent dramatic increase in
computational power available for mathematical
modeling and simulation raises the possibility that modern numerical
methods can play a significant role in the analysis of complex particulate flows. This
fact has motivated the work that will be presented in this monograph.
The text can be viewed as a research monograph, suitable for use in a
first year graduate course for students in the applied
sciences, engineering and applied mathematics with an interest in the
computational analysis of complex particulate flows. Although it is
tempting, a survey of all possible modeling and
computational techniques
will not be undertaken, since the field is growing at an
extremely rapid rate. This monograph is designed to provide a basic introduction, using
models that are as simple as possible.
Finally, I am certain that, despite painstaking efforts, there remain errors of one sort or
another. Therefore, if readers find such errata, I would appreciate if they would
contact me at zohdi@newton.berkeley.edu.
See link:
http://www.amazon.com/Introduction-Simulation-Particulate-Computational-Engineering/dp/0898716276
The authors consider the process of extraction from heterogeneous plant material; a novel model offering 3D spatial resolution is proposed and simulation possibilities by applying several modern numerical methods for three dimensional problems are discussed. These types of problems naturally arise when one wishes to mathematically describe the processes of the extraction with solvents such as supercritical carbon dioxide (scCO2). The results of this process meet the demand of the functional foods, nutraceutical, pharmaceutical and cosmetic industries on bioactive compounds. The models used in typical simulations by the industry offer no spatial resolution of the extraction process, however, when novel designs of extractors are developed, the three dimensional flow of the solvent and its interaction with the plant material should be considered. We propose a coupled system of equations consisting of fluid dynamics equations describing the flow of the solvent and reaction-advection-diffusion equations for the solute, plus equations describing the remaining concentration of solute in the biomass. The exchange of the active material between the solid and fluid is modelled by the Langmuir law. The initial distribution of solute in the plant material is not assumed to be homogeneous, nor are the extraction parameters, i.e. heterogeneous mixture of plant materials can be covered by this model. The equations are discretized by using finite volume techniques and currently implemented in Octave/Matlab environment. As a result, the temporal evolution of the three dimensional distribution of the solute is obtained along with the velocity field of the solvent, allowing detailed studies of the extraction process in a virtual design. The model is modular, allowing integrating tailor-made laws to describe various plant materials. The authors present simulation results and analyse the advantages and disadvantages of the proposed methods and approaches.
The methodology previously proposed by the authors to solve particle-laden turbulent flows through a multiscale approach is extended by introducing a continuous function for the dispersed phase concentration. The proposed continuous model is especially useful for studying the motion of particle streams in which gravitational and inertial effects cause the particles to deviate from a simple trajectory following the surrounding flow, as would be the case for the limit of very small, massless particles. The results show an excellent comparison between the solutions obtained using the continuous model and simulations evaluating the forces on each particle individually. Distinct advantages of the continuous approach are a much lower computational overhead, a better load balance and ease of parallelization. The multiscale methodology proposed may be used in the area of modeling and simulation of airborne infectious diseases.
Available online at: https://authors.elsevier.com/c/1fDv2AQEIzV~h
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Understanding multiphase flows is vital to addressing some of our most pressing human needs: clean air, clean water, and the sustainable production of food and energy. This article focuses on a subset of multiphase flows called particle-laden suspensions involving nondeforming particles in a carrier fluid. The hydrodynamic interactions in these flows result in rich multiscale physics, such as clustering and pseudo-turbulence, with important practical implications. Theoretical formulations to represent, explain, and predict these phenomena encounter peculiar challenges that multiphase flows pose for classical statistical mechanics. A critical analysis of existing approaches leads to the identification of key desirable characteristics that a formulation must possess in order to be successful at representing these physical phenomena. The need to build accurate closure models for unclosed terms that arise in statistical theories has motivated the development of particle-resolved direct numerical simulations (PR-DNS) for model-free simulation at the microscale. A critical perspective on outstanding questions and potential limitations of PR-DNS for model development is provided. Selected highlights of recent progress using PR-DNS to discover new multiphase flow physics and develop models are reviewed. Alternative theoretical formulations and extensions to current formulations are outlined as promising future research directions. The article concludes with a summary perspective on the importance of integrating theoretical, modeling, computational, and experimental efforts at different scales.
One group of mathematical models for supercritical fluid extraction from plants is based on the Broken-and-Intact Cell (BIC) concept. A simplified BIC model with analytical solution, derived for the extraction of vegetable oils from seeds, was published in 1994. It has been used by several researchers also for the extraction of other solutes from other plant parts. The aim of this contribution is to show how the simplified BIC model was derived from Lack’s model, for what type of extractions it is suited and where it fails, and how the BIC models have been improved since then.
Numerical simulations are extensively used to investigate the motion of suspended particles in a fluid and their influence on the dynamics of the overall flow. Contexts range from the rheology of concentrated suspensions in a viscous fluid to the dynamics of particle-laden turbulent flows. This review summarizes several current approaches to the numerical simulation of rigid particles suspended in a flow, pointing out both common features and differences, along with their primary range of application. The focus is on non-Brownian systems for which thermal fluctuations do not play a role, whereas interparticle forces may result in particle self-assembly. Applications may include the motion of a few isolated particles with complex shape or the collective dynamics of many suspended particles. Expected final online publication date for the Annual Review of Fluid Mechanics Volume 49 is January 03, 2017. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
