Granular Gaseous Flows: A Kinetic Theory Approach to Granular Gaseous Flows PDF
Preview Granular Gaseous Flows: A Kinetic Theory Approach to Granular Gaseous Flows
Soft and Biological Matter Vicente Garzó Granular Gaseous Flows A Kinetic Theory Approach to Granular Gaseous Flows Soft and Biological Matter Series Editors David Andelman, School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel Wenbing Hu, School of Chemistry and Chemical Engineering, Department of Polymer Science and Engineering, Nanjing University, Nanjing, China Shigeyuki Komura, Department of Chemistry, Graduate School of Science and Engineering, Tokyo Metropolitan University, Tokyo, Japan Roland Netz, Department of Physics, Free University of Berlin, Berlin, Germany Roberto Piazza, Department of Chemistry, Materials Science, and Chemical Engineering “G. Natta”, Polytechnic University of Milan, Milan, Italy Peter Schall, Van der Waals-Zeeman Institute, University of Amsterdam, Amsterdam, The Netherlands Gerard Wong, Department of Bioengineering, California NanoSystems Institute, UCLA, Los Angeles, CA, USA “SoftandBiologicalMatter”isaseriesofauthoritativebookscoveringestablished andemergentareasintherealmofsoftmatterscience,includingbiologicalsystems spanning all relevant length scales from the molecular to the mesoscale. It aims to serve a broad interdisciplinary community of students and researchers in physics, chemistry, biophysics and materials science. Pure research monographs in the series, as well as those of more pedagogical nature, will emphasize topics in fundamental physics, synthesis and design, characterization and new prospective applications of soft and biological matter systems. The series will encompass experimental, theoretical and computational approaches. Topics in the scope of this series include but are not limited to: polymers, biopolymers, polyelectrolytes, liquids, glasses, water, solutions, emul- sions, foams, gels, ionic liquids, liquid crystals, colloids, granular matter, complex fluids, microfluidics, nanofluidics, membranes and interfaces, active matter, cell mechanics and biophysics. Both authored and edited volumes will be considered. More information about this series at http://www.springer.com/series/10783 ó Vicente Garz Granular Gaseous Flows A Kinetic Theory Approach to Granular Gaseous Flows 123 Vicente Garzó Departamento deFísica andInstituto de ComputaciónCientíficaAvanzada (ICCAEx) Universidad deExtremadura Badajoz, Spain ISSN 2213-1736 ISSN 2213-1744 (electronic) Soft andBiological Matter ISBN978-3-030-04443-5 ISBN978-3-030-04444-2 (eBook) https://doi.org/10.1007/978-3-030-04444-2 LibraryofCongressControlNumber:2018966392 ©SpringerNatureSwitzerlandAG2019 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictionalclaimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Per a Ana, Alex i Leo Foreword by James W. Dufty Kinetic theory provides a “mesoscopic” description of matter, midway between a formal treatment based on Newton’s equations and a phenomenological treatment of continuum mechanics. It is perhaps the best practical approach for addressing both quantitative calculations and difficult conceptual foundations. Its adoption for granular media has a history within the engineering community extending over thirty-five years. During the past two decades, the physics and mathematics com- munitieshaverevisitedthisapproachwithrenewedattentiontodetails,comparison tocomputersimulations,andtestsagainstexactlysolvablemodelsystems.Vicente Garzó has been at the center of these recent developments and is a master of the intricate details required for quantitative predictions. Equally important, he is a masterofcritiquingthenewcontextofthesepredictionswithinahostofconceptual questions. MyfirstcollaborationwithVicentewasin1993wherewe(withothers)studieda rare exact solution to the nonlinear Boltzmann equation for molecular gases describing rheological phenomena far from equilibrium. It contained novel math- ematics,simulationanalysis,andunexpectedconceptualinterpretation.Thesewere tobecommoncharacteristicsofhislaterworkongranularkinetictheory.Hisinitial work in 1999 provided a derivation of Navier–Stokes hydrodynamics from the dense fluid Enskog kinetic equation extended to granular gases. Fundamental questions regarding the Chapman–Enskog solution to this equation, such as any limitation on the degree of inelasticity, solubility conditions, and stability of the hydrodynamic description, were addressed. Exact linear integral equations for the transport coefficients and cooling rate were given, and approximate numerical predictions obtained. The results were compared favorably to an exactly solvable model kinetic equation. That same year, he gave a similarly complete analysis of the homogeneous cooling solution to the multi-component Enskog kinetic equation, providing a basis for his subsequent derivation of hydrodynamics for dense granular mixtures. These were the beginning of Vicente’s focus on the kinetic theory of granular gasesforthenexttwodecades.Thepresentvolumecapturesthebroadscopeofthat intellectualachievementinaself-containedandpedagogicalform.Itiscompletein vii viii ForewordbyJamesW.Dufty thesensethatadiligentandinterestedscholarcanmasterthecomplexitiesofkinetic theoryandgranulargaseswithouttheneedforadditionaltextsorextensivereference to the literature. Nevertheless, there is an excellent extensive bibliography linking specifictopicstotheoriginalpapers.Thecalculationsaredifficultindetail,buttheir definitions are clear and unambiguous. There are many graphs for comparisons across a large parameter space, and there are two types of simulations given— DSMCtoconfirmapproximationstothekineticequationandMDtoconfirmresults independent of kinetic theory limitations. Predictions of the many unexpected fea- tures of granular flows are clearly supported in this way—phenomenology is sup- plantedby theoryin a unifiedcontext. Granular matter occurs broadly across the fields of chemical engineering, materialssciences,andphysicsinmanydifferentforms.Thepresenttextisfocused on activated (driven) granular flows in their fluid state. Furthermore, the nature oftheinteractionamongthegrainsisspecializedtothatofhardsphericalparticles. However, this specialization still captures the most important differences between granular and molecular gases. It allows the author to provide a very detailed analysis of the corresponding kinetic theory and its consequences in a logical progression for an in-depth understanding of the field in a single text. Vicente Garzóhasproducedaremarkableworkofscholarshipthatwillserveindividualsin a multi-disciplinary community both for training and as a stepping stone for new research. Gainesville, FL, USA James W. Dufty April 2018 Foreword by Rodrigo Soto The correct description of the dynamics of granular matter is key for the under- standing of phenomena that take place over a large range of temporal and spatial scales:fromtheastrophysicalscaleduringtheformationofplanetstoavalanchesin dunes.Thisdiversityofscalesisduetotheubiquityofgranularmaterialsinnatural systems and industrial processes. When energy is injected at a sufficient rate, granular materials enter into the so-called (rapid) granular flow regime, where collisions dominate over persistent contacts, which are otherwise relevant in the static and quasi-static regimes. The use of kinetic theory signified a major advancement in the description of granular flows. Vicente Garzó made important contributionsinthisprocess,andheis,hence,amostauthoritativescientisttowrite a book on the subject. With simple hypothesis, kinetic theoryallows toobtain thestatistical properties of granular flows and, also, to derive the hydrodynamic equations that govern the large-scale dynamics of the system, providing means to compute all the relevant transportcoefficients.Thecalculationsinkinetictheoryare,sometimes,lengthyand difficult. Vicente Garzó does not avoid any of these complexities, providing the readers all the necessary tools to understand the growing literature on the subject and make on their hand their own contributions. In all cases, the extensive calcu- lationsarecomparedwithMonteCarloormoleculardynamicssimulations,helping to establish the limits of validity of the different approximations made. Moreover, the author presents a comprehensive and detailed review of the literature, which is an invaluable starting point for any researcher. Vicente Garzó has written a wonderful book where he shows the power of kinetic theory to describe qualitatively and quantitatively the features of granular flows. There are many examples and applications in the book, but I would like to focus on one, where the description is brilliant. He shows how the transport coefficientsdependonthereferencestatethatisbeingperturbed,providingexplicit expressions for these when the reference state is homogeneous of a uniformly shearedone.Thankstohisdetailedcalculations,theoriginofthesenascentfeatures is transparent. ix x ForewordbyRodrigoSoto Besides the direct interest for those aiming to analyze and describe granular flows,thisbookwillalsoshowtobevaluableforresearcherswhoneedtodevelop kinetic models and tools for new regimes appearing in granular matter, but also in other non-equilibrium systems as, for example,active matter or traffic flow,just to mention a few. Santiago de Chile, Chile Rodrigo Soto July 2018
The list of books you might like
