Granular Gaseous Flows: A Kinetic Theory Approach to Granular Gaseous Flows

419 Pages·2019·12 MB·English

by  Vicente Garzó

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
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Both authored and edited volumes will be considered.
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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
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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