Table Of ContentComplexity and Complex
Chemo-Electric Systems
Complexity and Complex
Chemo-Electric Systems
Stanisław Sieniutycz
Warsaw University of Technology, Faculty of Chemical and Process Engineering, Poland
Elsevier
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Preface
The book on Complexity and Complex Chemo-Electric Systems is the second volume on
complexity and systems written by the same author. The first book titled Complexity and
Complex Thermo-Economic Systems, which was published at the beginning of 2020, was
focusedonthermodynamicandeconomicaspectsofcomplexityandcomplexsystems.Evenif
thefirstbookappearednotlongago,ourworldhaschangedhenceforthsignificantly.Now,we
attempttoliveandworkinaworldpartlyfragmentedbycoronavirusepidemic,i.e.,inaworld
differentthanpreviousone,onefullofproblemsdifferentthancouldbeexpected2yearsagoby
an ordinary human being. The structure and change in humans’ decisions must certainly
involvemorecoordinatesrelated to thecurrenthealthand medicalrecommendations.Weare
likely toexperience animpact uponorganizations,societies, environment,science,medicine,
etc., yet the proportionsbetween these components will be different than previously. All said
earlierimpliesthegrowingroleoftheknowledgerelatedtobiologicalandmedicalinformation
that will dominate for at least a period of time over the role of purely scientific information,
stemming from exact sciences. Needless to say, however, that thermodynamics, as the basic
macroscopic science, will invariably remain an inevitable component in modeling, analysis,
andoptimizationofthemajorityofpractical,biological,andevenlivingsystems,inparticular
those considered in the present book.
It is probably familiar to the majority of readers that most thermodynamic models take into
account energy and matter balances, the results of invariance principles of physics. These
balances incorporate limitations on working parameters of real processes, which should be
taken into account when formulating constraints on performance of all macroscopic systems,
including living systems. Thermodynamics kinetic theory and/or experiments providedata of
static and transport properties needed in calculations. These data are necessary to express
balance or conservation laws for energy and substances in terms of variables used in systems
modeling, analysis, synthesis, the stages terminating sometimes at an optimization problem
(aftermakingtheselectionofstatevariables,controls,andparameters).Infact,thermodynamic
variables constitute frequently state and/or control coordinates in systems optimizations;
moreover, some thermodynamic variables or their functions may constitute performance
criteriaofoptimization.Thermodynamicsmayalsoinfluencetheformulationofparaeconomic
optimizationcriteriagoverningthermoeconomicoptimizationofsystems,as,e.g.,thoseinour
first (2020) complexity book.
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Preface
Briefly, the basic purpose of the present book is to investigate formulations, solutions, and
applicationsdescribingoptimalorsuboptimalperformanceofselectedchemo-electricsystems,
including those considered from the standpoint of a prescribed optimization criterion
(complexity measure, chemical production, power yield, topological structure, economical
profit, discretization scheme, iterative strategy, simulation time, convergence test, technical
index, etc.).
Introductory Chapter 1 sketches the applications of classical thermodynamics to complex
disequilibrium systems such as solutions of macromolecules, magnetic hysteresis bodies,
viscoelastic fluids, polarizable media, etc. To be properly described, these systems require
certain extra variables, the so-called internal variables, introduced into the fundamental
equation of Gibbs. Irreversible systems belonging to extended irreversible thermodynamics
(EIT) are also included and briefly analyzed. In this extended case, dissipative fluxes are
independent variables treated on an equal footing with classical variables of thermostatics.
Systems governed by Gibbs equations with additional “internal” variables are studied to
consider viscoelastic and viscoplastic materials, and fluids with high diffusive fluxes of heat,
mass,andmomentum.Rationalandextendedthermodynamictheoriesareappropriatetoolsfor
theiranalysis.Finally,weconsidercomplexsolutionsofmacromolecules,magnetichysteresis
bodies, viscoelastic fluids, polarizable media, i.e., all systems which exhibit involved
thermodynamic behavior and for which the internal variables are essential in their
thermodynamic description.
Chapter 2 deals with systems characterized by complex states which undergo complex
transformations.Inthisbook,theyareillustratedbyequationsofchemicalinvariantsinsystems
of electroneutral components. The chapter synthesizes valuable investigations toward a
systematicmethodidentifyingreactioninvariantsandmolebalancesforcomplexchemistries.
Reactioninvariantsarequantitiesthattakethesamevaluesbefore,during,andafterareaction.
Dealingwiththeseinvariantsisusuallyrelatedtocontrolaspectsofasystemaswellastousing
them in process design and planning of experiments. The material balances for chemically
reactingmixturescorrespondexactlytoequatingtheseinvariantsbeforeandafterthereaction.
Following the important paper by Gadewar et al. (2001), we present a systematic method
for determining the reaction invariants from any postulated set of chemical reactions.
The described strategy not only helps in checking the consistency of experimental data and
reactionchemistrybutalsogreatlysimplifiesthetaskofwritingmaterialbalancesforcomplex
reactionchemistries.Oneoftheimportantapplicationsofthismethodistheautomationofmole
balances in the conceptual design of chemical processes. Further on, the text is devoted to
complex states and complex transformations occurring during optical instabilities as well as
in growth and aging phenomena.
In Chapter 3 we describe many meaningful aspects of Heylighen’s discussion of evolving
complexsystems.Althoughthegrowthofcomplexityduringevolutionseemsobvioustomany
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Preface
observers, it has sometimes been questioned whether such increase objectively exists. The
chapter tries to clarify the issue by analyzing the idea of complexity as a combination of two
factors: variety and dependency. For both living and nonliving systems, it is argued that
variation and selection automatically produce differentiation (variety) and integration
(dependency).Structuralcomplexificationisproducedbyspatialdifferentiationandaselection
of fit linkages between components. Functional complexification follows from the need to
increase actions in order to cope with more diverseenvironmental perturbations,and also the
need to integrate actions into higher-order complexes, to minimize the difficulty of
decision-making. Both processes produce a hierarchy of nested supersystems or metasystems
andtendtobeself-reinforcing.Simplicityisaselectivefactor,butitdoesnottendtoarrestor
reverseoverallcomplexification.Increaseintheabsolutecomponentsoffitnessassociatedwith
complexification defines a preferred direction for evolution, although the process remains
wholly unpredictable.
Chapter4treatsselectedaspectsofcomplexityinbiologicalsystems.Webeginwithpointing
outtheinteractionbetweenstatisticalmechanics,thermodynamics,andnonlineardynamicsin
order to stress the importance of Mandelbrot’s discovery that fractals occur vastly in nature.
This opens the door to new world of fractals, their origin, “production,” and properties. Of
particular interest are physical aspects of fractals which originate in Nature from the
self-organizedcriticalityofdynamicalprocesses.Arelevantapproachtotheunderstandingof
erythrocytebehavior(inparticular,erythrocytesedimentationanditsenhancement)isatheory
utilizing fractal analysis. Computer results may be compared with experimental values,
showing a progress in the performance of the operation. Blood poisoning phenomena are
discussedalongwithbasicaspectsofinvolvedbiodynamics.Themostrecentinvestigationsin
the field of erythrocytes are concentrated on their detrimental changes caused by the blood
infectionsofcoronavirusinthehumanorganism,asshowninFigs.4.1and4.2ofthisbook.The
firstfigureexposestheinfectedbloodflow,thesecondonepicturizesCoronavirusSARS-CoV-2.
AremarkablepaperavailableoncombinationpreventionforCOVID-19iscited.Thereaderis
referredtothecurrentliteratureonthistopicthatgrowsintime.
Chapter5reviewsinitslargeparttheexistingdynamicmodelsofmicrobialfuelcells(MFCs)
and microbial electrolysis cells (MEC) as well as the emerging approaches for their
optimization andcontrol. Themechanismof catalyst actionopens thegreatest possibilitiesin
theheterogeneouscatalysis.Heterogeneouscatalysisimpliestwobasicproblems:(a)asearch
for new catalysts, understood as scientifically substantiated substances showing catalytic
propertieswithrespecttoagivenreaction,and(b)finding(orworkingout)appropriatesupport
and binding linkage for a catalyst substance on this support, ensuring required properties of
chemical products. Bioelectrochemical systems (BESs), such as microbial fuel cells (MFCs)
and microbial electrolysis cells (MECs), are capable of producing energy from renewable
organic materials. Over the last decade, extensive experimental work has been dedicated to
exploringBESapplicationsforcombinedenergyproductionandwastewatertreatment.These
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efforts have led to significant advancement in areas of BES design, electrode materials
selection, as well as a deeper understanding of the associated microbiology, which helped to
bring BES-based technologies within commercial reach. Further progress toward BES
commercialization necessitates the development of model-based optimization and process
control approaches.
Chapter6dealswiththehierarchicalscalingcomplexities.Thecomplexitymeasuresdiscussed
therein refer explicitly to a hierarchical structure and to the infinite-depth limit of a certain
relevant quantity associated with the corresponding tree. The tree structure underlying a
hierarchicalsystemcanbecharacterizedbothtopologically,thatmeansbyreferringsolelytoits
shape,andmetrically,byconsideringthevaluesoftheobservablesassociatedwitheachofits
vertices (Badii and Politi, 1997). The former approach is particularly appropriate when
self-similarity does not hold. This appears to be the general case, as can be observed in
biological organisms, electric discharges, diffusion-limited aggregates, dynamical systems,
turbulent structures, and many other cases. Other researchers as, e.g., Huberman and Hogg
(1986) propose to associate complexity with the lack of self-similarity, evaluated in terms of
diversity of the hierarchy. This proposal seems to be accepted by Badii and Politi who assert
that the proposal is the best defined by referring to a tree with a finite depth n and maximal
branchingratiob,asshowninFig.9.1intheir1997book,whichisrepresentedbyFig.6.1inthe
present volume.
Chapter 7 deals with modeling of power yield in noncatalytic chemical and electrochemical
systems. The main objectives of this chapter are power generation limits, which are the basic
qualityindicatorsfortheenergysystems.Theselimitsareevaluatedviaoptimizationofvarious
converters, such as chemical or electrochemical engines, but also solar engines.
Thermodynamic analyseslead to converters’ efficiencies. Efficiency equationsserveto solve
problems of upgrading and downgrading of resources. While methods of static optimization,
i.e.,differentialcalculusandLagrangemultipliers,aresufficientforsteadyprocesses,dynamic
optimizationappliesthevariationcalculusanddynamicprogrammingforunsteadyprocesses.
In the reacting systems, chemical affinities constitute prevailing components of an overall
efficiency. Therefore the flux balances are applied to derive power in terms of active part of
chemicalaffinities.Examplesshowpowermaximainfuelcellsandprovetheapplicabilityof
the developed theory to chemical and electrochemical systems.
Chapter 8 synthesizes concomitant action of fuels, catalysts, wastes, and poisons in
chemo-electric systems. After the brief reviewing of a group of valuable papers treating the
effect of the catalyst decayon theperformance of chemical reactions, wepass to theanalysis
anddiscussionofthoseselectedworksthatcharacterizetheperformanceofchemicalreactors
and SOFCs with poisoning of catalysts or electrodes. Results for catalytic heterogeneous
systems are quite representative to reveal the progress in the field of their mathematical
modeling and optimization. Considered are kinetics of contact (catalytic) reactions, surface
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Preface
processes,externalandinternaldiffusion,chemicalnetworks,andanode-supportedSOFCsfor
determination of their poisoning limits. Outlined is a generalized approach to processes with
chemical reaction and catalyst deactivation, based on kinetic models proposed by N.M.
OstrovskiiofBoreskovInstituteofCatalysisinRussia.Hedemonstratesthatmanydeactivation
equations can be derived using the Bodenstain’s principle of the quasisteady state
approximation. With this principle, he suggests a general equation usable to any linear
mechanism and provides examples for various involved cases of chemical reaction subject to
catalyst deactivation. The reader is referred to his works, reach in new ideas and knowledge.
Chapter 9 develops modeling and simulation of chemo-electro-mechanical coupling in the
human heart. Computational modeling of the human heart allows to predict how chemical,
electrical, and mechanical fields interact throughout a cardiac cycle. Pharmacological
treatment of cardiac disease has advanced significantly over the past decades, yet it remains
unclear how the local biochemistry of individual heart cells translates into global cardiac
function. Following the basic research of Wong et al. (2013), the chapter applies a novel,
unifiedstrategytosimulateexcitablebiologicalsystemsacrossthreebiologicalscales;fromthe
molecularlevel,viathecellularlevel,totheorganlevel.Todiscretizethegoverningchemical,
electrical,andmechanicalequationsinspace,amonolithicfiniteelementschemeisproposed.
A global-local split is applied, in which the deformation of the mechanical problem and the
transmembranepotentialandelectricalstructureareintroducedgloballyasanodaldegreesof
freedom, while the state variables of the chemical problem are treated locally as internal
variablesontheintegrationpointlevel.Thisparticulardiscretizationschemeishighlyefficient
andinherentlymodular,sinceitallowstocombineavarietyofdifferentcelltypesthroughonly
minor local modifications on the constitutive level. To ensure unconditional algorithmic
stability, implicit backward Euler finite difference scheme is exploited to discretize the
resulting system in time. The incremental, iterative Newton-Raphson scheme is applied to
increasealgorithmicrobustnessandtoguaranteeoptimalquadraticconvergence.Theproposed
algorithm allows to simulate the interaction of chemical, electrical, and mechanical fields
during a cardiac cycle on a real patient-specific geometry, robust and stable, with calculation
times on the order of 4days on a standard desktop computer. For the real-time clinical
applications, the plain electrical problem only requires simulation times of less than 10s.
Systemsoptimizationandmathematicsinmanychaptersofourpreviousbooksoffertheformal
way of assuring the best intervention into complicated realities, either by providing limiting
values of certain quantities (extremum power, minimum cost, maximum yield, etc.) or by
finding economically optimal solutions (optimal trajectories and optimal controls). These
solutionsensureoptimalfeasibleprofitsorcostsattributedtoeconomicalorexergo-economical
models.Optimalsolutions,also called“bestsolutions,”areobtainedbycalculationsapplying
suitable computational algorithms. Corresponding computer programs use these algorithms,
each leading to optimal solution in its own way. Results of optimization calculations include
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Preface
optimal trajectories and controls usually in discrete forms (discrete representation of the
optimization solution).
The bookhas some uniquefeatures of related benefitto the reader, in view of still demanded
literature information on solutions of practical optimization problems. The book and its first
(2020) part extend the family of previously treated problems by inclusion of chemical
invariants, enriched references to experiments, information on growth of complexities in
evolution,extrainformationondeactivationofcatalysts,andotherfactorsappropriateforusing
thermodynamic models and advanced methods of optimization.
The literature of optimizations in chemical and economical worlds keeps growing, so that
efficientliteraturesearchesarestillnecessary.Thebookisintendedasacollectionofchapters
addressed to actively working scientists and students (both undergraduate and graduate).
Associated professionals are chemical engineers, physiologists, medical engineers, control
engineers, environmental engineers, pharmacologists, cardiologists, and some others. The
authors offer basically a textbook equipped in the feature of a reference book. Because of
abundance of literature discussion and citation of numerous references, the book should
constituteavaluableandhelpfulreferencevolumeforanyreader,includingreadersemployed
inindustriesanduniversities.Becauseofthetextbookpropertyoftheproposedvolume,names
and levels of appropriate courses are listed as follows. The book can be used in schools,
libraries, industries, and internet centers as a directory of guided tour described in the book
chapters, each tour representing a research problem.
One can ask: What type of knowledge do readers need before reading the book? The book
applies analytical reasoning and transfers to the reader a reasonable amount of analytical
mathematics. Therefore the knowledge of elementary and differential calculus is mandatory.
Basic equations of optimal control (Pontryagin’s maximum principle and the corresponding
optimization theory) should be the requirement only when reading Chapters 7 and 8. Since,
however,thesatisfactionofthisconditionmightbedifficulttothegeneralreader,Chapter12of
Sieniutycz’s and Szwast’s 2018 book Optimizing Thermal, Chemical and Environmental
Systems offers a synthesizing text on Pontryagin’s maximum principle and related criteria of
dynamic optimization.Because of the presence of the earlier theoretical information,it is not
assumedthatusingothersourceswillbenecessary.Inthemostadvancedexamples,complete
analyses are developed to achieve solutions enabling verbal descriptions of the discussed
problems.
Another question is: What should the readers gain (academically/professionally) from the
reading of the book? When the volume is used as a textbook, it can constitute a basic or
supplementarytextin thefollowingcourses,conductedmostlyinengineeringdepartmentsof
technical universities:
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Preface
(cid:129) Technical thermodynamics and industrial energetics (undergraduate).
(cid:129) Electrochemical reaction engineering (undergraduate).
(cid:129) Electrochemical description of biological cells (undergraduate).
(cid:129) Modeling and optimal control of bioelectrochemical systems (graduate).
(cid:129) Anode-supported SOFCs for determination of poisoning limits (graduate).
(cid:129) Complex chemo-electric systems: theory and applications (graduate).
(cid:129) Computational aspects of chemo-electro-mechanical systems (graduate).
Having read the book, the readers will gain the necessary information on what has been
achievedtodateinthefieldofcomplexityandcomplexsystems,whatnewresearchproblems
could be stated, or what kind of further studies should be developed within the specialized
modelingandoptimizationsofcomplexsystems.Itisexpectedthattheinformationcontained
in the book will be helpful to improve both abstract and technical skills of the reader. The
presentbookisespeciallyintendedtoattractgraduatestudentsandresearchersinengineering
departments(especiallyinchemical,electrochemical,andelectricalengineeringdepartments).
The author hopes that the book will also be a helpful source to actively working
electrochemists, engineers, and students.
Finally,wewouldliketolistotherrelatedbooksthatcantargetasimilaraudiencewiththistype
of content. Elsevier has recently published the following thermodynamically oriented books:
Variational and Extremum Principles in Macroscopic Systems (Ed. by S. Sieniutycz and
H. Farkas, Elsevier, Oxford, 2000).
Energy Optimization in Process Systems (by S. Sieniutycz and J. Jez(cid:1)owski, Elsevier,
Oxford, 2009).
EnergyOptimizationinProcessSystemsandFuelCells(byS.SieniutyczandJ.Jez(cid:1)owski,
Elsevier, Oxford, 2013 (2nd ed.)).
Thermodynamic Approaches in Engineering Systems (by S.Sieniutycz, Elsevier,
Oxford, 2016).
Optimizing Thermal, Chemical and Environmental Systems (by S. Sieniutycz and
Z. Szwast, Elsevier, Oxford, 2018).
EnergyOptimizationinProcessSystemsandFuelCells(byS.SieniutyczandJ.Jez(cid:1)owski,
Elsevier, Oxford, 2018 (3rd ed.)).
Complexity and Complex Thermo-Economic Systems (by S. Sieniutycz, Elsevier,
Oxford, 2020).
ReadingthepresentbookonComplexityandComplexChemo-ElectricSystemswillprovidethe
opportunityfortreatingallpreviouslymentionedbooksbecauseoftheirunityofteachingstyle
as a teaching cluster.
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