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Multicomponent flowsconsist of different chemical speciesthat are mixed at the molecular level andgenerally share the same velocityand temperature.They differ from multiphase flows where the different phases are immiscible(Drew and Passman 1999)and only occupy a fraction of the total volume.The chemical species may also interact through chemical reactionsand the resulting multicomponent reactive flowsare observed in various natural phenomena and engineering applications.

The Engineering Of Chemical Reactions L D Schmidt Solution Manual 2

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In chemical engineering,chemical reactors may be of various shapes and are typically designed to optimize a given set of chemical reactions.The corresponding processes may be highly complex with multiple reactant injections,heating or cooling devices,pumps to increase pressure, homogeneous chemistry as wellas heterogeneous chemistry with catalysts(Rosner 1986;Kee et al. 2003; Schmidt 2009).Optimizing reactors' shapes as well as chemical processes again requires a detailed knowledge ofthe corresponding multicomponent reactive flows.

A chemical mechanisminvolving \(n^\hskip-0.04em \rm r\geq 1\) elementary reactions for \(n\geq 1\) species may be written \[\beginequation\tag6\sum_k\in S \nu_ki^\rm f \; \mathfrak M_k \ \rightleftarrows \ \sum_k\in S \nu_ki^\rm b \; \mathfrak M_k,\qquad i\in \mathfrak R,\endequation\]where \(\mathfrak M_k\) is the chemical symbol of the \(k\)th species, \(\nu_ki^\rm f\) and \(\nu_ki^\rm b\)the forward and backward stoichiometric coefficients of the \(k\)th species in the \(i\)th reaction, and\(\mathfrak R=\ 1,\ldots,n^\hskip-0.04em \rm r\\) the set of reaction indices.The species molar production rates are in the form \[\beginequation\tag7\omega_k= \sum_i=1^m (\nu_ki^\rm b - \nu_ki^\rm f) \biggl[\cal K_i^\rm f \prod_l\in S \Bigl(\frac\rho_l^m_l\Bigr)^\nu_li^\rm f-\cal K_i^\rm b\prod_l\in S \Bigl(\frac\rho_l^m_l\Bigr)^\nu_li^\rm b\biggr],\qquadk\in S,\endequation\]where \(\mathcalK_i^\rm f\) and \(\mathcalK_i^\rm b\) are the forward and backward rate constants of the \(i\)th reaction,respectively.

These rates may be obtained from themass action law or fromthe kinetic theory of dilute gases when the chemicalcharacteristic times arelarger than the mean free times of the molecules and the characteristic times of internal energy relaxation(Giovangigli 1999;Nagnibeda and Kustova 2009).The reaction constants \(\mathcalK_i^\rm f\) and \(\mathcalK_i^\rm b\) are functions of temperature and are Maxwellian averaged values of molecular chemical transition probabilities and this impliesthe reciprocity relations \[\beginequation\tag8\mathcal K_i^\rm e(T) = \frac \mathcal K_i^\rm f (T) \mathcal K_i^\rm b (T),\qquad\log \mathcal K_i^\rm e(T) = - \sum_k\in S (\nu_ki^\rm b - \nu_ki^\rm f) \frac m_k g_k(T, m_k) R T,\qquadi\in\mathfrak R,\endequation\]where \(\mathcalK_i^\rm e(T)\)is the equilibrium constant of the \(i\)th reaction(Giovangigli 1999).The forward reaction constants\(\mathcal K_i^\rm f\),\(i\in\mathfrak R\),are usually evaluated with Arrhenius law\beginequation\tag9\mathcal K_i^\rm f = \mathfrakA_i T^\mathfrakb_i \exp \bigl( - \mathfrakE_i/R T \bigr),\qquadi\in\mathfrak R,\endequationwhere \(\mathfrakA_i\) is the preexponential factor, \(\mathfrakb_i\) the temperature exponent and \(\mathfrakE_i\) the activation energyof the \(i\)th reaction. The data required for each chemicalreaction then reduce to the stoichiometric coefficients\(\nu_ki^\rm f\)and \(\nu_ki^\rm b\),and the Arrhenius constants\(\mathfrakA_i\),\(\mathfrakb_i\),and\(\mathfrakE_i\),assuming that the species thermodynamic is known.The chemical reactionstoichiometric coefficients\(\nu_ki^\rm f\)and \(\nu_ki^\rm b\)are such that atomic elements are conserved.

The size of detailed chemicalreaction mechanismshas been steadily increasing over thepast years ranging from a few speciesand reactions to several thousandof species interacting through tensof thousands of chemical reactionsas for instance forbio-fuel or atmospheric pollution.

A first idea is to simplify the reactive aspects of the flow under consideration. In this situation, the number of species and chemical reactionsare decreased and the resulting set of partial differential equations issimplified.The transport fluxes andtransport property evaluationmay accordingly be simplified.A typical example is thatof a single irreversible chemical reaction (Williams 1985).Another type of chemistrysimplification is associated with the ideaof a slow manifold.In this framework,it is assumed that the state of the mixture,after some fast relaxation process that may be discarded,belongs to a manifold associated with a much slower dynamics.The manifold is then parametrized by a smallset of parameters,typically some concentrations or thermal parameters,that are governed by a reduced system of partial differential equations.In combustion science for instance,slow manifolds have first beendefined by solely looking at thesource terms (Peters 1985; Mass and Pope 1992) and then defined through thecalculation of libraries of flameletsthereby involving diffusive processes (Gicquel et al. 2000; Van Oijen et al. 2001;Bykov and Maas 2007;Auzillon et al. 2012).The chemical equilibrium model may also be seen as anultimate simplified slow manifold modelwhere the slow variables arethe atomic massdensities,momentum and energy.

Taking into account chemical reactions dramatically increases the difficulties,especially when detailed chemical and transport modelsare considered.Interactions between chemistry and fluid mechanics are especially complex inreentry problems (Anderson 1989),combustion phenomena (Poinsot and Veynante 2005),or chemical vapordeposition reactors(Hitchman and Jensen 1993;Kee et al. 2003).An important aspect of complex chemistry flows is the presence of multiple time scales which may range typically from \(10^-10\) secondup to several seconds.In the presence of multiple time scales, implicit methods are advantageous, since otherwise explicit schemes are limited by the smallest time scales (Descombes and Massot 2004; Oran and Boris 1987).A second potential difficulty associated with themulticomponent aspect is the presence of multiple space scales.In combustion applications for instance the flame fronts are very thin and typically requirespace steps of \(10^-3\) cm at atmospheric pressure,and even \(10^-5\) cm at \(100\) atm,whereas a typical engine scale may be of \(10\) cmor even \(100\) cm.The multiple scales can only be solved by using adaptive gridsobtained by successive refinements or by moving gridsfor unsteady problems (Smooke 1982; Oran and Boris 1987;Bennett and Smooke 1998;Smooke 2013).A goal of simplified models,in addition to decreasing the number ofunknowns,is also to suppress the fastest times scales and the steepest gradientsin chemical fronts,by eliminating also the most reactive intermediate species.

A two-dimensional Hydrogen/Oxygen flame stabilized behind a splitter plate with a mean pressureof 100 bar is investigated (Ruiz et al. 2012).At such high pressures,above the critical pressure,the fluids are nonideal,and a real gas equation of state is used.The \(\rm O_2\) fluid is in a liquid-like dense state, whereas the \(\rm H_2\) stream hasa gas-like density. The two-dimensional splitter plate represents the lip of an injector and the operating point is typical of a real engine.The mixture involves the \(n = 8\) species\(\rm H_2\), \(\rm O_2\), \(\rm H_2\rm O\), \(\rm H\), \(\rm O\), \(\rm O\rm H\), \(\rm H\rm O_2\), \(\rm H_2\rm O_2\) interacting through \(n^\hskip-0.04em \rm r = 12\) chemical reactions(Ruiz et al. 2012).

Hydrazine is an inorganic compound with the chemical formula N2H4. It is a simple pnictogen hydride, and is a colourless flammable liquid with an ammonia-like odour. Hydrazine is highly toxic unless handled in solution as, for example, hydrazine hydrate (N2H4xH2O).

Polymers, including photopolymers, photo-crosslinkable hydrogels, and natural proteins, are among the most well-known material for the fabrication of microrobots using 3D printing. Photopolymers are advantageous as they can be laser-printed into 3D objects through a photochemical reaction method67. Photoinitiators, monomers, and additives are the fundamental photopolymer materials used in laser 3D printing68. Complementary data regarding photopolymers can be found elsewhere1,69,70,71. In addition to SU-8 (an epoxy-based negative photoresist mainly composed of bisphenol72), IP-series photoresists (e.g., IP-S, IP-Dip, and IP-L) are a group of standard photopolymerizable substances established for high-resolution 3D microfabrication. Advantages of using IP-series included ease of handling and shape fidelity which makes them a proper substance for the fabrication of functional micro-optics and biomedical microdevices.

Chemical self-actuation is the generation of a force by a chemical reaction of on-board molecules such as platinum179,180, silver181, iron182, zinc183, magnesium184, and/or carbonates185,186 with the surrounding environment (e.g., hydrogen peroxide187). For instance, the ability of zinc to produce hydrogen bubbles in acidic environments (such as a gastric fluid) was exploited to propel zinc-loaded microrockets in HCl solution with high speed188. Although chemical actuation enables high-speed locomotion of microrobots, the toxicity of the most common fuels (e.g., metal particles) constrains their usage in biological applications10. Additionally, side products of the propulsion reaction may result in an undesired pH change in tissues63. Biocatalytic propulsion of nanomotors, as a biocompatible alternative to toxic fuel sources, can produce power from urea and glucose solutions with the addition of urease and glucose oxidase enzymes to robots, respectively189,190.

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