Continuum thermodynamics of chemically reacting fluid mixtures

We consider viscous, heat conducting mixtures of molecularly miscible chemical species forming a fluid in which the constituents can undergo chemical reactions. Assuming a common temperature for all components, we derive a closed system of partial mass and partial momentum balances plus a mixture balance of internal energy. This is achieved by careful exploitation of the entropy principle and requires appropriate definitions of absolute temperature and chemical potentials, based on an adequate definition of thermal energy excluding diffusive contributions. The resulting interaction forces split into a thermo-mechanical and a chemical part, where the former turns out to be symmetric in case of binary interactions. For chemically reacting systems and as a new result, the chemical interaction force is a contribution being non-symmetric outside of chemical equilibrium. The theory also provides a rigorous derivation of the so-called generalized thermodynamic driving forces, avoiding the use of approximate solutions to the Boltzmann equations. Moreover, using an appropriately extended version of the entropy principle and introducing cross-effects already before closure as entropy invariant couplings between principal dissipative mechanisms, the Onsager symmetry relations become a strict consequence. With a classification of the factors in the binary products of the entropy production according to their parity--instead of the classical partition into so-called fluxes and driving forces--the apparent anti-symmetry of certain couplings is thereby also revealed. If the diffusion velocities are small compared to the speed of sound, the Maxwell-Stefan equations follow in the case without chemistry, thereby neglecting wave phenomena in the diffusive motion. This results in a reduced model with only mass being balanced individually. In the reactive case ..

Continuum thermodynamics of chemically reacting fluid mixtures

We consider viscous and heat conducting mixtures of molecularly miscible chemical species forming a fluid in which the constituents can undergo chemical reactions. Assuming a common temperature for all components, a first main aim is the derivation of a closed system of partial mass and partial momentum balances plus a common balance of internal energy. This is achieved by careful exploitation of the entropy principle which, in particular, requires appropriate definitions of absolute temperature and chemical potentials based on an adequate definition of thermal energy that excludes diffusive contributions. The latter is crucial in order to obtain a closure framework for the interaction forces between the different species. The interaction forces split into a thermo-mechanical and a chemical part, where the former turns out to be symmetric if binary interactions are assumed. In the non-reactive case, this leads to a system of Navier-Stokes type sub-systems, coupled by interspecies friction forces. For chemically reacting systems and as a new result, the chemical interaction force is identified as a contribution which is non-symmetric, unless chemical equilibrium holds. The theory also provides a rigorous derivation of the so-called generalized thermodynamic driving forces, avoiding the use of approximate solutions to the Boltzmann equations which is common in the engineering literature. Moreover, starting with a continuum thermodynamic field theory right away, local versions of fundamental relations known from thermodynamics of homogeneous systems, like the Gibbs-Duhem equation, are derived. Furthermore, using an appropriately extended version of the entropy principle and introducing cross-effects already before closure as entropy invariant couplings between principal dissipative mechanisms, the Onsager symmetry relations are a strict consequence. With a classification of the factors forming the binary products in the entropy production according to their parity instead of the classical distinction between so-called fluxes and driving forces, the apparent anti-symmetry of certain couplings is thereby also revealed. If the diffusion velocities are small compared to the speed of sound, the well-known Maxwell-Stefan equations together with the so-called generalized thermodynamic driving forces follow in the special case without chemical reactions, thereby neglecting wave phenomena in the diffusive motion. This results in a reduced model having only the constituents mass balances individually. In the reactive case, this approximation via a scale separation argument is no longer possible. Instead, we first employ the partial mass and mixture internal energy balances, common to both model classes, to identify all constitutive quantities. Combined with the concept of entropy invariant model reduction, leaving the entropy production unchanged under the reduction from partial momentum balances to a single common mixture momentum balance, the chemical interactions yield an additional contribution to the transport coefficients, leading to an extension of the Maxwell-Stefan equations to chemically active mixtures. Within the considered model class for reactive fluid mixtures the new results are achieved for arbitrary free energy functions

Multicomponent incompressible fluids -- An asymptotic study

This paper investigates the asymptotic behavior of the Helmholtz free energy of mixtures at small compressibility. We start from a general representation for the local free energy that is valid in stable subregions of the phase diagram. On the basis of this representation we classify the admissible data to construct a thermodynamically consistent constitutive model. We then analyze the incompressible limit, where the molar volume becomes independent of pressure. Here we are confronted with two problems: (i) Our study shows that the physical system at hand cannot remain incompressible for arbitrary large deviations from a reference pressure unless its volume is linear in the composition. (ii) As a consequence of the 2nd law of thermodynamics, the incompressible limit implies that the molar volume becomes independent of temperature as well. Most applications, however, reveal the non-appropriateness of this property. According to our mathematical treatment, the free energy as a function of temperature and partial masses tends to a limit in the sense of epi-- or Gamma--convergence. In the context of the first problem, we study the mixing of two fluids to compare the linearity with experimental observations. The second problem will be treated by considering the asymptotic behavior of both a general inequality relating thermal expansion and compressibility and a PDE-system relying on the equations of balance for partial masses, momentum and the internal energy

Rigid, Complete Annuloplasty Rings Increase Anterior Mitral Leaflet Strains in the Normal Beating Ovine Heart

Background-Annuloplasty ring or band implantation during surgical mitral valve repair perturbs mitral annular dimensions, dynamics, and shape, which have been associated with changes in anterior mitral leaflet (AML) strain patterns and suboptimal long-term repair durability. We hypothesized that rigid rings with nonphysiological three-dimensional shapes, but not saddle-shaped rigid rings or flexible bands, increase AML strains

Optimierung des Säulenperkolationsverfahrens durch Automatisierung

Elutionstests im Labormaßstab werden zur Ermittlung der Freisetzung von Schadstoffen aus Böden oder mineralischen Abfällen für die Verwertung in technischen Erdbauwerken durchgeführt. Sie sollen die Feldbe¬dingungen möglichst realitätsnah wider¬spiegeln und auch die Beurteilung der Freisetzung von Schadstoffen über längere Zeiträume ermöglichen. Aus diesem Grunde werden im Entwurf der novellierten BBodSchV neue Verfahren zur Eluatgewinnung aus den genannten Materialien festgeschrieben. Dazu zählt unter anderem das Säulenperkolationsverfahren nach DIN 19528:2009-01 zur gemeinsamen Untersuchung des Elutionsverhaltens von anorganischen und organischen Stoffen. Mit der DIN 19528 wurde im Vergleich zu bis¬herigen Normen statt der Festschreibung der Säulendimension und Fließrate des Eluenten die Kontaktzeit zwischen Elutions¬mittel und Untersuchungsmaterial festgelegt. Dieses Konzept ermöglicht vergleichbare Versuchsergebnisse bei verschiedenen Säulendimensionen. Über die festgelegte Kontaktzeit wird für jede gepackte Säule die spezifische Fließgeschwindigkeit des Eluenten berechnet. Abhängig von den Eigenschaften des jeweiligen Untersuchungsmaterials können sich daraus Probenahmezeitpunkte ergeben, die außerhalb üblicher Laborarbeitszeiten liegen. Daher ist eine Automatisierung der Versuchsdurchführung von erheblichem Vorteil sowie von Interesse bei Anwendern des vor- und nachsorgenden Bodenschutzes, da eine flexiblere Ausführung größerer Versuchsserien ermöglicht wird. Im Rahmen eines ZIM-Projektes (FKZ kf2201007MK9) wurde durch die ecoTech GmbH in Zusammenarbeit mit der BAM eine automatisierte Säulenperkolations-anlage (ASPA) entwickelt. Der Schwerpunkt der Arbeiten der BAM lag auf materialwissenschaftlichen Untersuchungen zu den Wechselwirkungen von Werkstoffen der Versuchseinrichtung, die mit den zu unter¬suchenden Schadstoffen in Kontakt stehen, da Sorptions- und Desorp-tionsprozesse zu Minderbefunden oder Über¬schätzungen der Eluatkonzentration und damit zu Fehlinterpretationen bei der Gefahrenbeurteilung führen können. Desweiteren wurden Testläufe mit dem Prototypen unter Einbeziehung weiterer prioritärer organischer Schadstoffe vorgenommen, da das neue Säulenperkolationsverfahren hier bisher nur für PAK validiert ist. Ergebnisse von Werkstoffuntersuchungen und Säulenversuchen mit kontaminierten Bodenmaterialien werden im Beitrag exemplarisch dargestellt

The effect of pure mitral regurgitation on mitral annular geometry and three-dimensional saddle shape

ObjectiveChronic ischemic mitral regurgitation is associated with mitral annular dilatation in the septal-lateral dimension and flattening of the annular 3-dimensional saddle shape. To examine whether these perturbations are caused by the ischemic insult, mitral regurgitation, or both, we investigated the effects of pure mitral regurgitation (low pressure volume overload) on annular geometry and shape.MethodsEight radiopaque markers were sutured evenly around the mitral annulus in sheep randomized to control (CTRL, n = 8) or experimental (HOLE, n = 12) groups. In HOLE, a 3.5- to 4.8-mm hole was punched in the posterior leaflet to generate pure mitral regurgitation. Four-dimensional marker coordinates were obtained radiographically 1 and 12 weeks postoperatively. Mitral annular area, annular septal-lateral and commissure–commissure dimensions, and annular height were calculated every 16.7 ms.ResultsMitral regurgitation grade was 0.4 ± 0.4 in CTRL and 3.0 ± 0.8 in HOLE (P < .001) at 12 weeks. End-diastolic left ventricular volume index was greater in HOLE at both 1 and 12 weeks; end-systolic volume index was larger in HOLE at 12 weeks. Mitral annular area increased in HOLE predominantly in the commissure–commissure dimension, with no difference in annular height between HOLE versus CTRL at 1 or 12 weeks, respectively.ConclusionIn contrast with annular septal-lateral dilatation and flattening of the annular saddle shape observed with chronic ischemic mitral regurgitation, pure mitral regurgitation was associated with commissure–commissure dimension annular dilatation and no change in annular shape. Thus, infarction is a more important determinant of septal-lateral dilatation and annular shape than mitral regurgitation, which reinforces the need for disease-specific designs of annuloplasty rings

Data-driven analysis of interactions between people with dementia and a tablet device

Abstract In the project I-CARE a technical system for tablet devices is developed that captures the personal needs and skills of people with dementia. The system provides activation content such as music videos, biographical photographs and quizzes on various topics of interest to people with dementia, their families and professional caregivers. To adapt the system, the activation content is adjusted to the daily condition of individual users. For this purpose, emotions are automatically detected through facial expressions, motion, and voice. The daily interactions of the users with the tablet devices are documented in log files which can be merged into an event list. In this paper, we propose an advanced format for event lists and a data analysis strategy. A transformation scheme is developed in order to obtain datasets with features and time series for popular methods of data mining. The proposed methods are applied to analysing the interactions of people with dementia with the I-CARE tablet device. We show how the new format of event lists and the innovative transformation scheme can be used to compress the stored data, to identify groups of users, and to model changes of user behaviour. As the I-CARE user studies are still ongoing, simulated benchmark log files are applied to illustrate the data mining strategy. We discuss possible solutions to challenges that appear in the context of I-CARE and that are relevant to a broad range of applications.</jats:p

Multicomponent incompressible fluids -- An asymptotic study

This paper investigates the asymptotic behavior of the Helmholtz free energy of mixtures at small compressibility. We start from a general representation for the local free energy that is valid in stable subregions of the phase diagram. On the basis of this representation we classify the admissible data to construct a thermodynamically consistent constitutive model. We then analyze the incompressible limit, where the molar volume becomes independent of pressure. Here we are confronted with two problems: (i) Our study shows that the physical system at hand cannot remain incompressible for arbitrary large deviations from a reference pressure unless its volume is linear in the composition. (ii) As a consequence of the 2nd law of thermodynamics, the incompressible limit implies that the molar volume becomes independent of temperature as well. Most applications, however, reveal the non-appropriateness of this property. According to our mathematical treatment, the free energy as a function of temperature and partial masses tends to a limit in the sense of epi-- or Gamma--convergence. In the context of the first problem, we study the mixing of two fluids to compare the linearity with experimental observations. The second problem will be treated by considering the asymptotic behavior of both a general inequality relating thermal expansion and compressibility and a PDE-system relying on the equations of balance for partial masses, momentum and the internal energy