Quantitative relationships between microstructure and effective transport properties based on virtual materials testing. Issue 6 (25th February 2014)

• Record Type: Journal Article
• Authors: Gaiselmann, Gerd; Neumann, Matthias; Schmidt, Volker; Pecho, Omar; Hocker, Thomas; Holzer, Lorenz
• Is Part Of: AIChE journal. Volume 60:Issue 6(2014:Jun.)
• Page Start: 1983
• Page End: 1999
• Publication Date: 2014-02-25
• Subjects: Chemical engineering -- Periodicals; Génie chimique -- Périodiques; 660.28
• DOI: 10.1002/aic.14416
• Languages: English
• ISSNs: 0001-1541

Abstract

<abstract abstract-type="main"> <title> <x xml:space="preserve">Abstract</x> </title> <p>The microstructure influence on conductive transport processes is described in terms of volume fraction ε, tortuosity τ, and constrictivity β. Virtual microstructures with different parameter constellations are produced using methods from stochastic geometry. Effective conductivities <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgg5nnq1gjr" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00011541:media:aic14416:aic14416-math-0001" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mtext>eff</mml:mtext><mml:mo> </mml:mo></mml:mrow></mml:msub></mml:mrow></mml:math></alternatives> are obtained from solving the diffusion equation in a finite element model. In this way, a large database is generated which is used to test expressions describing different micro–macro relationships such as Archie's law, tortuosity, and constrictivity equations. It turns out that the constrictivity equation has the highest accuracy indicating that all three parameters <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgg5nnq1gdj" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00011541:media:aic14416:aic14416-math-0002" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>ε</mml:mi><mml:mo>, </mml:mo><mml:mi>τ</mml:mi><mml:mo>, </mml:mo><mml:mi>β</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math></alternatives> are necessary to capture the microstructure influence correctly. The predictive capability of the constrictivity equation is improved by introducing modifications of it and using error‐minimization, which leads to the following expression: <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgg5nnq1gf3" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00011541:media:aic14416:aic14416-math-0003" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mtext>eff</mml:mtext><mml:mo> </mml:mo></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>σ</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mn>2.03</mml:mn><mml:msup><mml:mi>ε</mml:mi><mml:mrow><mml:mn>1.57</mml:mn></mml:mrow></mml:msup><mml:msup><mml:mi>β</mml:mi><mml:mrow><mml:mn>0.72</mml:mn></mml:mrow></mml:msup><mml:mo>/</mml:mo><mml:msup><mml:mi>τ</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:math></alternatives> with intrinsic conductivity <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgg5nnq1ggn" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley:00011541:media:aic14416:aic14416-math-0004" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>σ</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:math></alternatives>. The equation is important for future studies in, for example, batteries, fuel cells, and for transport processes in porous materials. © 2014 American Institute of Chemical Engineers <italic>AIChE J</italic>, 60: 1983–1999, 2014</p> </abstract>