Consequences of the Brenner modification to the Navier–Stokes equations for dynamic light scattering |
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| Affiliation: | 1. Department of Chemistry, Middle East Technical University, Ankara 06800, Turkey;2. Central Laboratory, Middle East Technical University, Ankara 06800, Turkey;3. Polymer Science and Technology Program, Middle East Technical University, Ankara 06800, Turkey;1. School of Mathematical Sciences, Peking University, Beijing, China;2. CAPT, LMAM & School of Mathematical Sciences, Peking University, Beijing, China;3. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong;1. Institute of Chemical and Environmental Engineering, Faculty of Chemical and Food Technology, Slovak University of Technology, Radlinského 9, 812 37 Bratislava, Slovakia;2. Institute of Biotechnology and Food Science, Faculty of Chemical and Food Technology, Slovak University of Technology, Radlinského 9, 812 37 Bratislava, Slovakia;1. Department of Mathematics and Statistics, Al-Imam University, Riyadh, Saudi Arabia;2. Department of Mathematics and Statistical Sciences & Department of Mechanical, Energy and Industrial Engineering, Botswana International University of Science and Technology, Palapye, Botswana;3. Centro de Investigación en Creatividad y Educación Superior y Departamento de Ingeniería Mecánica, Universidad de Santiago de Chile, Santiago, Chile |
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| Abstract: | A modification of the classical Navier–Stokes equations has recently been proposed by Brenner [Is the tracer velocity of a fluid continuum equal to its mass velocity? Phys. Rev. E 70 (2004) Art. No. 061201; Kinematics of volume transport, Physica A 349 (2005) 11–59; Navier–Stokes revisited, Physica A 349 (2005) 60–132] and then formalized by Öttinger [Beyond Equilibrium Thermodynamics, Wiley, Hoboken, 2005]. In the modified theory, a contribution for mass diffusion is included in the continuity equation. The argument was based on experimental support from thermophoresis which however depends on the correct formulation of boundary conditions. The controversy therefore remained. Since such an additional mass diffusion transport mode should contribute to dynamic light scattering spectra, the consequences of the modified theory for light scattering spectra are discussed in this work. For liquids, the new theory is consistent with measured scattering data since the modification to the spectrum is usually negligible. The effect could, however, be observable in gases. |
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