# American Institute of Mathematical Sciences

November  2015, 20(9): 3267-3299. doi: 10.3934/dcdsb.2015.20.3267

## Stabilizing interplay between thermodiffusion and viscoelasticity in a closed-loop thermosyphon

 1 Grupo de Dinámica No Lineal (DNL), Escuela Técnica Superior de Ingeniería (ICAI), Universidad Pontificia Comillas, Madrid E-28015, Spain, Spain, Spain

Received  June 2013 Revised  May 2014 Published  September 2015

Viscoelastic fluids represent a major challenge both from an engineering and from a mathematical point of view. Recently, we have shown that viscoelasticity induces chaos in closed-loop thermosyphons. This induced behavior might interfere with the engineering choice of using a specific fluid. In this work we show that the addition of a solute to the fluid can, under some conditions, stabilize the system due to thermodiffusion (also known as the Soret effect). Unexpectedly, the role of viscoelasticity is opposite to the case of single-element fluids, where it (generically) induces chaos. Our results are derived by combining analytical results based on the projection of the dynamics on an inertial manifold as well as numerical simulations characterized by the calculation of Lyapunov exponents.
Citation: Justine Yasappan, Ángela Jiménez-Casas, Mario Castro. Stabilizing interplay between thermodiffusion and viscoelasticity in a closed-loop thermosyphon. Discrete & Continuous Dynamical Systems - B, 2015, 20 (9) : 3267-3299. doi: 10.3934/dcdsb.2015.20.3267
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