The effect of thermocapillarity on the dynamics of an exterior coating film flow down a fibre subject to an axial temperature gradient
•A long-wave model is derived to describe film flowing down a fibre with thermocapillary effect.•Nonlinear dynamics is investigated by numerical simulations.•Coherent solutions are tracked.•Thermocapillarity plays adverse roles in different flow regimes. The dynamics of a viscous film flowing down a...
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| Published in | International journal of heat and mass transfer Vol. 123; pp. 718 - 727 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Oxford
Elsevier Ltd
01.08.2018
Elsevier BV |
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| Abstract | •A long-wave model is derived to describe film flowing down a fibre with thermocapillary effect.•Nonlinear dynamics is investigated by numerical simulations.•Coherent solutions are tracked.•Thermocapillarity plays adverse roles in different flow regimes.
The dynamics of a viscous film flowing down a vertical fibre under the action of gravity and the thermocapillarity induced by an axial temperature gradient is investigated theoretically. The instability of this exterior coating flow is driven by a Rayleigh-Plateau mechanism modified by the presence of gravity as well as the thermocapillarity. We derived an evolution equation for the interface in the framework of the long wave approximation. A linear stability analysis and a nonlinear simulation are performed to investigate the influence of the thermocapillarity on the dynamics of axisymmetric disturbances. The results of linear stability showed that the thermocapillarity does not influence the growth rate of the disturbance and only affects its frequency. For the nonlinear evolution, the thermocapillarity plays an important role in influencing the profile of the interface in different flow regimes. We also examined the effect of thermocapillarity on the wave speed and the characteristics of the structures of travelling wave solutions. |
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| AbstractList | The dynamics of a viscous film flowing down a vertical fibre under the action of gravity and the thermocapillarity induced by an axial temperature gradient is investigated theoretically. The instability of this exterior coating flow is driven by a Rayleigh-Plateau mechanism modified by the presence of gravity as well as the thermocapillarity. We derived an evolution equation for the interface in the framework of the long wave approximation. A linear stability analysis and a nonlinear simulation are performed to investigate the influence of the thermocapillarity on the dynamics of axisymmetric disturbances. The results of linear stability showed that the thermocapillarity does not influence the growth rate of the disturbance and only affects its frequency. For the nonlinear evolution, the thermocapillarity plays an important role in influencing the profile of the interface in different flow regimes. We also examined the effect of thermocapillarity on the wave speed and the characteristics of the structures of travelling wave solutions. •A long-wave model is derived to describe film flowing down a fibre with thermocapillary effect.•Nonlinear dynamics is investigated by numerical simulations.•Coherent solutions are tracked.•Thermocapillarity plays adverse roles in different flow regimes. The dynamics of a viscous film flowing down a vertical fibre under the action of gravity and the thermocapillarity induced by an axial temperature gradient is investigated theoretically. The instability of this exterior coating flow is driven by a Rayleigh-Plateau mechanism modified by the presence of gravity as well as the thermocapillarity. We derived an evolution equation for the interface in the framework of the long wave approximation. A linear stability analysis and a nonlinear simulation are performed to investigate the influence of the thermocapillarity on the dynamics of axisymmetric disturbances. The results of linear stability showed that the thermocapillarity does not influence the growth rate of the disturbance and only affects its frequency. For the nonlinear evolution, the thermocapillarity plays an important role in influencing the profile of the interface in different flow regimes. We also examined the effect of thermocapillarity on the wave speed and the characteristics of the structures of travelling wave solutions. |
| Author | Ding, Zijing Liu, Rong Chen, Xue |
| Author_xml | – sequence: 1 givenname: Rong surname: Liu fullname: Liu, Rong email: rongliu@guet.edu.cn organization: School of Mechanical and Electrical Engineering, Gui Lin University of Electronic Technology, Gui Lin 541004, China – sequence: 2 givenname: Zijing surname: Ding fullname: Ding, Zijing email: z.ding@damtp.cam.ac.uk organization: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, CB30WA, United Kingdom – sequence: 3 givenname: Xue surname: Chen fullname: Chen, Xue email: chenxue@guet.edu.cn organization: School of Mechanical and Electrical Engineering, Gui Lin University of Electronic Technology, Gui Lin 541004, China |
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| Cites_doi | 10.1017/S0022112003004373 10.1103/PhysRevLett.98.244502 10.1209/0295-5075/18/7/003 10.1017/S0022112008001225 10.1017/S0022112094000297 10.1063/1.1286594 10.1103/PhysRevE.90.033005 10.1063/1.4974076 10.1017/S0022112088002484 10.1017/S0022112006008706 10.1016/j.ijheatmasstransfer.2015.06.035 10.1016/j.ijheatmasstransfer.2016.12.066 10.1016/j.cej.2010.08.040 10.1017/S0022112000003268 10.1146/annurev.fluid.31.1.347 10.1017/S0022112083001512 10.1017/S0022112098003632 10.1016/j.ijheatmasstransfer.2017.05.030 10.1016/S0017-9310(99)00180-5 10.1017/S0022112085002798 10.1080/14786449208620301 10.1209/0295-5075/13/8/009 |
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| SubjectTerms | Coating effects Coating flow Dynamic stability Evolution Flow stability Gravitation Non-Newtonian fluids Nonlinear analysis Reynolds number Stability analysis Temperature gradients Thermocapillarity Thin films Traveling waves Travelling wave solutions Viscosity |
| Title | The effect of thermocapillarity on the dynamics of an exterior coating film flow down a fibre subject to an axial temperature gradient |
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