Babor, L., & Kuhlmann, H. (2021). Linear stability of thermocapillary convection in non-volatile sessile droplets on a heated substrate [Conference Presentation]. 74th Annual Meeting of the APS Division of Fluid Dynamics (APS-DFD 2021), Phoenix, Arizona, United States of America (the).
74th Annual Meeting of the APS Division of Fluid Dynamics (APS-DFD 2021)
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Event date:
21-Nov-2021 - 23-Nov-2021
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Event place:
Phoenix, Arizona, United States of America (the)
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Keywords:
thermocapillary flow; hydrodynamic instability; droplet; linear stability
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Abstract:
The linear stability of the incompressible steady axisymmetric thermocapillary flow in spherical sessile droplets is calculated numerically. The governing equations are discretized on Taylor-Hood finite elements using FEniCS. A combination of Newton's law of cooling and radiative heat transfer is imposed on the free surface. We compute the dependence of the critical Marangoni number on the contact angle for a range of Prandtl and convective and radiative Biot numbers. As the contact angle is increased from small values the basic flow is destabilized and the critical Marangoni number reaches a minimum. The minimum is followed by a very strong stabilization which is associated with a frequent change of the critical mode and a partial re-stabilization when the neutral curves turn backward. We find a range of intermediate contact angles where the basic flow is stable up to high Marangoni numbers. When the contact angle is increased even further, the basic flow is destabilized again.