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Viscous drops on a layer of the same fluid: from sinking, wedging and spreading to their long-time evolution

Published online by Cambridge University Press:  16 March 2018

Nico Bergemann Open the ORCID record for Nico Bergemann [Opens in a new window] ,
Anne Juel Open the ORCID record for Anne Juel [Opens in a new window]  and
Matthias Heil Open the ORCID record for Matthias Heil [Opens in a new window]
Nico Bergemann
Affiliation:
School of Mathematics and Manchester Centre for Nonlinear Dynamics, The University of Manchester, Oxford Road, Manchester M13 9PL, UK Manchester Centre for Nonlinear Dynamics and School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
Anne Juel
Affiliation:
Manchester Centre for Nonlinear Dynamics and School of Physics and Astronomy, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
Matthias Heil*
Affiliation:
School of Mathematics and Manchester Centre for Nonlinear Dynamics, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
*
†Email address for correspondence: M.Heil@maths.manchester.ac.uk
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Abstract

We study the axisymmetric spreading of drops deposited on a pre-existing horizontal layer of the same viscous fluid. Using a combination of experiments, numerical modelling based on the axisymmetric free-surface Navier–Stokes equations and scaling analyses, we explore the drops’ behaviour in a regime where the flow is driven by gravitational and/or capillary forces while inertial effects are small. We find that during the early stages of the drops’ evolution there are three distinct spreading behaviours depending on the thickness of the liquid layer. For thin layers the fluid ahead of a clearly defined spreading front is at rest and the overall behaviour resembles that of a drop spreading on a dry substrate. For thicker films, the spreading is characterised by an advancing wedge which is sustained by fluid flow from the drop into the layer. Finally, for thick layers the drop sinks into the layer, accompanied by significant flow within the layer. As the drop keeps spreading, the evolution of its shape becomes self-similar, with a power-law behaviour for its radius and its excess height above the undisturbed fluid layer. We employ lubrication theory to analyse the drop’s ultimate long-term behaviour and show that all drops ultimately enter an asymptotic regime which is reached when their excess height falls below the thickness of the undisturbed layer.

JFM classification

Drops and Bubbles: Drops Interfacial Flows (free surface): Interfacial Flows (free surface) Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 843 , 25 May 2018 , pp. 1 - 28
Copyright
© 2018 Cambridge University Press 

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