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Shear flow over a surface containing a groove covered by an incompressible surfactant phase

Published online by Cambridge University Press:  30 September 2022

Tobias Baier Open the ORCID record for Tobias Baier [Opens in a new window]  and
Steffen Hardt Open the ORCID record for Steffen Hardt [Opens in a new window]
Tobias Baier*
Affiliation:
Fachbereich Maschinenbau, Technische Universität Darmstadt, 64287 Darmstadt, Germany
Steffen Hardt
Affiliation:
Fachbereich Maschinenbau, Technische Universität Darmstadt, 64287 Darmstadt, Germany
*
†Email address for correspondence: baier@nmf.tu-darmstadt.de
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Abstract

We study shear-driven liquid flow over a planar surface with an embedded gas-filled groove, with the gas–liquid interface protruding slightly above or below the planar surface. The flow direction is along the groove, which is taken to be much longer than it is wide, and the gas–liquid interface is assumed to be covered by an incompressible surface fluid, representing a surfactant phase. Using the incompressibility condition for the surface fluid, the equations of motion and corresponding boundary conditions for the liquid phase are obtained by minimizing the dissipation rate. Assuming a moderate deformation of the interface, a domain perturbation technique with the maximal deformation as the small parameter is employed. The Stokes equation in the liquid phase under corresponding boundary conditions is solved to second order in the deformation using the Keldysh–Sedov formalism. The obtained analytical results are compared with numerical calculations of the same problem, allowing an assessment of the limits of validity of the expansion. While on a planar gas–liquid interface no flow is induced, a recirculating flow is observed on an interface protruding slightly above or below the planar surface. The study sheds light onto the mobility of curved gas–liquid interfaces in the presence of surfactants acting as an incompressible surface fluid.

JFM classification

Flow Control: Drag reduction Micro-/Nano-fluid dynamics: Microfluidics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 949 , 25 October 2022 , A34
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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