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Stability analysis of a Newtonian film flow over hydrophobic microtextured substrates

D. Pettas1, G. Karapetsas2, Y. Dimakopoulos1, and J. Tsamopoulos1,*

  • 1Laboratory of Fluid Mechanics and Rheology, Department of Chemical, University of Patras, Patras 26500, Greece
  • 2Department of Chemical Engineering, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece

  • *Corresponding author: tsamo@chemeng.upatras.gr
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Phys. Rev. Fluids 7, 034004 – Published 21 March, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.034004

Abstract

We consider the flow of a Newtonian liquid film over an inclined hydrophobic wall textured with periodical microgrooves, the depth of which is much longer than their width, which is of the order of the capillary length of the liquid. Due to their structure, these grooves can be likened to slits. The flowing liquid fails to thoroughly wet the topography forming a second liquid-gas interface, with air encapsulated inside the topographical features. Under these conditions, two possible flow configurations may arise: (1) the inner interface will be pinned at the edges of the slit (ideal Cassie-Baxter state) and (2) the film may partially wet the sidewalls of the slits, forming two additional contact lines with the substrate. We investigate both the steady flow and the stability of a Newtonian liquid film flowing over various substrates with such flow configuration. We solve the 2D Navier-Stokes equations and develop a finite element model to accurately describe the exact shape of all liquid-gas interfaces at a steady state. We determine the linear stability of the steady-state solutions when subjected to perturbations in the streamwise direction and employ the Floquet-Bloch theory to account for disturbances of arbitrary wavelengths, i.e., not necessarily matching the periodicity of the substrate. Through numerical simulations, we highlight the effect of inertia, viscous and capillary forces, and the mobility of the contact line on the stability of the fluid flow. We examine the impact of substrate wettability and orientation with respect to gravity and geometric characteristics of the substrate. It is demonstrated that when the film partially wets the sidewalls of the trench, multiple steady states may arise, which are analyzed for their stability characteristics. It is also shown that the second air-liquid interface and the air pockets inside the grooves of a structured hydrophobic surface may considerably stabilize the flow mainly by the capillary forces, which act as a damper, preventing the disturbances of the outer free surface to grow.

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Outline

Information

Phys. Rev. Fluids 7, 034004– Published 21 March, 2022
  • Received 31 July 2021
  • Revised 8 January 2022
  • Accepted 24 February 2022
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