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Steady film flow over a substrate with rectangular trenches forming air inclusions

S. Varchanis, Y. Dimakopoulos, and J. Tsamopoulos*

  • Laboratory of Fluid Mechanics and Rheology, Department of Chemical Engineering, University of Patras, Greece

  • *tsamo@chemeng.upatras.gr
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Phys. Rev. Fluids 2, 124001 – Published 7 December, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.124001

Abstract

Film flow along an inclined, solid substrate featuring periodic rectangular trenches may either completely wet the trench floor (Wenzel state) or get pinned on the entrance and exit corners of the trench (Cassie state) or assume other configurations in between these two extremes. Such intermediate configurations are examined in the present study. They are bounded by a second gas-liquid interface inside the trench, which adheres to its walls forming two three-phase contact lines, and encloses a different amount of air under different physical conditions. The Galerkin finite-element method is used to solve the Navier-Stokes equations in a physical domain, which is adaptively remeshed. Multiple steady solutions, connected by turning points and transcritical bifurcations as well as isolated solution branches, are revealed by pseudo-arc-length continuation. Two possible configurations of a single air inclusion inside the trench are examined: the inclusion either surrounds the upstream convex corner or is attached to the upstream trench wall. The penetration of the liquid inside the trench is enhanced primarily by increasing either the wettability of the substrate or capillary over viscous forces or by decreasing the flow rate. Flow hysteresis may occur when the liquid wetting of the upstream wall decreases abruptly, leading to drastically different flow patterns for the same parameter values. The interplay of inertia, viscous, gravity, and capillary forces along with substrate wettability determines the volume of the air encapsulated in the trench and the extent of deformation of the outer free surface.

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Phys. Rev. Fluids 2, 124001– Published 7 December, 2017
  • Received 1 September 2017

©2017 American Physical Society

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