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Dynamic wetting failure in surfactant solutions

Published online by Cambridge University Press:  19 January 2016

Chen-Yu Liu ,
Eric Vandre ,
Marcio S. Carvalho  and
Satish Kumar
Chen-Yu Liu
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA
Eric Vandre
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA
Marcio S. Carvalho*
Affiliation:
Department of Mechanical Engineering, Pontificia Universidade Católica do Rio de Janeiro, Rio de Janeiro, RJ 22451-900, Brazil
Satish Kumar*
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA
*
†Email addresses for correspondence: kumar030@umn.edu, msc@puc-rio.br
†Email addresses for correspondence: kumar030@umn.edu, msc@puc-rio.br
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Abstract

The influence of insoluble surfactants on dynamic wetting failure during displacement of Newtonian fluids in a rectangular channel is studied in this work. A hydrodynamic model for steady Stokes flows of dilute surfactant solutions is developed and evaluated using three approaches: (i) a one-dimensional (1D) lubrication-type approach, (ii) a novel hybrid of a 1D description of the receding phase and a 2D description of the advancing phase, and (iii) an asymptotic theory of Cox (J. Fluid Mech., vol. 168, 1986b, pp. 195–220). Steady-state solution families in the form of macroscopic contact angles as a function of the capillary number are determined and limit points are identified. When air is the receding fluid, Marangoni stresses are found to increase the receding-phase pressure gradients near the contact line by thinning the air film without significantly changing the capillary-pressure gradients there. As a consequence, the limit points shift to lower capillary numbers and the onset of wetting failure is promoted. The model predictions are then used to interpret decades-old experimental observations concerning the influence of surfactants on air entrainment (Burley & Kennedy, Chem. Engng Sci., vol. 31, 1976, pp. 901–911). In addition to being a computationally efficient alternative for the rectangular geometries considered here, the hybrid modelling approach developed in this paper could also be applied to more complicated geometries where a thin air layer is present near a contact line.

JFM classification

Materials Processing Flows: Coating Interfacial Flows (free surface): Contact lines Interfacial Flows (free surface): Interfacial Flows (free surface)
Type
Papers
Information
Journal of Fluid Mechanics , Volume 789 , 25 February 2016 , pp. 285 - 309
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© 2016 Cambridge University Press 

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