Reports: ND950606-ND9: Wetting Failure in Fluid-Fluid Displacement

Satish Kumar, University of Minnesota

The displacement of one fluid by another lies at the core of two practical applications relevant to the petroleum industry and alternative energy technologies: liquid-applied coating processes and enhanced oil recovery. Successful displacement of one fluid by the other requires that the fluid-fluid interface maintain contact lines at the boundaries, i.e., wetting failure must not occur.  Remarkably, despite the importance of successful fluid-fluid displacement to these applications, two major issues have received relatively little attention.  These are (i) the role of the confining geometry, and (ii) the role of the viscosity of the displaced phase.  Our research is addressing these issues using a combination of flow visualization experiments, lubrication-approximation-based models, and finite element simulations.

During the first grant reporting period, we completed a study of how meniscus confinement influences dynamic wetting failure.  A novel experimental system was designed to simultaneously view confined and unconfined wetting systems as they approach wetting failure.  The experimental apparatus consists of a scraped steel roll that rotates into a bath of glycerol.  Confinement is imposed via a gap formed between a coating die and the roll surface. Flow visualization is used to record the critical roll speed at which wetting failure occurs.  Comparison of the confined and unconfined data shows a clear increase in the relative critical speed as the meniscus becomes more confined. A hydrodynamic model for wetting failure was developed and analyzed with (i) lubrication theory and (ii) a two-dimensional finite-element method (FEM).  Both approaches do a remarkable job of matching the observed confinement trend, but only the two-dimensional model yields accurate estimates of the absolute values of the critical speeds due to the highly two-dimensional nature of the stress field in the displacing liquid. The overall success of the hydrodynamic model suggests a wetting failure mechanism primarily related to viscous bending of the meniscus.  A paper describing this work was published in the Journal of Fluid Mechanics.

Our results are important because they help rationalize why so-called "bead coating"  methods work.  These methods are used extensively in industry to delay wetting failure, and involve using a coating die to confine the wetting meniscus.  However, how these methods work remained a puzzle until our work.  In addition, our results demonstrate that all that is needed to understand the onset of wetting failure in these systems is a relatively simple mathematical model that involves hydrodynamics, a microscopic contact angle, and a Navier slip law.  There does not appear to be a compelling reason to bring in additional physical processes, as others have speculated.

During the most recent grant reporting period, we have conducted a thorough parametric study using the hydrodynamic model described above.  The model is evaluated with three distinct approaches: (i) the low-speed asymptotic theory of Cox [J. Fluid Mech. 168 (1986) 169], (ii) a one-dimensional (1D) lubrication approach, and (iii) a two-dimensional (2D) flow model solved with the Galerkin finite element method (FEM).  Approaches (ii) and (iii) predict the onset of wetting failure at a critical capillary number (ratio of viscous to surface-tension forces), which coincides with a turning point in the steady-state solution family for a given set of system parameters.  The 1D model fails to accurately describe interface shapes near the three-phase contact line when air is the receding fluid, producing large errors in estimates of the critical capillary number for these systems.  Analysis of the 2D flow solution reveals that strong pressure gradients are needed to pump the receding fluid away from the contact line.  A mechanism is proposed in which wetting failure results when capillary forces can no longer support the pressure gradients necessary to steadily displace the receding fluid.  The effects of viscosity ratio, substrate wettability, and fluid inertia are then investigated through comparisons of the critical capillary number and characteristics of the interface shape.  Surprisingly, the low-speed asymptotic theory (i) matches trends computed from (iii) throughout the entire investigated parameter space.  Furthermore, predictions of the critical capillary number from the 2D flow model compare favorably to values measured in experimental air-entrainment studies, supporting the proposed wetting-failure mechanism.  A paper on this work was recently accepted in Physics of Fluids.

The results of the work described above represent a comprehensive study of the onset of wetting failure in planar geometries, definitively elucidate for the first time the mechanisms underlying wetting failure, and lay the foundation for further studies exploring transient and three-dimensional dynamics.  Current work is focused on performing additional experiments with a new apparatus that allows for considerably better visualization, extending the model to incorporate more complex system geometries, and understanding wetting failure in complex fluids through both experiment and theory.  

Our research on wetting failure has already led to interactions with companies such as 3M and Corning, which has been an excellent educational experience for the students working on this problem.  In addition,  these interactions will help me to establish a longer-range research program on the fundamentals of dynamic wetting.  Overall, our work will significantly advance fundamental understanding of the conditions under which wetting failure occurs, and open the door to major improvements in our ability to control wetting failure.