Stability in systems with moving contact lines

1986 ◽  
Vol 173 ◽  
pp. 115-130 ◽  
Author(s):  
E. B. Dussan V. ◽  
S. H. Davis
Keyword(s):  
Mechanical Energy ◽  
Contact Lines ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Vertical Slot ◽  
Stability And Instability ◽  
Moving Contact Lines ◽  
Taylor Problem ◽  
Dynamical Properties ◽  
General Material

An energy stability theory is formulated for systems having moving contact lines. The method derives from criteria obtained from the integral mechanical-energy balance manipulated to reflect general material and dynamical properties of moving-contact-line regions. The method yields conditions for both stability and instability and is applied to the two-dimensional Rayleigh-Taylor problem in a vertical slot.

A theoretical study of two-phase flow through a narrow gap with a moving contact line: viscous fingering in a Hele-Shaw cell

1990 ◽  
Vol 221 ◽  
pp. 53-76 ◽  
Author(s):  
Steven J. Weinstein ◽  
E. B. Dussan ◽  
Lyle H. Ungar
Keyword(s):  
Thin Films ◽  
Contact Angle ◽  
Contact Line ◽  
Viscous Fingering ◽  
Contact Lines ◽  
Fluid Interface ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Moving Contact Lines ◽  
Hele Shaw Cell

The problem of viscous fingering in a Hele-Shaw cell with moving contact lines is considered. In contrast to the usual situation where the displaced fluid coats the solid surface in the form of thin films, here, both the displacing and the displaced fluids make direct contact with the solid. The principal differences between these two situations are in the ranges of attainable values of the gapwise component of the interfacial curvature (the component due to the bending of the fluid interface across the small gap of the Hele-Shaw cell), and in the introduction of two additional parameters for the case with moving contact lines. These parameters are the receding contact angle, and the sensivity of the dynamic angle to the speed of the contact line. Our objective is the prediction of the shape and widths of the fingers in the limit of small capillary number, Uμ/σ. Here, U denotes the finger speed, μ denotes the dynamic viscosity of the more viscous displaced fluid, and σ denotes the surface tension of the fluid interface. As might be expected, there are similarities and differences between the two problems. Despite the fact that different equations arise, we find that they can be analysed using the techniques introduced by McLean & Saffman and Vanden-Broeck for the thin-film case. The nature of the multiplicity of solutions also appears to be similar for the two problems. Our results indicate that when contact lines are present, the finger shapes are sensitive to the value of the contact angle only in the vicinity of its nose, reminiscent of experiments where bubbles or wires are placed at the nose of viscous fingers when thin films are present. On the other hand, in the present problem at least two distinct velocity scales emerge with well-defined asymptotic limits, each of these two cases being distinguished by the relative importance played by the two components of the curvature of the fluid interface. It is found that the widths of fingers can be significantly smaller than half the width of the cell.

The velocity field near moving contact lines

1997 ◽  
Vol 337 ◽  
pp. 49-66 ◽  
Author(s):  
Q. CHEN ◽  
E. RAMÉ ◽  
S. GAROFF
Keyword(s):  
Velocity Field ◽  
Flow Field ◽  
Contact Line ◽  
Flow Fields ◽  
Quantitative Agreement ◽  
Interface Shape ◽  
Moving Contact Line ◽  
Liquid Body ◽  
Moving Contact ◽  
Moving Contact Lines

The dynamics of a spreading liquid body are dictated by the interface shape and flow field very near the moving contact line. The interface shape and flow field have been described by asymptotic models in the limit of small capillary number, Ca. Previous work established the validity and limitations of these models of the interface shape (Chen et al. 1995). Here, we study the flow field near the moving contact line. Using videomicroscopy, particle image velocimetry, and digital image analysis, we simultaneously make quantitative measurements of both the interface shape and flow field from 30 μm to a few hundred microns from the contact line. We compare our data to the modulated-wedge solution for the velocity field near a moving contact line (Cox 1986). The measured flow fields demonstrate quantitative agreement with predictions for Ca[les ]0.1, but deviations of ∼5% of the spreading velocity at Ca≈0.4. We observe that the interface shapes and flow fields become geometry independent near the contact line. Our experimental technique provides a way of measuring the interface shape and velocity field to be used as boundary conditions for numerical calculations of the macroscopic spreading dynamics.

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