Contact Line Instabilities

A second example is provided by a ribbon of liquid deposited on a plate and subjected to a temperature gradient Angers reach out towards the colder region (see Fig. 1.31). 

And finally, fingering will develop in a droplet under the effect of a centrifugal force, as happens when a droplet is spread by the spin-coating technique (see Fig. 1.32). 

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Fig. 1.32. Fingering instability in the contact line. Instability in a droplet undergoing induced spreading by spin coating (Fauve, S.)...

A. Miinch and B. Wagner, Contact-line instability of dewetting thin films, Physica D, 209,178-190 (2005). 

Davis SH. (1980) Moving contact lines and rivulet instabilities. Part 1. The static rivulet. J Fluid Mech 98 225-242. 

For very small dynamic contact angles, the liquid is not completely removed by the split streamline and it is entrained between the film and the solid surface, creating what is known as a wet LB film. Water trapped between the solid surface and the LB monolayer prevents adhesion and is a leading cause of monolayer instability. Petrov etal. (1980) sketched the flow pattern near the moving contact line. The flow pattern is the one described here for region IV. The authors, however, reference Huh and Scriven (1971)... 

If the concentration is low, rather than thin films dissipative structures (e.g., convection patterns, fingering instabilities) are produced [87]. Such work was subsequently used to topographically control neurite extension on stripe-patterned polymer films [150], fabrication of periodic micro-structured honeycomb films having multiple periodicities, and polymer nanoparticles [151]. Large-scale ordering was observed. This was defined by the periodic thickness modulation of a block-copolymer film due to the self-organization of the receding contact line [152]. 

Huh, C, Capillary hydrodynamics interfacial instability and the solid/fluid/fluid contact line, Ph.D. dissertation. University of Minnesota, 1969. 

Fig. 1.34. Marangoni instability of a dilute drop of polymer solution, (a) The drop spreads too much and too fast. The shape becomes flat, (b) Undulation of the contour is observed coupled to the formation of an unstable rim and digitation, whereas the contact line recedes (dewetting), (c) The figure breaks into droplets and a rim is reformed, which contracts toward the center, (d, e) Interactions of the process are observed, (f) Final stage microdroplets are left on a substrate. [Figure taken from R. Fondeca Macromolecules, Vol. 31, No. 26,1998]...

Surface tension variations affect the mobility of the fluid-fluid interface and cause Marangoni flow instabilities. Surfactant-laden flows exhibit surface tension variations at the gas-liquid or liquid-liquid contact line due to surfactant accumulation close to stagnation points [2,53]. For gas-liquid systems, these Marangoni effects can often be accounted for by assuming hardening of the gas bubble, i.e. by replacing the no-shear boundary condition that is normally associated with a gas-liquid (free) boundary with a no-slip boundary condition. It should be noted that such effects can drastically alter pressure drop in microfluidic networks and theoretical predictions based on no-shear at free interfaces must be used with care in practical applications [54]. 

S. H. Davis, Moving contact line and rivulet instabilities. Part 1 the static rivulet,/ FluidMedi., 98, 225-242 (1980). 

Figure 14.12 Process to form hierarchical bilayer structure, (a) Polymer bilayer of PMMA and PS. The polymer-air surface is first destabilized by an electric field generated between the two Si electrodes. The initial instability results in the formation of columns spanning from the surface of the lower layer to the top electrode, (b) During the column formation process, the bottom polymer layer is deformed at the polymer-polymer-air contact line, (c) In the second instability, the deformation of the lower layer is enhanced by the electric field. The polymer moves upward, surrounding the columns and finally leading to form a mantle-like structure. (Images taken from Ref. 65.)...

Irrespective of the precise origin of an instability, the amplification of the capillary waves leads to the deformation of the free surface (film-air interface) and results in localized flow of liquid from the thinner parts to the thicker parts of the film [38, 56-168]. This phenomenon eventually results in the rupture of the film with the formation of dry patches or holes, when the growing amplitude of the capillary wave spectrum equals the film thickness [65]. As the film ruptures, the two distinct interfaces (film-air and film-substrate) merge and a three phase contact line (film-air-substrate) is formed. Depending on the thermodynamics of the system. 

Experimentally this one dimensional profile is not stable and shows a fingering instability. In order to show that this profile is indeed linearly unstable, we perturb the contact line in the direction y perpendicular to the motion by a value q= o(t) cos qC where we use the same scaling along the x and y direction C = y/1 first approximation the liquid profile in the vicinity of... 

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