Fingering instability

A drop of surfactant solution will, under certain conditions, undergo a fingering instability as it spreads on a surface [27, 28]. This instability is attributed to the Marongoni effect (Section IV-2D) where the process is driven by surface tension gradients. Pesach and Marmur have shown that Marongoni flow is also responsible for enhanced spreading... 

Recently it has been reported that even colloidal particle suspensions themselves, without added polymers, can form dissipative structures. Periodic stripes of colloidal particles (monodisperse particles of diameter 30 nm and 100 nm, respectively) and polystyrene particles (monodisperse diameters from 0.5 to 3 pm) can be formed from dilute aqueous suspensions. The stripes are parallel to the receding direction of the edge of the suspension droplet and thus indicate that a fingering instability... 

Directing Convection Marangoni Convection/ Evaporation/Self- assembly Coffee rings, polygonal network structures, fingering instabilities, cracks, chevron patterns, etc. Nanometer to micrometer Marangoni convection and stick-slip motion can determine the final patterns observed [132-134]... 

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]. 

Pauliac-Vaujour, E., Stannard, A., Martin, C.P., Blunt, M.O., Notingher, I., Moriarty, P.J., Vancea, I., Thiele, U. Fingering instabilities in dewetting nanofluids. Phys. Rev. Lett. 100,... 

Cazabat, A., Heslot, F., Troian, S., Carles, P. Fingering instability of thin spreading films driven by temperature gradients. Nature 346, 824—826 (1990)... 

Under a Featureless Mask Nucleation and Viscous Fingering Instabilities... 

Troian SM, Herbolzheimer E, Safran SA, Joanny JF (1989) Fingering instabilities of driven spreading films. Europhys Lett 10 25-30... 

Fig. 1.31. Fingering instability in the contact line. A PDMS ribbon developing fingers towards the cold (Brzoska, J.B.)...

Leizerson, I., Lipson, S.G., and Lyushnin, A.V. (2003) Finger instability in wetting-dewetting phenomena. Langmuir, 20, 291-294. 

Carles P, Troian SM, Cazabat AM, Heslot F. (1990) Hydrodynamic fingering instability of driven wetting films hindrance by diffusion./Condens Matter 2 SA477 A482. 

Figure 10 Dissipative structures fonned in casting polymer solution (a) Benard cells and lingering instability fonned in chloroform solution of polyion complex of 1 and 11 (b) snapshots of stripe formation from the fingering instability at the three-phase line synchronized with receding front (c) regularly arrayed polymer dots formed by dewetting in the stripes.

Bragg peaks with 3.6 nm spacing, that is, well corresponding to the bilayer thickness, observed in the X-ray diffraction pattern of the honeycomb film strongly suggest that the mesoscopic honeycomb patterns are constituted from nanostructured lamella assemblies of the polyion complexes. UV-visible absorption spectra of the patterned films (honeycomb, dots, and stripes) prepared from the polyion complexes of the azobenzene amphiphiles are identical to those of the macroscopically homogeneous cast films described in the previous section. It is concluded that the dissipative structures (Benard cell, fingering instability)... 

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... 

The mechanism of the fingering instability is thus related to the lateral flux of liquid from the bumpy edge into the fingers that feeds these fingers and make them grow. 

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