Capillary instabilities

D. J. Srolowitz, S. A. Safran. Capillary instabilities in thin films. J Appl Phys 60 247-260, 1986. 

Breakup due to capillary instabilities dominates when the length of the filament is more than 15 times the initial radius of the drop. 

The number of satellite drops produced upon breakup by capillary instabilities decreases as p increases (minimum of 3 to maximum of 16). 

Threads breaking by capillary instabilities break into a distribution of drops rather than drop sizes of equal size. 

The interaction between the dispersed-phase elements at high volume fractions has an impact on breakup and aggregation, which is not well understood. For example, Elemans et al. (1997) found that when closely spaced stationary threads break by the growth of capillary instabilities, the disturbances on adjacent threads are half a wavelength out of phase (Fig. 43), and the rate of growth of the instability is smaller. Such interaction effects may have practical applications, for example, in the formation of monodisperse emulsions (Mason and Bibette, 1996). 

Linear stability theories have also been applied to analyses of liquid sheet breakup processes. The capillary instability of thin liquid sheets was first studied by Squire[258] who showed that instability and breakup of a liquid sheet are caused by the growth of sinuous waves, i.e., sideways deflections of the sheet centerline. For a low viscosity liquid sheet, Fraser et al.[73] derived an expression for the wavelength of the dominant unstable wave. A similar formulation was derived by Li[539] who considered both sinuous and varicose instabilities. Clark and DombrowskF540 and Reitz and Diwakar13161 formulated equations for liquid sheet breakup length. 

Capillary Instability. The meniscus shape may become unstable in the sense that small perturbations to it cause the melt to separate from the... 

In addition, patterns created by surface instabilities can be used to pattern polymer films with a lateral resolution down to 100 nm [7]. Here, I summarize various possible approaches that show how instabilities that may take place during the manufacture of thin films can be harnessed to replicate surface patterns in a controlled fashion. Two different approaches are reviewed, together with possible applications (a) patterns that are formed by the demixing of a multi-component blend and (b) pattern formation by capillary instabilities. 

This occurs by an instability of one of the free interfaces the polymer-polymer interface, the film surface, or a combination of the two, each of which gives rise to a distinct lateral length scale. Which of the two capillary instabilities is selected is a complex issue. It depends on various parameters, such as polymer-polymer and polymer-solvent compatibility, solvent volatility, substrate properties, etc. in a way which is not understood. Despite this lack of knowledge, playing with these parameters permits the selection of one of the two distinct length scales associated with these two mechanisms, or a combination thereof. 

FIGURE 1.8. (a) Schematic representation of the device used to study capillary surface instabilities. A polymer-air bilayer of thicknesses /ip and /ia, respectively, is formed by two planar silicon wafer held at a separation d by spacers. A capillary instability with wavelength k = 27t/q is observed upon applying a voltage U or a temperature difference AT. (b) Dispersion relation (prediction of Eq. (1.6)). While all modes are damped (r < 0) in the absence of an interfacial pressure pei, the application of an interfacial force gradient leads to the amplification of a range of k-values, with /.m the maximally amplified mode. 

The electric field experiment shown here can be considered as a test case for the quantitative nature of capillary instability experiments. It shows the precision, with which the capillary wave pattern reflects the underlying destabilizing force. In the case of electric fields, this force is well understood. Therefore, the good fit in Fig. 1.10b demonstrates the use of film instability experiments as a quantitative tool to measure interfacial forces. The application of this technique to forces that are much less well understood is described in the following section. 

All the examples of pattern formation and replication by capillary instabilities discussed so far rely on the amplification of a single very narrow band of instability wavelength. Pattern replication succeeds only if (within certain bounds—see for example Fig. 1.16) the length scale of the master pattern matches the instability wavelength. For many practical applications, the simultaneous replication of more than one length scale and more than one material is required. 

Estimate the temperature of laser torch plasma corresponding to the threshold of capillary instability of liquid 100 nm copper drop. This estimate can be done using the instability threshold condition (1) rewritten in the form ... 

In this article we have shown how a capillary instability may generate a well-defined characteristic size. The materials that derive are essentially emulsions made of liquid or crystallizable droplets. The monodispersity make it possible to obtain materials with perfectly controlled and reproducible properties, which certainly cannot be achieved in presence of polydisperse emulsions. This is why monodisperse emulsions are not only model systems for fundamental science but also materials with commercial applications. 

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