Capillary wave pattern

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. 

A more elaborated theoretical model based on interfacial Taylor instability triggering the surface wave was developed by Peskin and Raco [39]. A thin layer of a liquid, wetting the surface of a solid resonator wbch vibrates to its plane, forms a chessboard-like pattern of stationary capillary waves. This phenomenon occurs when the vibration amplibde exceeds a threshold value. Further on, ligament breakup of the liquid occurs and droplets are hurled from the crests of the capillary waves. Together with the wavelength, they introduced wave amplibde and the sheet thickness as parameters to determine the droplet size [39]. 

Another class of methods for achieving patterning of polymer surfaces on a length scale of micrometers or less relies on a physical instability with an intrinsic length scale. Examples of such processes, which will not be further discussed in this review, include dewetting [86,87], buckling produced by stresses arising from dispersion forces [88,89] or residual mechanical stress [65]. Further approaches exploit the amplification of capillary waves by various means [90,91]. 

The general theory of rhombic patterns recently developed by Gunaratne [13,47] has resolved some mysteries around our previous reports of a mixed state , which is now realized to be a type of rhombic patterns [46]. Our experimental results on rhombic pattern formation and selection are in good accord with the theory [13, 47]. Rhombic patterns should occur widely in other nonequilibrium systems, including surface tension driven convection, ferrofluids, Rayleigh-B nard convection, and driven capillary waves, but we know of no other laboratory studies of rhombic patterns. We hope that our work will stimulate a search for rhombic patterns in other systems. 

We carefully dissected rat tail arteries and loaded them with a Ca2+ indicator, Fluo-3. After a rectangular glass capillary was inserted into the lumen of the excised arteries, [Ca2+] in smooth muscle cells within the arterial wall was visualized using a confocal microscope. Brief electrical shocks were delivered at 5 Hz to the preparations to stimulate the sympathetic nerve network present in the adventitia. We found Ca2+ signals with diverse spatiotemporal patterns, Ca2+ waves and oscillations in individual smooth muscle cells during the sympathetic nerve stimulation (lino et al 1994). 

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