Linear stability analysis wavelength

The morphological stability of initially smooth electrodeposits has been analyzed by several authors [48-56]. In a linear stability analysis, the current distribution on a low-amplitude sinusoidal surface is found as an expansion around the distribution on the flat surface. The first order current distribution is used to calculate the rate of amplification of the surface corrugation. A plot of amplification rate versus mode number or wavelength separates the regimes of stable and unstable fluctuation and... 

Linearized stability analysis has been performed (BIO) by superposing a sinusoidal disturbance of wavelength (which equals iTt/k, with k the... 

The following calculations are based on a linear stability analysis taking into account only the first order of. Furthermore, we use two approximations. One is the long wavelength approximation the wavelength of perturbation of the solid-liquid interface is much larger than the mean thickness of the liquid film, then we can define a small dimensionless wavenumber The other is the quasistationary approximation we... 

Before the details are carried out, however, it is useful to revisit the scaling that led to the nondimensionalized equation, (6-107), because we can show that a slight modification allows us to eliminate the coefficients ( 1 and A. This involves just two steps. First, we specify the length scale lc- An appropriate and convenient choice is the wavelength of the disturbance separating stable and unstable solutions in the linear stability analysis. Going back to (6-103), we see that the critical point (i.e., the point where s = 0) occurs when... 

We assume that the flat interface between the two fluids, now designated as z = 0, is perturbed with an arbitrary infinitesimal perturbation of shape. As usual, for a linear stability analysis, we consider only a single Fourier mode in each of the x and y directions, with the wave number (or wavelength) as a parameter in the stability analysis. Hence we consider a perturbation of the form... 

One alternative that has been explored [27] is to conduct an axisymmettic computation (with its associated efficiency) and use a linear stability analysis to fractionate annular ring-shaped ligaments shed from the jet periphery in this case. A Boundary Element Method (BEM) was employed to compute the local surface dynamics. See Chap. 15 for details regarding the computational methodology. While Fig. 27.6 indicates that 3-D instabilities occur prior to pinching of axisym-metric structures, the wavelengths of the azimuthal modes appear to be comparable to those of the axisymmetric waves. Nevertheless, the axisymmetric assumption, while providing drastic simplification, still provides much room for improvement as more computational power becomes available. 

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