Abstract
It is shown that the limit of validity of a linear stability analysis for diffusive-growth type problems such as viscous fingering and crystal growth can be estimated without solving the problem to higher orders. As an application, we derive a rule often used by experimentalists, namely that the linear regime breaks down when the amplitude and the wavelength of the perturbations are approximately equal. Assuming that noisy (DLA-type) growth occurs when no linear regime exists at all, a morphological phase diagram is drawn for viscous fingering.
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© 1990 Springer-Verlag New York, Inc.
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Gingras, M.J.P., Ràcz, Z. (1990). Stability Analysis of Diffusion-Controlled Growth: Onset of Instabilities and Breakdown of the Linear Regime. In: Lam, L., Morris, H.C. (eds) Nonlinear Structures in Physical Systems. Woodward Conference. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3440-1_7
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DOI: https://doi.org/10.1007/978-1-4612-3440-1_7
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