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- W2022898025 startingPage "5199" @default.
- W2022898025 abstract "Unstable viscous fingers may be stabilized either by applying a local perturbation near the tip such as a bubble or a wire, or by providing a lattice anisotropy. The former case is a problem of singular perturbation that can be understood from the solvability theory by assuming a cusp at the contact point. An alternative way of understanding this problem is to relax surface tension locally near the perturbing region. We show that the cusp model requires a ensuremath{delta}-function perturbation in the surface tension. We then show how the relaxation of this ensuremath{delta} function into a Gaussian or an oscillatory function naturally provides a link between the two models. Apart from the numerical factor, we find that both models essentially predict the same scaling behavior. Next, we show that only the perturbations acting near the tip satisfy the solvability condition, thus providing a theoretical ground for modeling the lattice anisotropy by an oscillatory surface tension near the tip. This model enables one to quantify the strength of the lattice anisotropy and yields a simple relation between the tip radius ensuremath{rho} and the spacing between the grooves. Finally, we show why, regardless of the types of the local perturbations, the anomalous fingers that advance with speed U might be selected by the relation ensuremath{rho}${mathit{U}}^{2}$ensuremath{approxeq}const, the relation that holds for dendritic solidification." @default.
- W2022898025 created "2016-06-24" @default.
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- W2022898025 date "1991-05-01" @default.
- W2022898025 modified "2023-10-16" @default.
- W2022898025 title "Lattice anisotropy and the solvability theory of pattern selection" @default.
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- W2022898025 doi "https://doi.org/10.1103/physreva.43.5199" @default.
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