Bi-Laplacian Growth Patterns in Disordered Media
Statistical Mechanics
2009-11-07 v1 Materials Science
Pattern Formation and Solitons
Abstract
Experiments in quasi 2-dimensional geometry (Hele Shaw cells) in which a fluid is injected into a visco-elastic medium (foam, clay or associating-polymers) show patterns akin to fracture in brittle materials, very different from standard Laplacian growth patterns of viscous fingering. An analytic theory is lacking since a pre-requisite to describing the fracture of elastic material is the solution of the bi-Laplace rather than the Laplace equation. In this Letter we close this gap, offering a theory of bi-Laplacian growth patterns based on the method of iterated conformal maps.
Cite
@article{arxiv.cond-mat/0208403,
title = {Bi-Laplacian Growth Patterns in Disordered Media},
author = {Anders Levermann and Itamar Procaccia},
journal= {arXiv preprint arXiv:cond-mat/0208403},
year = {2009}
}
Comments
Submitted to PRL. For further information see http://www.weizmann.ac.il/chemphys/anders