Harmonic moment dynamics in Laplacian growth
| dc.contributor.utaustinauthor | Leshchiner, Alexander | en_US |
| dc.contributor.utaustinauthor | Thrasher, Matthew | en_US |
| dc.contributor.utaustinauthor | Swinney, Harry L. | en_US |
| dc.creator | Leshchiner, Alexander | en_US |
| dc.creator | Thrasher, Matthew | en_US |
| dc.creator | Mineev-Weinstein, Mark B. | en_US |
| dc.creator | Swinney, Harry L. | en_US |
| dc.date.accessioned | 2017-07-18T20:10:23Z | |
| dc.date.available | 2017-07-18T20:10:23Z | |
| dc.date.issued | 2010-01 | en_US |
| dc.description.abstract | Harmonic moments are integrals of integer powers of z=x+iy over a domain. Here, the domain is an exterior of a bubble of air growing in an oil layer between two horizontal closely spaced plates. Harmonic moments are a natural basis for such Laplacian growth phenomena because, unlike other representations, these moments linearize the zero surface tension problem [S. Richardson, J. Fluid Mech. 56, 609 (1972)], so that all moments except the lowest one (the area of the bubble) are conserved in time. In our experiments, we directly determine the harmonic moments and show that for nonzero surface tension, all moments (except the lowest one) decay in time rather than exhibiting the divergences of other representations. Further, we derive an expression that relates the derivative of the k(th) harmonic moment M(k) to measurable quantities (surface tension, viscosity, the distance between the plates, and a line integral over the contour encompassing the growing bubble). The laboratory observations are in good accord with the expression we derive for dM(k)/dt, which is proportional to the surface tension; thus in the zero surface tension limit, the moments (above k=0) are all conserved, in accord with Richardson's theory. In addition, from the measurements of the time evolution of the harmonic moments we obtain a value for the surface tension that is within 20% of the accepted value. In conclusion, our analysis and laboratory observations demonstrate that an interface dynamics description in terms of harmonic moments is physically realizable and robust. | en_US |
| dc.description.department | Physics | en_US |
| dc.description.sponsorship | American Chemical Society Petroleum Research Fund | en_US |
| dc.description.sponsorship | LDRD at Los Alamos National Laboratory 20070083ER | en_US |
| dc.identifier | doi:10.15781/T20863M9R | |
| dc.identifier.citation | Leshchiner, Alexander, Matthew Thrasher, Mark B. Mineev-Weinstein, and Harry L. Swinney. "Harmonic moment dynamics in Laplacian growth." Physical Review E 81, no. 1 (2010): 016206. | en_US |
| dc.identifier.doi | 10.1103/PhysRevE.81.016206 | en_US |
| dc.identifier.issn | 1539-3755 | en_US |
| dc.identifier.uri | http://hdl.handle.net/2152/61124 | |
| dc.language.iso | English | en_US |
| dc.relation.ispartof | UT Faculty/Researcher Works | en_US |
| dc.relation.ispartofserial | Physical Review E | en_US |
| dc.rights | Administrative deposit of works to Texas ScholarWorks: This works author(s) is or was a University faculty member, student or staff member; this article is already available through open access or the publisher allows a PDF version of the article to be freely posted online. The library makes the deposit as a matter of fair use (for scholarly, educational, and research purposes), and to preserve the work and further secure public access to the works of the University. | en_US |
| dc.rights.restriction | open | en_US |
| dc.subject | diffusion-limited aggregation | en_US |
| dc.subject | hele-shaw cell | en_US |
| dc.subject | pattern-formation | en_US |
| dc.subject | interface dynamics | en_US |
| dc.subject | domains | en_US |
| dc.subject | stability | en_US |
| dc.subject | equations | en_US |
| dc.subject | liquid | en_US |
| dc.subject | fluid | en_US |
| dc.title | Harmonic moment dynamics in Laplacian growth | en_US |
| dc.type | Article | en_US |