Gravity-driven instability in a spherical Hele-Shaw cell
Soft Condensed Matter
2009-10-31 v2 Pattern Formation and Solitons
Fluid Dynamics
Abstract
A pair of concentric spheres separated by a small gap form a spherical Hele-Shaw cell. In this cell an interfacial instability arises when two immiscible fluids flow. We derive the equation of motion for the interface perturbation amplitudes, including both pressure and gravity drivings, using a mode coupling approach. Linear stability analysis shows that mode growth rates depend upon interface perimeter and gravitational force. Mode coupling analysis reveals the formation of fingering structures presenting a tendency toward finger tip-sharpening.
Cite
@article{arxiv.cond-mat/0010224,
title = {Gravity-driven instability in a spherical Hele-Shaw cell},
author = {Jose A. Miranda and Fernando Parisio and Fernando Moraes and Michael Widom},
journal= {arXiv preprint arXiv:cond-mat/0010224},
year = {2009}
}
Comments
13 pages, 4 ps figures, RevTex, to appear in Physical Review E