Confined ferrofluid droplet in crossed magnetic fields.
When a ferrofluid drop is trapped in a horizontal Hele-Shaw cell and subjected to a vertical magnetic field, a fingering instability results in the droplet evolving into a complex branched structure. This fingering instability depends on the magnetic field ramp rate but also depends critically on the initial state of the droplet. Small perturbations in the initial droplet can have a large influence on the resulting final pattern. By simultaneously applying a stabilizing (horizontal) azimuthal magnetic field, we gain more control over the mode selection mechanism. We perform a linear stability analysis that shows that any single mode can be selected by appropriately adjusting the strengths of the applied fields. This offers a unique and accurate mode selection mechanism for this confined magnetic fluid system. We present the results of numerical simulations that demonstrate that this mode selection mechanism is quite robust and "overpowers" any initial perturbations on the droplet. This provides a predictable way to obtain patterns with any desired number of fingers.
Jackson
D P
DP
Department of Physics and Astronomy, Dickinson College, Carlisle, PA 17013, USA. jacksond@dickinson.edu
Miranda
J A
JA
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Sep;68(3 Pt 2):035301
14524821
Science. 1995 Jan 27;267(5197):476-83
17788780
Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Sep;70(3 Pt 2):036311
15524637
Phys Rev Lett. 2001 May 14;86(20):4532-5
11384276
Phys Rev Lett. 2000 May 29;84(22):5106-9
10990878
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Nov;64(5 Pt 2):056230
11736077
Phys Rev Lett. 2002 Jun 10;88(23):236801
12059386
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Mar;75(3 Pt 2):036310
17500794
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Jan;67(1 Pt 2):017301
12636637
Phys Rev Lett. 1986 Mar 24;56(12):1260-1263
10032615
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Mar;75(3 Pt 2):036314
17500798
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Oct;66(4 Pt 2):046306
12443321
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1994 Jul;50(1):298-307
9961968
Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Feb;69(2 Pt 1):021605
14995456
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Aug;62(2 Pt B):2985-8
11088789
Science. 1989 Mar 3;243(4895):1150-6
17799896
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Dec;62(6 Pt A):7941-8
11138077
Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Jun;69(6 Pt 2):066312
15244731
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1996 May;53(5):4801-4806
9964808
Phys Rev Lett. 1986 Mar 24;56(12):1264-1267
10032616
Phys Rev A. 1992 Oct 15;46(8):4894-4904
9908709
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Mar;73(3 Pt 2):036309
16605653
Science. 1993 Aug 20;261(5124):1012-5
17739618
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1996 Dec;54(6):6260-6267
9965846
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Jul;74(1 Pt 2):015201
16907143
Phys Rev A Gen Phys. 1986 Apr;33(4):2621-2633
9896946