Available online at www.sciencedirect.com Physica A 328 (2003) 305–314 www.elsevier.com/locate/physa Finger velocities in the lifting Hele–Shaw cell Subrata K. Kabiraj, Sujata Tarafdar ∗ Physics Department, Condensed Matter Physics Research Centre, Jadavpur University, Kolkata 700032, India Received 24 September 2002 Abstract Velocities of viscous ngers growing in a lifting Hele–Shaw cell are studied. The plates are separated by a pneumatic cylinder arrangement exerting a constant force. It is observed that with air invading a non-Newtonian oil-paint, nger velocities show an anomalous behaviour, with a rapid growth towards the end of the process. The correlation coecient between neighbouring ngers shows the dominant modes selected as the pattern develops. c  2003 Elsevier B.V. All rights reserved. PACS: 47.54.+r; 47.20.Gv; 89.75.Fb Keywords: Viscous ngers; Hele–Shaw cell; Velocity correlation 1. Introduction Viscous ngering (VF) in the Hele–Shaw (HS) cell [1] is now a well-studied prob- lem. VF is the pattern arising due to an instability at the interface, when a less viscous uid is forced under pressure, into a more viscous uid [2,3]. The HS cell, consisting of two parallel glass plates, with a very small gap in between, is the most popular model for study of VF patterns. The more viscous ‘defending’ uid, is kept sand- wiched between the two plates, and the less viscous ‘invading’ uid is forced in the gap, through a small hole at the centre of the upper glass plate. The less viscous uid forms complex, sometimes fractal patterns, depending on the characteristic properties of the two uids. The viscosities of the uids, their interface tension, the rate of ow of the invading uid are some of the properties aecting the pattern. Many modications of this simple HS cell have been developed. * Corresponding author. Fax: +91-33-473-1481. E-mail address: sujata@juphys.ernet.in (S. Tarafdar). 0378-4371/$-see front matter c  2003 Elsevier B.V. All rights reserved. doi:10.1016/S0378-4371(03)00523-5