Details of Grant 

EPSRC Reference:	EP/J007927/1
Title:	Viscous fingering under elastic membranes
Principal Investigator:	Juel, Professor A
Other Investigators:	Heil, Professor M
Researcher Co-Investigators:
Project Partners:
Department:	Mathematics
Organisation:	University of Manchester, The
Scheme:	Standard Research
Starts:	01 August 2012	Ends:	31 January 2016	Value (£):	363,683
EPSRC Research Topic Classifications:	Continuum Mechanics Multiphase Flow
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:	Panel Date Panel Name Outcome 30 Jan 2012 Mathematics Prioritisation Panel Meeting January 2012 Announced
Summary on Grant Application Form
The research proposed here is motivated by recent striking and unexpected observations of the suppression of a viscous fingering instability in elastic-walled Hele-Shaw cells. The dendritic patterns that readily develop when a thin fluid layer contained in a narrow gap between two rigid plates is displaced by a less viscous fluid, is an archetype for front-propagating, pattern-forming phenomena. We have observed that elastic deformations of the plates that bound the fluid can have a dramatic effect on the onset and nonlinear development of this instability. Specifically, in an elastic-walled Hele-Shaw cell where one of the bounding plates is replaced by a latex membrane, the interface remains axisymmetric for values of the injection rate at which the rigid system already exhibits strongly nonlinear interfacial growth. The critical injection rate beyond which the axisymmetrically expanding interface becomes unstable in the elastic-walled system is approximately 1000 times larger than the corresponding value in the rigid system. Wall elasticity not only affects the onset of the instability but also has a strong effect on the structure of the fingers that develop subsequently. Moreover, if the variations in fluid pressure along the bounding plate are sufficiently large (relative to the plate's stiffness), the fluid loading can cause the plate to buckle (or wrinkle), leading to a strong interaction between two fluid- and solid-based instabilities. We propose to employ a combination of experimental, theoretical and computational approaches to provide a comprehensive understanding of the mechanisms responsible for these novel elasto-hydrodynamic phenomena.
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Organisation Website:	http://www.man.ac.uk