%0 Journal Article
%T From viscous fingering to elastic instabilities
%+ Laboratoire Charles Coulomb (L2C)
%A Mora, Serge
%A Manna, Miguel
%< avec comité de lecture
%Z L2C:12-214
%@ 0377-0257
%J Journal of Non-Newtonian Fluid Mechanics
%I Elsevier
%V 173
%P 30-39
%8 2012-04
%D 2012
%R 10.1016/j.jnnfm.2012.01.010
%K Viscoelastic properties
%K Surface instability
%K Analytical theory
%K Experiments
%Z Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph]
%Z Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph]Journal articles
%X An analytical and numerical study of the linear Saffman-Taylor instability for a Maxwell viscoelastic fluid is presented. Results obtained in a rectangular Hele-Shaw cell are complemented by experiments in a circular cell corroborating the universality of our main result: The base flow becomes unstable and the propagating disturbances develop into crack-like features. The full hydrodynamics equations in a regime where viscoelasticity dominates show that perturbations to the pressure remain Laplacian. Darcy's law is expressed as an infinite series in the cell thickness. An unique dimensionless parameter Delta-bar, equivalent to a relaxation time, controls the growth rate of the perturbation. Delat-bar depends on the applied gradient of pressure, the surface tension, the cell thickness, and the elastic modulus of the fluid. For small values of Delta-bar, Newtonian behavior dominates whereas for higher values of Delta-bar viscoelastic effects appear. For the critical value Dalta-bar ~= 10 a blowup is predicted and fracture-like patterns are observed.
%G English
%L hal-00749940
%U https://hal.science/hal-00749940
%~ CNRS
%~ L2C
%~ MIPS
%~ UNIV-MONTPELLIER
%~ UM-2015-2021