کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
670793 | 1459057 | 2012 | 10 صفحه PDF | دانلود رایگان |

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 λ¯, equivalent to a relaxation time, controls the growth rate of the perturbation. λ¯ depends on the applied gradient of pressure, the surface tension, the cell thickness, and the elastic modulus of the fluid. For small values of λ¯, Newtonian behavior dominates whereas for higher values of λ¯ viscoelastic effects appear. For the critical value λ¯=λc¯≃10 a blowup is predicted and fracture-like patterns are observed.
► Viscoelasticity changes the most unstable wavenumber in Saffman–Taylor instability.
► A blow up occurs at large Deborah numbers.
► Fracture-like patterns are a consequence of viscoelasticity.
► New phenomena are expected in microfluidic devices.
Journal: Journal of Non-Newtonian Fluid Mechanics - Volumes 173–174, April 2012, Pages 30–39