Interfacial instabilities of a fluid annulus in a rotating Hele-Shaw cell

We have studied the interfacial instabilities experienced by a liquid annulus as it moves radially in a circular Hele-Shaw cell rotating with angular velocity Omega. The instability of the leading interface (oil displacing air) is driven by the density difference in the presence of centrifugal forcing, while the instability of the trailing interface (air displacing oil) is driven by the large viscosity contrast. A linear stability analysis shows that the stability of the two interfaces is coupled through the pressure field already at a linear level. We have performed experiments in a dry cell and in a cell coated with a thin fluid layer on each plate, and found that the stability depends substantially on the wetting conditions at the leading interface. Our experimental results of the number of fingers resulting from the instability compare well with the predictions obtained through a numerical integration of the coupled equations derived from a linear stability analysis. Deep in the nonlinear regime we observe the emission of liquid droplets through the formation of thin filaments at the tip of outgrowing fingers.

Perturbing Hele-Shaw flow with a small gap gradient

A controlled perturbation is introduced into the Saffman-Taylor flow problem by adding a gradient to the gap of a Hele-Shaw cell. The stability of the single-finger steady state was found to be strongly affected by such a perturbation. Compared with patterns in a standard Hele-Shaw cell, the single Saffman-Taylor finger was stabilized or destabilized according to the sign of the gap gradient. While a linear stability analysis shows that this perturbation should have a negligible effect on the early-stage pattern formation, the experimental data indicate that the characteristic length for the initial breakup of a flat interface has been changed by the perturbation.

[Illustrations de Oeuvres poissardes] / M. Monsiau, dess. ; A. Clément, grav. ; Jean-Joseph Vadé, aut. du texte

Comprend : [Pl. en reg. p.5 : La pipe cassée. Poème. Chant I.] [Cote : Res Yf 52/Microfilm R 122340] ; [Pl. en reg. p.12 : La pipe cassée. Poème. Chant II.] [Cote : Res Yf 52/Microfilm R 122340] ; [Pl. en reg. p.25 : La pipe cassée. Poème. Chant III.] [Cote : Res Yf 52/Microfilm R 122340] ; [Pl. en reg. p.43 : La pipe cassée. Poème. Chant IV.] [Cote : Res Yf 52/Microfilm R 122340]