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

We have studied the interfacial instabilities experienced by a liquid annul us as it moves radially in a circular Hele-Shaw cell rotating with angular velocity Omega. The instability of the leading interface (oil displacing ai r) is driven by the density difference in the presence of centrifugal forci ng, 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 fi eld 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 leadin g interface. Our experimental results of the number of fingers resulting fr om the instability compare well with the predictions obtained through a num erical integration of the coupled equations derived from a linear stability analysis. Deep in the nonlinear regime we observe the emission of liquid d roplets through the formation of thin filaments at the tip of outgrowing fi ngers. (C) 2000 American Institute of Physics. [S1070-6631(00)01007-2].