Viscoelastic effects in fingering between miscible fluids

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Abstract
Fingering of water injected in concentrated suspensions of clay particles in water (pastes) has been studied in Hele Shaw channels with the aim of investigating the relationships of the paste viscoelastic properties with three fingers characteristics : the average finger width, the finger profile and the branching angle. The main result is that the elastic modulus, G, approximated by the yield stress, σ0, of the paste is a key parameter in these relationships. Increasing the solid/liquid (weight by weight) ratio in the paste from 0.05 to 0.10 leads (i) to a dramatic rise of σ0, from — 1.5 Pa to ∼ 140 Pa ; (ii) to a decrease of the average finger width, according to a σ- 0.250 power law ; (iii) to an abrupt change of the tips profile — from convex to concave — which can be rationalized either in terms of the cusp singularity predicted by Shraiman and Bensimon in the zero surface tension limit, or, more likely, in terms of the onset of fracture phenomena ; (iv) to an opening of the average branching angle β up to β = π /2 and to the development of asymmetric branching. When taken together, the results suggest that the highly branched structure of viscoelastic fingers is controlled to a large extent by the elastic properties of the pushed medium, the elastic response limiting the speed of the tips. Branching might be associated to fluctuations close to this limit