Viscous fingering at the liquid/liquid interface between two coexisting phases of mixtures with a miscibility gap

Abstract

AbstractThe influence of the viscosity contrast factor A [( = η“‐η′)/(η“+η), η, shear viscosity: (′)(”), indices of the coexisting phases; η“>η′]on the formation of viscous fingers at a mechanically unstable liquid/liquid interface of mixtures with a miscibility gap in a narrow rectangular glass cell (closed Hele‐Shaw cell) is studied. The systems used for the experiments are: (a) 2‐butoxyethanol (C4E1)/water mixtures of critical composition. They are studied in the vicinity of the lower critical point at temperatures above the critical temperature [1.05 < (η”η') < 2.0, corresponding to 0.05<A<0.4]. A is varied by changing the temperature of the mixture; (b) poly(ethylene glycol) (PEG)/dextran (D)/water mixtures at different compositions in the vicinity of the plait point at constant temperature [10<(η“/η')<40, corresponding to 0.762<A<0.950]. The liquid/liquid interfacial tension of both systems is small (σ<0.1 mN m−1). The experimental results are analysed in terms of theoretical work of Tryggvason and Aref (J. Fluid. Mech. 177, 207 (1985)). The viscous fingering process is treated as a two‐dimensional viscous flow. For small values of A (<0.12; system (C4El1/water) the growth rates of the viscous fingers in the upward and downward direction have about the same value and the fingers have a similar shape. At larger values of A (>0.3) the fingers formed by the phase with the higher viscosity advance faster into the phase with the lower viscosity than the fingers advancing in the opposite direction. This effect is pronounced in the system PEG/D/water for which A has large values (A>0.75). In this system the viscous fingers formed by the phase with the higher viscosity are long and narrow whereas that formed by the low viscosity phase are short and broad. The temperature dependence of the mean distance <l> between viscous fingers of the system C4E1/water advancing in opposite directions approaches the theoretically expected dependence at temperature differences (Tp‐Tc)>l K corresponding to a ratio (λmax/b) > 3 (λmax, wave length of fasted growing interfacial instability; b, width of the glass cell). The experiments show that the preferential wetting of the glass walls of the Hele‐Shaw cell by one of the coexisting liquid phases leads to a three‐dimensional shape of the viscous fingers.