Viscous fingering is a pattern forming phenomenon in which the interface between two immiscible fluids destabilizes when the more viscous fluid is displaced by the less viscous one. The use of intrinsically anisotropic, non-Newtonian, or complex fluids (e.g., liquid crystals) as a more viscous fluid results in a much richer morphological diagram than that for isotropic fluids due to shear thinning/thickening effects, or plastic/elastic effects. Moreover, because of the dielectric and magnetic anisotropy of the liquid crystals, their relevant (e.g., viscous, elastic) properties can be easily tuned by electric or magnetic fields.   


Main results


The influence of an external electric field on the morphology of the nematic-liquid-crystal–air interface has been studied in radial Hele-Shaw geometry. The effective viscosity μeff of the nematic has been tuned by the electric field E and by the flow. At low excess pressure pe (where the growth of the interface is controlled mainly by the surface tension σ), the applied E has no significant influence on the morphology of the interface, but decreases its normal velocity due to the increase of μeff. At higher pe (where the growth is not only controlled by σ, but also by the kinetic term that depends on the effective viscosity) a significant difference in the morphology has been observed as a function of E. Experiments have shown that the influence of the electric field on the pattern morphology increases with the driving force (pressure gradient).

[Phys. Rev. E 67, 041717/1-7 (2003)] (pdf)


Viscous fingering of an air-nematic interface in a radial Hele-Shaw cell has been studied when periodically switching on and off an electric field, which reorients the nematic and thus changes its viscosity, as well as the surface tension and its anisotropy (mainly enforced by a single groove in the cell). Undulations at the sides of the fingers have been observed that correlate with the switching frequency and with tip oscillations that give maximal velocity to smallest curvatures. These lateral undulations appear to be decoupled from spontaneous (noise induced) side branching. It is concluded that the lateral undulations are generated by successive relaxations between two limiting finger widths. The change between these two selected pattern scales is mainly due to the change in the anisotropy. This scenario is confirmed by numerical simulations in the channel geometry, using a phase-field model for anisotropic viscous fingering.

[Phys. Rev. E 64, 056225/1-9 (2001)] (pdf)


The morphological pressure-temperature phase diagram for viscous fingering patterns observed in the isotropic, nematic and smectic A phases of the liquid crystal 8CB has been presented. In addition to the dense branching structure, two distinct dendritic regimes were observed in the nematic and smectic phases. The dependence of characteristic finger width on pressure was studied, and the effects of surface and magnetic field alignment were considered.

[J. Phys (France) 49, 1319-1323 (1988)]


The Saffman-Taylor instability has been studied in a Hele-Shaw cell containing nematic liquid crystal 4, 4'-n-octylcyanobiphenyl (8CB). Air injected into the center of the cell gives rise to viscous fingering patterns, which show a sequence of dense-branching, dendritic, dense-branching morphologies as a function of temperature. A qualitative explanation of these morphological transitions is given in terms of the flow alignment of the director field and the resulting anisotropic viscosity in the nematic phase of the liquid crystal. The analysis of the fingering patterns shows that while the perimeter of the pattern is fractal, the pattern itself is not. The extent to which the pattern is space filling depends on the morphology and this quantity may serve to indicate the morphological transitions.

[Phys. Rev. A 36, 3984-3989 (1987)] (pdf)


Experimental data of viscous fingering patterns have been presented in a radial Hele-Shaw cell filled with the liquid crystal 8CB. A dense-branching—dendritic-dense-branching morphological phase sequence has been observed as a function of temperature. The wave number of the fastest growing mode can be selected by varying experimental parameters, and the number of initially growing fingers on a circular interface is in good agreement with linear stability analysis which includes the full kinetic term. A mechanism is proposed for tip stabilization by anisotropic viscosity; the critical viscosity ratio for circular tips is ≈2.

[Phys. Rev. A 36, 1527-1529(R) (1987)] (pdf)


A Hele-Shaw experimental geometry has been introduced which uses a nematic liquid crystal as the more viscous fluid, so that there is anisotropy in the medium itself. It has been found that the effective anisotropy may be tuned by varying the pressure with which the low-viscosity liquid (air, in this case) enters the cell. As a result re-entrant morphological transitions have been obtained between random patterns (tip splitting) and quasi-regular patterns qualitatively resembling dendritic growth (stable tips).

[Nature 323, 424-425 (1986)]