We study theoretically the Saffman-Taylor instability of an air bubble expanding into a non-Newtonian fluid in a Hele-Shaw cell, with the motivation of understanding suppression of tip-splitting and the formation of dendritic structures observed in the flow of complex fluids, such as polymeric liquids or liquid crystals. A standard visco-elastic flow model is simplified in the case of flow in a thin gap, and it is found that there is a distinguished limit where shear thinning and normal stress differences are apparent, but elastic response is negligible. This observation allows formulation of a generalized Darcy's law, where the pressure satisfies a nonlinear elliptic boundary value problem. Numerical simulation shows that shear-thinning alone modifies considerably the pattern formation and can produce fingers whose tip-splitting is suppressed, in agreement with experimental results. These fingers grow in an oscillating fashion, shedding "side-branches" from their tips, closely resembling solidification patterns. A careful analysis of the parametric dependencies of the system provides an understanding of the conditions required to suppress tip-splitting, and an interpretation of experimental observations, such as emerging length-scales. (C) 2001 American Institute of Physics.
Surface Anchoring and Growth-Pattern of the Field-Driven 1St-Order Transition in a Smectic-A Liquid-Crystal07/11/1994
It is demonstrated that a surface energy anisotropy (anchoring) defines the growth pattern of the field-induced transition in a smectic-A liquid crystal (Sm-A). The stable domain phase nucleates as rounded domains but expands as stripes. The change in growth pattern is accounted for a large anchoring strength Wa∼10-2-10-3 J/m2 which is connected with the layer breaking in the vicinity of the cell plates. The temperature dependence of Wa for Sm-A (substance CCN-47) is measured for the first time: Wa∼(TA-N-T)0.65±0.09.