Instabilities and flow-induced structures in anisotropic systems

Abstract

The natural world is full of patterns that spontaneously emerge across length scales and material properties. Examples range from microscopic dendritic snowflakes to macroscopic sand ripples and intricate river networks. Central to the formation of patterns is the concept of an instability; complex forms spontaneously develop when a system is driven out of equilibrium. Nature leverages instabilities to ‘fabricate’ complex structures that maximize performance using minimal resources, exploiting the self-amplification of small perturbations. The potential to use instabilities in practical applications, for example to engineer or assemble structured materials, is barely exploited due to the notorious difficulty and limited available strategies to control the self-amplified and non-linear growth that characterizes instabilities. In this thesis, we focus on fluid instabilities due to the adaptivity of fluids to their environments, and establish novel strategies to tune the growth morphology of interfacial instabilities and flow-induced structures at different length scales.

At the macroscale, we induce a morphology transition from the generic dense-branching growth characterized by repeated tip-splitting of the growing fingers to dendritic growth characterized by stable fingertips in the presence of anisotropy in the viscous-fingering instability. This instability arises when a less viscous fluid displaces a more viscous one in a confined environment. When the growth environment is rendered anisotropic by engraving a lattice of channels on a Hele-Shaw cell, we show that the morphology transition and the global symmetry of the dendrites can be controlled by tuning the viscosity ratio between the two fluids or the degree of anisotropy set by the lattice topography. We further exploit a material with shear-enhanced anisotropy where the anisotropy is intrinsic to the fluid, a lyotropic chromonic liquid crystal (LCLC) in the nematic phase. For high enough flow velocities, the tumbling behavior of LCLC solutions can be suppressed, which results in a flow-alignment of the material. This microscopic change in the director field macroscopically enhances the liquid crystal anisotropy to induce the transition from dense-branching to dendritic growth.

Microscopically, we discover the emergence of flow-induced defects and structures in LCLC solutions. Pure-twist disclination loops form in a range of shear rates as a consequence of the low twist elastic constant of LCLC solutions. We demonstrate that the size of the pure-twist disclination loops is governed by the balance between nucleation and annihilation forces, which can be tuned by controlling the flow velocity. Strikingly, at lower shear rates, chiral periodic double-twist structures spontaneously emerge, even though the LCLC is achiral. We show that the mirror symmetry breaking is triggered at regions of biaxial-splay deformations that are unstable and evolve into the energetically cheaper double-twist elastic mode. Our results reveal a novel path to structural chirality in an achiral system.

The control gained over the pattern morphology and structure formation from fluid instabilities can open pathways to harnessing unstable growth to design programmable microstructures in materials and to control assembly and flow of biological systems in microfluidic devices.