On droplet interactions and suspension flow

Abstract

Micron to millimetre sized droplets, precisely generated or sustained in controlled environment, have great potential in myriads of engineering applications functioning as the basic element to assemble metamaterials, deliver drugs, host surfactant, reduce friction and damp turbulence. The interaction of droplets from pairwise to collective levels is the most important factor in controlling these processes, yet little is known about the detailed mechanisms in various nonideal conditions. The present thesis combines a number of studies aiming to elucidate the physical principles of droplet interactions and suspension flow using both high- and low-fidelity numerical simulations.

We first study flow-assisted droplet assembly in microfluidic channels, seeking to harness the droplet interactions to produce photonic bandgap materials. A novel interface-correction level set/ghost fluid method (ICLS/GFM) is developed to directly simulate liquid droplets under depletion forces. Comparing to previous methods, ICLS/GFM conserves the global mass of each fluid using a simple mass-correction scheme, accurately computes the surface tension and depletion forces under the same framework, and has subsequently been applied to investigate the droplet clustering observed in a microfluidic experiment. Our simulations, supported by theoretical derivations, suggest that the observed fast self-assembly arises from a combination of strong depletion forces, confinement-mediated shear alignments of the droplets, and fine-tuned inflow conditions of the microchannel. However, the interplay of these 3D effects negates a simple droplet interaction model of parametric dependence, rendering the design of microfluidic chips for photonic crystal fabrications difficult in practice.

The next objective of the thesis is the implementation of a minimal hybrid lubrication/granular dynamics (HLGD) model for simulation of dense particle suspensions. The main ingredients of HLGD include (i) a frame-invariant, short-range lubrication model for spherical particles, and (ii) a soft-core, stick/slide frictional contact model activated when particles overlap. Since contact interactions dominate at high particle concentrations, we expect the methodology to be applicable for probing the jamming of non-spherical particles and the rheology of foams as well.

Finally, we include two miscellaneous studies concerning the slippage property of liquid-infused surfaces and droplets statistics in a homogeneous turbulent shear flow. Overall, results of these simulations provide detailed flow visualisations and qualitative dependence of the target functional on various governing parameters, facilitating experimental and theoretical investigations to design more robust drag-reducing surfaces and predict droplet distributions in emulsions.

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