Flow-assisted droplet assembly in a 3D microfluidic channel.

Self-assembly of soft matter, such as droplets or colloids, has become a promising scheme to engineer novel materials, model living matter, and explore non-equilibrium statistical mechanics. In this article, we present detailed numerical simulations of few non-Brownian droplets in various flow conditions, specifically, focusing on their self-assembly within a short distance in a three-dimensional (3D) microfluidic channel, cf. [Shen et al., Adv. Sci., 2016, 3(6), 1600012]. Contrary to quasi two-dimensional (q2D) systems, where dipolar interaction is the key mechanism for droplet rearrangement, droplets in 3D confinement produce much less disturbance to the underlying flow, thus experiencing weaker dipolar interactions. Using confined simple shear and Poiseuille flows as reference flows, we show that the droplet dynamics is mostly affected by the shear-induced cross-stream migration, which favors chain structures if the droplets are under an attractive depletion force. For more compact clusters, such as three droplets in a triangular shape, our results suggest that an inhomogeneous cross-sectional inflow profile is further required. Overall, the accelerated self-assembly of a small-size droplet cluster results from the combined effects of strong depletion forces, confinement-mediated shear alignments, and fine-tuned inflow conditions. The deterministic nature of the flow-assisted self-assembly implies the possibility of large throughputs, though calibration of all different effects to directly produce large droplet crystals is generally difficult.

General hydrodynamic features of elastoviscoplastic fluid flows through randomised porous media.

Abstract: A numerical study of yield-stress fluids flowing in porous media is presented. The porous media is randomly constructed by non-overlapping mono-dispersed circular obstacles. Two class of rheological models are investigated: elastoviscoplastic fluids (i.e. Saramito model) and viscoplastic fluids (i.e. Bingham model). A wide range of practical Weissenberg and Bingham numbers is studied at three different levels of porosities of the media. The emphasis is on revealing some physical transport mechanisms of yield-stress fluids in porous media when the elastic behaviour of this kind of fluids is incorporated. Thus, computations of elastoviscoplastic fluids are performed and are compared with the viscoplastic fluid flow properties. At a constant Weissenberg number, the pressure drop increases both with the Bingham number and the solid volume fraction of obstacles. However, the effect of elasticity is less trivial. At low Bingham numbers, the pressure drop of an elastoviscoplastic fluid increases compared to a viscoplastic fluid, while at high Bingham numbers we observe drag reduction by elasticity. At the yield limit (i.e. infinitely large Bingham numbers), elasticity of the fluid systematically promotes yielding: elastic stresses help the fluid to overcome the yield stress resistance at smaller pressure gradients. We observe that elastic effects increase with both Weissenberg and Bingham numbers. In both cases, elastic effects finally make the elastoviscoplastic flow unsteady, which consequently can result in chaos and turbulence.

Elasto-inertial focusing and particle migration in high aspect ratio microchannels for high-throughput separation.

The combination of flow elasticity and inertia has emerged as a viable tool for focusing and manipulating particles using microfluidics. Although there is considerable interest in the field of elasto-inertial microfluidics owing to its potential applications, research on particle focusing has been mostly limited to low Reynolds numbers (Re<1), and particle migration toward equilibrium positions has not been extensively examined. In this work, we thoroughly studied particle focusing on the dynamic range of flow rates and particle migration using straight microchannels with a single inlet high aspect ratio. We initially explored several parameters that had an impact on particle focusing, such as the particle size, channel dimensions, concentration of viscoelastic fluid, and flow rate. Our experimental work covered a wide range of dimensionless numbers (0.05 < Reynolds number < 85, 1.5 < Weissenberg number < 3800, 5 < Elasticity number < 470) using 3, 5, 7, and 10 µm particles. Our results showed that the particle size played a dominant role, and by tuning the parameters, particle focusing could be achieved at Reynolds numbers ranging from 0.2 (1 µL/min) to 85 (250 µL/min). Furthermore, we numerically and experimentally studied particle migration and reported differential particle migration for high-resolution separations of 5 µm, 7 µm and 10 µm particles in a sheathless flow at a throughput of 150 µL/min. Our work elucidates the complex particle transport in elasto-inertial flows and has great potential for the development of high-throughput and high-resolution particle separation for biomedical and environmental applications.

A dual resolution phase-field solver for wetting of viscoelastic droplets.

We present a new and efficient phase-field solver for viscoelastic fluids with moving contact line based on a dual-resolution strategy. The interface between two immiscible fluids is tracked by using the Cahn-Hilliard phase-field model, and the viscoelasticity incorporated into the phase-field framework. The main challenge of this approach is to have enough resolution at the interface to approach the sharp-interface methods. The method presented here addresses this problem by solving the phase field variable on a mesh twice as fine as that used for the velocities, pressure, and polymer-stress constitutive equations. The method is based on second-order finite differences for the discretization of the fully coupled Navier-Stokes, polymeric constitutive, and Cahn-Hilliard equations, and it is implemented in a 2D pencil-like domain decomposition to benefit from existing highly scalable parallel algorithms. An FFT-based solver is used for the Helmholtz and Poisson equations with different global sizes. A splitting method is used to impose the dynamic contact angle boundary conditions in the case of large density and viscosity ratios. The implementation is validated against experimental data and previous numerical studies in 2D and 3D. The results indicate that the dual-resolution approach produces nearly identical results while saving computational time for both Newtonian and viscoelastic flows in 3D.

Yield-stress fluids in porous media: a comparison of viscoplastic and elastoviscoplastic flows.

A numerical and theoretical study of yield-stress fluid flows in two types of model porous media is presented. We focus on viscoplastic and elastoviscoplastic flows to reveal some differences and similarities between these two classes of flows. Small elastic effects increase the pressure drop and also the size of unyielded regions in the flow which is the consequence of different stress solutions compare to viscoplastic flows. Yet, the velocity fields in the viscoplastic and elastoviscoplastic flows are comparable for small elastic effects. By increasing the yield stress, the difference in the pressure drops between the two classes of flows becomes smaller and smaller for both considered geometries. When the elastic effects increase, the elastoviscoplastic flow becomes time-dependent and some oscillations in the flow can be observed. Focusing on the regime of very large yield stress effects in the viscoplastic flow, we address in detail the interesting limit of 'flow/no flow': yield-stress fluids can resist small imposed pressure gradients and remain quiescent. The critical pressure gradient which should be exceeded to guarantee a continuous flow in the porous media will be reported. Finally, we propose a theoretical framework for studying the 'yield limit' in the porous media.

On the axial distribution of plaque stress: Influence of stenosis severity, lipid core stiffness, lipid core length and fibrous cap stiffness.

Numerical simulations of blood flow through a partially-blocked axisymmetric artery are performed to investigate the stress distributions in the plaque. We show that the combined effect of stenosis severity and the stiffness of the lipid core can drastically change the axial stress distribution, strongly affecting the potential sites of plaque rupture. The core stiffness is also an important factor when assessing plaque vulnerability, where a mild stenosis with a lipid-filled core presents higher stress levels than a severe stenosis with a calcified plaque. A shorter lipid core gives rise to an increase in the stress levels. However, the fibrous cap stiffness does not influence the stress distributions for the range of values considered in this work. Based on these mechanical analyses, we identify potential sites of rupture in the axial direction for each case: the midpoints of the upstream and downstream regions of the stenosis (for severe, lipid-filled plaques), the ends of the lipid core (for short cores), and the middle of the stenosis (for mild stenoses with positive remodelling of the arterial wall).