Lattice Boltzmann simulation of droplet generation in a microfluidic cross-junction

Using the lattice Boltzmann multiphase model, numerical simulations have been performed to understand the dynamics of droplet formation in a microfluidic cross-junction. The influence of capillary number, flow rate ratio, viscosity ratio, and viscosity of the continuous phase on droplet formation has been systematically studied over a wide range of capillary numbers. Two different regimes, namely the squeezing-like regime and the dripping regime, are clearly identified with the transition occurring at a critical capillary number Cacr. Generally, large flow rate ratio is expected to produce big droplets, while increasing capillary number will reduce droplet size. In the squeezing-like regime (Ca ≤ Cacr), droplet breakup process is dominated by the squeezing pressure and the viscous force; while in the dripping regime (Ca > Cacr), the viscous force is dominant and the droplet size becomes independent of the flow rate ratio as the capillary number increases. In addition, the droplet size weakly depends on the viscosity ratio in both regimes and decreases when the viscosity of the continuous phase increases. Finally, a scaling law is established to predict the droplet size

Lattice Boltzmann simulation of droplet behaviour in microfluidic devices

We developed a lattice Boltzmann model to investigate the droplet dynamics in microfluidic devices. In our model, a stress-free boundary condition was proposed to conserve the total mass of flow system and improve the numerical stability for flows with low Reynolds number The model was extensively validated by the benchmark cases including the Laplace law, the static contact angles at solid surface, and the droplet deformation and breakup under simple shear flow We applied our model to study the effects of the Pelcect number the Capillary number and wettability on droplet formation. The results showed that the Peclet number has little effect on droplet size though it slightly affects the time of droplet formation. In the creeping flow regime, the Capillary number plays a dominating role in the droplet generation process. Wettability of fluids affects the position of droplet detachment, the droplet shape and size, and its impact becomes more significant when the Capillary number decreases. We also found that the hydrophobic surface generally can produce smaller droplet

Influence of external flows on crystal growth: numerical investigation

We use a combined phase-field/lattice-Boltzmann scheme [D. Medvedev, K. Kassner, Phys. Rev. E {\bf 72}, 056703 (2005)] to simulate non-facetted crystal growth from an undercooled melt in external flows. Selected growth parameters are determined numerically. For growth patterns at moderate to high undercooling and relatively large anisotropy, the values of the tip radius and selection parameter plotted as a function of the Peclet number fall approximately on single curves. Hence, it may be argued that a parallel flow changes the selected tip radius and growth velocity solely by modifying (increasing) the Peclet number. This has interesting implications for the availability of current selection theories as predictors of growth characteristics under flow. At smaller anisotropy, a modification of the morphology diagram in the plane undercooling versus anisotropy is observed. The transition line from dendrites to doublons is shifted in favour of dendritic patterns, which become faster than doublons as the flow speed is increased, thus rendering the basin of attraction of dendritic structures larger. For small anisotropy and Prandtl number, we find oscillations of the tip velocity in the presence of flow. On increasing the fluid viscosity or decreasing the flow velocity, we observe a reduction in the amplitude of these oscillations.Comment: 10 pages, 7 figures, accepted for Physical Review E; size of some images had to be substantially reduced in comparison to original, resulting in low qualit

Ordering dynamics of blue phases entails kinetic stabilization of amorphous networks

The cubic blue phases of liquid crystals are fascinating and technologically promising examples of hierarchically structured soft materials, comprising ordered networks of defect lines (disclinations) within a liquid crystalline matrix. We present the first large-scale simulations of their domain growth, starting from a blue phase nucleus within a supercooled isotropic or cholesteric background. The nucleated phase is thermodynamically stable; one expects its slow orderly growth, creating a bulk cubic. Instead, we find that the strong propensity to form disclinations drives the rapid disorderly growth of a metastable amorphous defect network. During this process the original nucleus is destroyed; re-emergence of the stable phase may therefore require a second nucleation step. Our findings suggest that blue phases exhibit hierarchical behavior in their ordering dynamics, to match that in their structure.Comment: 11 pages, 5 figures, 2 supplementary figures, 2 supplementary tables, accepted by PNA

Comparison of multiphase SPH and LBM approaches for the simulation of intermittent flows

Smoothed Particle Hydrodynamics (SPH) and Lattice Boltzmann Method (LBM) are increasingly popular and attractive methods that propose efficient multiphase formulations, each one with its own strengths and weaknesses. In this context, when it comes to study a given multi-fluid problem, it is helpful to rely on a quantitative comparison to decide which approach should be used and in which context. In particular, the simulation of intermittent two-phase flows in pipes such as slug flows is a complex problem involving moving and intersecting interfaces for which both SPH and LBM could be considered. It is a problem of interest in petroleum applications since the formation of slug flows that can occur in submarine pipelines connecting the wells to the production facility can cause undesired behaviors with hazardous consequences. In this work, we compare SPH and LBM multiphase formulations where surface tension effects are modeled respectively using the continuum surface force and the color gradient approaches on a collection of standard test cases, and on the simulation of intermittent flows in 2D. This paper aims to highlight the contributions and limitations of SPH and LBM when applied to these problems. First, we compare our implementations on static bubble problems with different density and viscosity ratios. Then, we focus on gravity driven simulations of slug flows in pipes for several Reynolds numbers. Finally, we conclude with simulations of slug flows with inlet/outlet boundary conditions. According to the results presented in this study, we confirm that the SPH approach is more robust and versatile whereas the LBM formulation is more accurate and faster

Growth saturation of unstable thin films on transverse-striped hydrophilic-hydrophobic micropatterns

Using three-dimensional numerical simulations, we demonstrate the growth saturation of an unstable thin liquid film on micropatterned hydrophilic-hydrophobic substrates. We consider different transverse-striped micropatterns, characterized by the total fraction of hydrophilic coverage and the width of the hydrophilic stripes. We compare the growth of the film on the micropatterns to the steady states observed on homogeneous substrates, which correspond to a saturated sawtooth and growing finger configurations for hydrophilic and hydrophobic substrates, respectively. The proposed micropatterns trigger an alternating fingering-spreading dynamics of the film, which leads to a complete suppression of the contact line growth above a critical fraction of hydrophilic stripes. Furthermore, we find that increasing the width of the hydrophilic stripes slows down the advancing front, giving smaller critical fractions the wider the hydrophilic stripes are. Using analytical approximations, we quantitatively predict the growth rate of the contact line as a function of the covering fraction, and predict the threshold fraction for saturation as a function of the stripe width.Comment: 11 pages, 5 figure