Droplet formation in a T-shaped microfluidic junction

Using a phase-field model to describe fluid/fluid interfacial dynamics and a lattice Boltzmann model to address hydrodynamics, two dimensional (2D) numerical simulations have been performed to understand the mechanisms of droplet formation in microfluidic T-juntion. Although 2D simulations may not capture underlying physics quantitatively, our findings will help to clarify controversial experimental observations and identify new physical mechanisms. We have systematically examined the influence of capillary number, flow rate ratio, viscosity ratio, and contact angle in the droplet generation process. We clearly observe that the transition from the squeezing regime to the dripping regime occurs at a critical capillary number of 0.018, which is independent of flow rate ratio, viscosity ratio, and contact angle. In the squeezing regime, the squeezing pressure plays a dominant role in the droplet breakup process, which arises when the emerging interface obstructs the main channel. The droplet size depends on both the capillary number and the flow rate ratio, but is independent of the viscosity ratio under completely hydrophobic wetting conditions. In the dripping regime, the droplet size will be significantly influenced by the viscosity ratio as well as the built-up squeezing pressure. When the capillary number increases, the droplet size becomes less dependent on the flow rate ratio. The contact angle also affects the droplet shape, size, and detachment point, especially at small capillary numbers. More hydrophobic wetting properties are expected to produce smaller droplets. Interestingly, the droplet size is dependent on the viscosity ratio in the squeezing regime for less hydrophobic wetting conditions

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

Droplet formation in microfluidic cross-junctions

Using a lattice Boltzmann multiphase model, three-dimensional numerical simulations have been performed to understand droplet formation in microfluidic cross-junctions at low capillary numbers. Flow regimes, consequence of interaction between two immiscible fluids, are found to be dependent on the capillary number and flow rates of the continuous and dispersed phases. A regime map is created to describe the transition from droplets formation at a cross-junction (DCJ), downstream of cross-junction to stable parallel flows. The influence of flow rate ratio, capillary number, and channel geometry is then systematically studied in the squeezing-pressure-dominated DCJ regime. The plug length is found to exhibit a linear dependence on the flow rate ratio and obey power-law behavior on the capillary number. The channel geometry plays an important role in droplet breakup process. A scaling model is proposed to predict the plug length in the DCJ regime with the fitting constants depending on the geometrical parameters

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 the trapping of a microdroplet in a well of surface energy

In this paper, a three-dimensional phase-field lattice Boltzmann method is used to simulate the dynamical behavior of a droplet, subject to an outer viscous flow, in a microchannel that contains a cylindrical hole etched into its top surface. The influence of the capillary number and the hole diameter (expressed as the ratio of hole diameter to channel height, b) is investigated. We demonstrate numerically that the surface energy gradient induced by the hole can create an anchoring force to resist the hydrodynamic drag from the outer flow, resulting in the droplet anchored to the hole when the capillary number is below a critical value. As b increases, the droplet can be anchored more easily. For b 2, the spherical cap of droplet reaches the top wall of the hole, making the hole depth into an additional important parameter. These observations are consistent with the previously reported experiments. However, the droplet does not fully fill the hole for b > 2, departing from the expectation of Dangla et al. [R. Dangla, S. Lee, C. N. Baroud, Trapping microfluidic drops in wells of surface energy, Phys. Rev. Lett. 107 (2011) 124501]. Also, it is observed in the anchored state that the rear of the droplet rests at a small distance away from the junction. Finally, the droplet undergoes a slow-down process only when itsrear passes through the hole, regardless of b

ConDefects: A New Dataset to Address the Data Leakage Concern for LLM-based Fault Localization and Program Repair

With the growing interest on Large Language Models (LLMs) for fault localization and program repair, ensuring the integrity and generalizability of the LLM-based methods becomes paramount. The code in existing widely-adopted benchmarks for these tasks was written before the the bloom of LLMs and may be included in the training data of existing popular LLMs, thereby suffering from the threat of data leakage, leading to misleadingly optimistic performance metrics. To address this issue, we introduce "ConDefects", a novel dataset of real faults meticulously curated to eliminate such overlap. ConDefects contains 1,254 Java faulty programs and 1,625 Python faulty programs. All these programs are sourced from the online competition platform AtCoder and were produced between October 2021 and September 2023. We pair each fault with fault locations and the corresponding repaired code versions, making it tailored for in fault localization and program repair related research. We also provide interfaces for selecting subsets based on different time windows and coding task difficulties. While inspired by LLM-based tasks, ConDefects can be adopted for benchmarking ALL types of fault localization and program repair methods. The dataset is publicly available, and a demo video can be found at https://www.youtube.com/watch?v=22j15Hj5ONk.Comment: 5pages, 3 figure

Influence of intermolecular potentials on rarefied gas flows: fast spectral solutions of the Boltzmann equation

The Boltzmann equation with an arbitrary intermolecular potential is solved by the fast spectral method. As examples, noble gases described by the Lennard-Jones potential are considered. The accuracy of the method is assessed by comparing both transport coefficients with variational solutions and mass/heat flow rates in Poiseuille/thermal transpiration flows with results from the discrete velocity method. The fast spectral method is then applied to Fourier and Couette flows between two parallel plates, and the influence of the intermolecular potential on various flow properties is investigated. It is found that for gas flows with the same rarefaction parameter, differences in the heat flux in Fourier flow and the shear stress in Couette flow are small. However, differences in other quantities such as density, temperature, and velocity can be very large

Lattice Boltzmann modeling of contact angle and its hysteresis in two-phase flow with large viscosity difference

Contact angle hysteresis is an important physical phenomenon omnipresent in nature and various industrial processes, but its effects are not considered in many existing multiphase flow simulations due to modeling complexity. In this work, a multiphase lattice Boltzmann method (LBM) is developed to simulate the contact-line dynamics with consideration of the contact angle hysteresis for a broad range of kinematic viscosity ratios. In this method, the immiscible two-phase flow is described by a color-fluid model, in which the multiple-relaxation-time collision operator is adopted to increase numerical stability and suppress unphysical spurious currents at the contact line. The contact angle hysteresis is introduced using the strategy proposed by Ding and Spelt [Ding and Spelt, J. Fluid Mech. 599, 341 (2008)], and the geometrical wetting boundary condition is enforced to obtain the desired contact angle. This method is first validated by simulations of static contact angle and dynamic capillary intrusion process on ideal (smooth) surfaces. It is then used to simulate the dynamic behavior of a droplet on a nonideal (inhomogeneous) surface subject to a simple shear flow. When the droplet remains pinned on the surface due to hysteresis, the steady interface shapes of the droplet quantitatively agree well with the previous numerical results. Four typical motion modes of contact points, as observed in a recent study, are qualitatively reproduced with varying advancing and receding contact angles. The viscosity ratio is found to have a notable impact on the droplet deformation, breakup, and hysteresis behavior. Finally, this method is extended to simulate the droplet breakup in a microfluidic T junction, with one half of the wall surface ideal and the other half nonideal. Due to the contact angle hysteresis, the droplet asymmetrically breaks up into two daughter droplets with the smaller one in the nonideal branch channel, and the behavior of daughter droplets is significantly different in both branch channels. Also, it is found that the contact angle hysteresis is strengthened with decreasing the viscosity ratio, leading to an earlier droplet breakup and a decrease in the maximum length that the droplet can reach before the breakup. These simulation results manifest that the present multiphase LBM can be a useful substitute to Ba et al. [Phys. Rev. E 88, 043306 (2013)] for modeling the contact angle hysteresis, and it can be easily implemented with higher computational efficiency