Kinetic theory based lattice Boltzmann method to simulate multiphase flow of droplet pinch-off
- Abstract:
The pinch-off dynamics of a drop from a leaky faucet have received significant attention of researchers in the last few decades owing to the complex but fascinating physics involved with it. The scaling laws are proposed to characterize the thinning of the neck based on forces balance (inertia, capillary, and viscous forces) for Newtonian fluids. It was found that the neck thinning follows a 2/3 scaling law initially, where the flow is dominated by inertia-capillary balance followed by a linear scaling law where flow is controlled by viscous-inertia-capillary balance. Accurately underpinning the physics of multiphase flow problems which involve significant topological changes using numerical methods is a challenging task. In the continuum regime, researchers have used methods such as Volume-of-Fluid Method, Level-Set Method, and Phase-Field Method to numerically handle such complex topological changes. The Lattice Boltzmann Method (LBM) is another popular method based on the kinetic theory that uses a mesoscopic approach and has shown robustness in simulating such intricate topological changes. Moreover, LBM is known for its simplicity and efficient computational advantage. This work aims to implement a single-relaxation-time (SRT) phase-field lattice Boltzmann method (PF-LBM) capable of handling density ratios up to 1000 and viscosity ratios up to 100 to conduct a realistic numerical study of drop formation and its dynamics. The present work uses a dual distribution technique wherein one distribution function is used for the flow-field, which captures the pressure and velocity, and the other distribution function is used for the interface tracking by solving the conservative Allen-Cahn equation to study dripping regime and droplet pinch-off.
- Subject areas: Computational Physics, discrete Boltzmann equation, multiphase flow.
The pinch-off dynamics of a drop from a leaky faucet have received significant attention of researchers in the last few decades owing to the complex but fascinating physics involved with it. The scaling laws are proposed to characterize the thinning of the neck based on forces balance (inertia, capillary, and viscous forces) for Newtonian fluids. It was found that the neck thinning follows a 2/3 scaling law initially, where the flow is dominated by inertia-capillary balance followed by a linear scaling law where flow is controlled by viscous-inertia-capillary balance. Accurately underpinning the physics of multiphase flow problems which involve significant topological changes using numerical methods is a challenging task. In the continuum regime, researchers have used methods such as Volume-of-Fluid Method, Level-Set Method, and Phase-Field Method to numerically handle such complex topological changes. The Lattice Boltzmann Method (LBM) is another popular method based on the kinetic theory that uses a mesoscopic approach and has shown robustness in simulating such intricate topological changes. Moreover, LBM is known for its simplicity and efficient computational advantage. This work aims to implement a single-relaxation-time (SRT) phase-field lattice Boltzmann method (PF-LBM) capable of handling density ratios up to 1000 and viscosity ratios up to 100 to conduct a realistic numerical study of drop formation and its dynamics. The present work uses a dual distribution technique wherein one distribution function is used for the flow-field, which captures the pressure and velocity, and the other distribution function is used for the interface tracking by solving the conservative Allen-Cahn equation to study dripping regime and droplet pinch-off.
- Subject areas: Computational Physics, discrete Boltzmann equation, multiphase flow.
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