Deformation Of Single Droplet Research Articles

A second-order phase field-lattice Boltzmann model with equation of state inputting for two-phase flow containing soluble surfactants

In this paper, we propose a phase field-lattice Boltzmann (LB) model with an equation of state (EOS) inputting for two-phase flow containing soluble surfactants. In this model, both the order parameter for the phase field and the surfactant concentration are described by second-order partial differential equations, along with Navier–Stokes equations for the flow field. Changes in surfactant concentration do not affect the order parameter distribution; hence, an unwanted sharpening effect cannot arise. Most importantly, in the existing models, the EOS of surface tension is determined by posterior simulation tests instead of being directly set as an input parameter before the simulations. Hence, it is difficult to determine the model parameters in practical applications. To address this issue, we systematically develop a fully analytical EOS for surface tension based on the Gibbs–Duhem equation. Subsequently, an approximate explicit form for EOS is provided by utilizing the Jacobi–Gauss quadrature rule. Furthermore, a multiple-relaxation-time LB scheme is utilized to numerically solve the governing equations of three physical fields. Two benchmark examples are simulated to validate the accuracy of the present model. The consistency between the numerical results and the analytical EOS is verified. Moreover, the dynamics of droplets with surfactant in simple shear flow is investigated, unveiling the profound impact of various factors, such as surfactant bulk concentration, capillary number, and viscosity ratio, on single droplet deformation and two equal-sized droplets interaction. A detailed exploration of the fluid mechanism involved in two-phase flow with soluble surfactants is presented.

Modeling of droplet dynamics with soluble surfactant by multi-relaxation-time phase-field lattice Boltzmann method

The multiphase fluid system in the presence of surfactant is frequently encountered in numerous scientific and engineering applications. Developing a model for accurately simulating such a complex system is of great significance. In this work, we propose a multi-relaxation-time phase-field lattice Boltzmann model for simulating droplet dynamics with soluble surfactants. The accuracy and validity of the model are verified by benchmark cases including static droplet and Rayleigh–Taylor instability tests. The effects of surfactant, capillary number, and density ratio on single-droplet deformation and two-droplet interaction under shear flow are investigated. Simulation results indicate that the Marangoni stress generated by the inhomogeneous distribution of surfactant at the interface plays the role of promoting droplet deformation and hindering droplet coalescence. Within the studied range, it tends to be much easier for droplets to deform with the decrease in density ratio. The increase in the capillary number and surfactant concentration is conducive to promoting the deformation and breakup of droplets. In addition, a higher surfactant concentration is found to result in greater liquid film thickness between droplets, which would hinder the coalescence of the droplets.

Numerical investigation on the characteristics of single droplet deformation in the airflow at different temperatures

Micro-sized droplets in air may impact aircraft wings and induce severe ice accretion. The deformation and acceleration of a single droplet in a continuous airflow are simulated using the multiphase lattice Boltzmann flux solver to compute the flow field, and the phase-field method is used to track the droplet–air interface. The effects of droplet size, airflow velocity, and ambient temperature on the morphological evolution, flow field structure, and droplet motion are analyzed. The results indicate that the deformation of the droplet increases with Weber number, which distinguishes different deformation modes. With the increase in the droplet size and airflow velocity, the deformation of the droplet becomes greater in less time, and the characteristic alternate compressions in the axial and radial directions disappear. Moreover, different subzero temperatures have little effect on the droplet acceleration despite a different deformation amplitude, while the droplet acceleration is attenuated at normal temperatures.

Numerical study on droplet deformation in periodic pulsatile shear flow and effects of inertia

Abstract Single droplet deformation in pulsatile shear flow is numerically studied by using meso-scopic dissipative particle dynamics method. Numerical model and simulation method are fully validated with three typical cases in which transient flow behaviors are well captured. Cases in quasi-Stokes regime are first investigated with flow Reynolds number to be less than O ( 1 0 − 2 ) . In early stage, droplet deforms gradually in the manner of periodic oscillation but irreversible. Later, droplet deformation gets into a stable state of oscillation and becomes reversible. The mean deformation parameter in stable state is frequency independent and its relationship to mean Capillary number is close to the trend in steady shear. Cases with finite inertia are studied with flow Reynolds number to be approximately to 1. In contrast, the inertial effects make the mean deformation parameters have a strong frequency dependence. The shear and relax tests are conducted to explain above dynamic behavior of droplet deformation. It is found that the droplet deformations in shear and relax are antisymmetric in quasi-Stokes regime while in finite inertia regime droplet deforms slower in shear process than it is in relax process. The frequency dependent behavior of droplet in pulsatile shear might provide a reliable strategy in the control of droplet deformation.

An improved phase-field-based lattice Boltzmann model for droplet dynamics with soluble surfactant

We present an improved phase-field model in the lattice Boltzmann scheme to investigate the droplet dynamics in the presence of soluble surfactant. The phase-field model based on the Ginzburg–Landau free energy is developed in which the immiscible binary fluid interfacial profile is independent of the surfactant concentration. The improved model is validated and then employed to study the surfactant effect on single droplet deformation, two droplets interactions and interactions among four droplets in the shear flow. The results show that the increase of surfactant concentration promotes droplet deformation, droplet breakup and more complex droplet-droplet interaction compared to the clean droplet. Moreover, the effects of capillary number, viscosity ratio, as well as peclet number on the behavior of surfactant-covered droplets in the shear flow are investigated. The results indicate that the droplet Taylor deformation parameter increases with the increase of capillary number but the decrease of viscosity ratio. The minimum distance between two interacting droplets enlarges with both capillary number and peclet number.

Effect of surfactants on the deformation of single droplet in shear flow studied by dissipative particle dynamics

ABSTRACTThe behaviour of a single droplet in shear flow is a fundamental problem in immiscible liquid–liquid multiphase fluid systems. In this article, the deformation and inclination angle of single droplet covered with surfactants in shear flow at moderate Reynolds number, when both the inertial effects and interfacial tension are the key governing factors, were simulated by dissipative particle dynamics (DPD). Weber number We was adopted to indicate the force state of the droplet and a linear relationship between the deformation parameter D and We was found when Reynolds number Re is about 1–10, which is similar to the relation of D and Capillary number Ca when Re ≪ 1. When the surfactant concentration is lower than the critical micelle concentration (CMC), the distribution of surfactants, the droplet inclination angle θ and the droplet deformation parameter D were investigated at different surfactant density at interface ds and shear rate . When the droplet size is close to the characteristic size of surfactant molecules, phase interfaces of water in oil (W/O) and oil in water (O/W) systems have different microstructures, which result in differences in the surfactant distribution, the droplet inclination angle and deformation of the two systems.

Numerical simulation of deformation behavior of droplet in gas under the electric field and flow field coupling

ABSTRACTThe water droplets in the process of electrostatic coalescence are important when studying electrohydrodynamics. In the present study, the electric field and flow field are coupled through the phase field method based on the Cahn–Hilliard formulation. A numerical simulation model of single droplet deformation under the coupling field was established. It simulated the deformation behavior of the movement of a droplet in the continuous phase and took the impact of droplet deformation into consideration which is affected by two-phase flow velocity, electric field strength, the droplet diameter, and the interfacial tension. The results indicated that under the single action of the flow field, when the flow velocity was lower, the droplet diameter was greater as was the droplet deformation degree. When the flow velocity was increased, the droplet deformation degree of a small-diameter droplet was at its maximum size, the large-diameter droplet had a smaller deformation degree, and the middle-diameter droplet was at a minimum deformation degree. When the flow velocity was further increased, the droplet diameter was smaller, and the droplet deformation degree was greater. Under the coupled effect of the electric field and flow field, the two-phase flow velocity and the electric field strength were greater, and the degree of droplet deformation was greater. While the droplet diameter and interfacial tension were smaller, the degree of droplet deformation was greater. Droplet deformation degree increased along with the two-phase flow velocity. The research results provided a theoretical basis for gas–liquid separation with electrostatic coalescence technology.

Motion and deformation of immiscible droplet in plane Poiseuille flow at low Reynolds number

Droplet migration in plane Poiseuille flow is numerically investigated with a dissipative particle dynamics method. The single droplet deformation in the channel flow is first studied to verify the current method and the physical model. The effect of the viscosity ratio between the droplet and the solvent and the effect of the confinement are systematically investigated. The droplet is in an off-centerline equilibrium position with a specific selection of the parameters. A large viscosity ratio makes the droplet locate in a near-wall equilibrium position, and a large capillary number makes the droplet migrate to the near-centerline region of the channel. For the droplet migration at the same Capillary number, there is a critical width of the channel, which is less than twice of the droplet diameter, and the droplet will only migrate to the channel centerline if the width is less than this critical value.

Experimental validation of a lumped model of single droplet deformation, oscillation and detachment on the GDL surface of a PEM fuel cell

Proton Exchange Membrane Fuel Cell (PEMFC) performance significantly depends on electrodes water content. Liquid water emerging from the Gas Diffusion Layer (GDL) micro-channels can form droplets, films or slugs in the Gas Flow Channel (GFC). In the regime of droplets formation, the interaction with the gas flow leads to an oscillating mechanisms that is fundamental to study the detachment from the GDL surface. In this work, a numerical model of a droplet growing on the GDL surface is developed to describe the interaction between droplet and gas flow. Therefore, a lumped force balance is enforced to determine the center of mass motion law. Oscillation frequencies during growth and at detachment are found as a function of droplet size. The model is also exploited to find the relationship between droplet critical detachment size and gas velocity. The numerical results are compared with the experimental data previously published by the authors as well as with other experimental results available in the literature. The matching between the numerical and experimental data is very good. The low computational burden and the conciseness of the proposed approach make the model suitable for applications such as control and optimization strategies development to enhance PEMFC performance. Additionally, the model can be exploited to implement monitoring and diagnostic algorithm as well.

Effects of Inertia and Viscosity on Single Droplet Deformation in Confined Shear Flow

AbstractLattice Boltzmann simulations based on the Cahn-Hilliard diffuse interface approach are performed for droplet dynamics in viscous fluid under shear flow, where the degree of confinement between two parallel walls can play an important role. The effects of viscosity ratio, capillary number, Reynolds number, and confinement ratio on droplet deformation and break-up in moderately and highly confined shear flows are investigated.

Research on Plasma Spray Particle Impact Matrix Process Simulation

Plasma spraying rapid making of functionally graded mold is an effective preparation method. In this paper, finite element method simulation of the plasma spray process a single droplet deformation and matrix effects in the process. Studies have shown that: speed large solidification time is short, more conducive to the formation of the coating; speed large residual thermal stress is small; preheat temperatures are high, the particle flattening effect, The research results will provide theoretic basis for improving spraying coating quality.

Inertial theories for dilute viscoelastic polymer blends with a volume preserving microstructure

The rheology, microstructure, and non-Newtonian fluid mechanics of dilute immiscible polymer blends are investigated. To derive thermodynamically consistent flow equations for these materials, the Hamiltonian framework of non-equilibrium Thermodynamics is adopted. For a given set of non-equilibrium variables, this formalism allows to derive a set of local rate equations from a Poisson bracket, a dissipation bracket, and a Hamiltonian functional. Flow equations for polymer blends with inertia are developed and the theory is reduced to a set of flow equations without inertia. Furthermore, the viscosity coefficients of the non-inertial theory (coarser level of description) are expressed in terms of the viscosity coefficients of the inertial theory (finer level of description). It is shown that non-equilibrium Thermodynamics allows to derive local rate equations for materials as complex as polymer blends and that non-equilibrium Thermodynamics allows to coarse or fine grain between several levels of description. Finally, it is explained how the flow equations derived herein can be applied to describe polymer blend flow and single droplet deformation in flow geometries which are so small to influence the microstructural dynamics and in particular the droplet dynamics in polymer blends.

Lattice Boltzmann simulations of three-dimensional single droplet deformation and breakup under simple shear flow

We present three-dimensional numerical simulations of the classical Taylor experiment on droplet deformation within a shear flow. We have used the promising lattice Boltzmann method numerical scheme to simulate single droplet deformation and breakup under simple shear flow. We first compute the deformation of the droplet, and find excellent agreement with the theoretical prediction. We have used the same method to simulate the shear and breakup for larger values of the shear rate. We find that the lattice Boltzmann method used in conjunction with the interface force model of Shan and Chen [Phys. Rev. E 47, 1815 (1993); 49, 2941 (1994)] results in an excellent treatment of the entire process from small deformation to breakup into multiple droplets. Our results could be extended to study the rheology of dispersed droplets and the dynamics of droplet breakup and coalescence in shear flow.