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In this paper, three-dimensional computations of drop–drop interactions using the lattice Boltzmann method (LBM) are reported. The LBM multiphase flow model employed is evaluated for single drop problems and binary drop interactions. These include the verification of Laplace–Young relation for static drops, drop oscillations, and drop deformation and breakup in simple shear flow. The results are compared with experimental data, analytical solutions and numerical solutions based on other computational methods, as applicable. Satisfactory agreement is shown. Initial studies of drop–drop interactions involving the head-on collisions of drops in quiescent medium and off-center collision of drops in the presence of ambient shear flow are considered. As expected, coalescence outcome is observed for the range of parameters studied.

The lattice Boltzmann method (LBM) has been applied to electrohydrodynamics (EHD) in recent years. In this paper, Shan–Chen (SC) single-component multiphase LBM is developed to study large-density-ratio EHD problems. The deformation/motion of a droplet suspended in a viscous liquid under an applied external electric field is studied with three different electric field models. The three models are leaky dielectric model, perfect dielectric model and constant surface charge model. They are used to investigate the effects of the electric field, electric properties of liquids and electric charges. The leaky dielectric model and the perfect dielectric model are validated by the comparison of LBM results with theoretical analysis and available numerical data. It shows that the SC LBM coupled with these electric field models is able to predict the droplet deformation under an external electric field. When net charges are present on the droplet surface and an electric field is applied, both droplet deformation and motion are reasonably predicted. The current numerical method may be an effective approach to analyze more complex EHD problems.

Originally, the color-gradient model proposed by Rothman and Keller (R–K) was unable to simulate immiscible two-phase flows with different densities. Later, a revised version of the R–K model was proposed by Grunau et al. [D. Grunau, S. Chen and K. Eggert, Phys. Fluids A: Fluid Dyn. 5, 2557 (1993).] and claimed it was able to simulate two-phase flows with high-density contrast. Some studies investigate high-density contrast two-phase flows using this revised R–K model but they are mainly focused on the stationary spherical droplet and bubble cases. Through theoretical analysis of the model, we found that in the recovered Navier–Stokes (N–S) equations which are derived from the R–K model, there are unwanted extra terms. These terms disappear for simulations of two-phase flows with identical densities, so the correct N–S equations are fully recovered. Hence, the R–K model is able to give accurate results for flows with identical densities. However, the unwanted terms may affect the accuracy of simulations significantly when the densities of the two fluids are different. For the simulations of spherical bubbles and droplets immersed in another fluid (where the densities of the two fluids are different), the extra terms may not be important and hence, in terms of surface tension, accurate results can be obtained. However, generally speaking, the unwanted term may be significant in many flows and the R–K model is unable to obtain the correct results due to the effect of the extra terms. Through numerical simulations of parallel two-phase flows in a channel, we confirm that the R–K model is not appropriate for general two-phase flows with different densities. A scheme to eliminate the unwanted terms is also proposed and the scheme works well for cases of density ratios less than 10.

In this paper, a thermodynamically consistent phase-field model is employed to simulate the thermocapillary migration of a droplet. The model equations consist of a general Navier–Stokes equation for the two-phase flows, a Cahn–Hilliard equation for the diffuse interface, and a heat equation, and meanwhile satisfy the balance laws of mass, energy and entropy. In particular, the total energy of the system includes kinetic energy, potential energy and internal energy, which leads to a highly coupled and nonlinear equation system. We therefore develop a linear mass and energy conserving, semi-decoupled numerical method for the numerical simulations. As the model contains a heat (energy) equation, a simple error term introduced by the temporal discretization of the momentum equation can be absorbed into the heat equation, such that the numerical solutions satisfy the conservation laws of mass and energy exactly at the temporal discrete level. Several numerical tests are carried out to validate our numerical method.

This study reports the results of the characterization of an air-water two-phase experimental apparatus and the preliminary analyses of the experimental time series. The test section of the apparatus consists of a vertical pipe equipped with an impedance void fraction sensor. The carrying frequency of the impedance sensor has been chosen in order to operate it as a resistive sensor. The calibration of the sensor has been performed through comparison of the instantaneous two-phase mixture conductivity signal and the local actual dimension of the bubble as estimated from high resolution photograph. The calibration curve allows, therefore, reliable estimation of the void fraction time series.

A preliminary analysis of the time series has been performed both in time and frequency domains, evaluating also the time series autocorrelation. These analyses have pointed out the inadequacy of linear tools for the characterization of two-phase flow dynamics, which are nonetheless characterized by strong recurrence and autocorrelation, which need to be further exploited by mean of nonlinear analysis in phase space. Phase space representation of different typical flow patterns, corresponding to a succession of bifurcation, shows the high potential of nonlinear analytical tools, to be adopted in order to exploit the system dynamics.

This paper presents a direct numerical simulation of particle sedimentation in two-phase flow with thermal convection. The sedimentation processes of elliptical particles are investigated in three different scenarios with isotherm, hot, and cold Newtonian fluids. We demonstrate that different particle shapes and orientations can result in quite different flow behaviors. Some interesting results have been obtained, which are very helpful for better understanding of the particle sedimentation processes.

The comparative study on seven equation models with two different six equations model for compressible two-phase flow analysis is proposed. The seven equations model is derived for compressible two-phase flow that is in the nonconservation form. In the present work, two different six equations model are derived for two pressures, two velocities and single temperature with the derivation of the equation of state. The closing equation for one of the six equations model is energy conservation equation while another one is closed by entropy balance equation. The partial differential form of governing equations is hyperbolic and written in the conservative form. At this point, the set of governing equations are derived based on the principle of extended thermodynamics. The method of solving single temperature from both six equation models are simple and direct solution can be obtained. Numerical simulation has been tried using one of the six equation models for air–water shock tube problems. Explicit fourth order Runge–Kutta scheme is used with Finite Volume Shock Capturing method for solving the governing equations numerically. The pressure, velocity and volume fraction variations are captured along the shock tube length through flow solver. Experimental work is carried out to magnify the initial stage of liquid injection into a gas. The outcome of six equations model for compressible two-phase flow has revealed the multi-phase flow characteristics that are similar to the actual conditions.