Lattice Boltzmann simulation of the dispersion of aggregated particles under shear flows

The lattice Boltzmann method (LBM) for multicomponent immiscible fluids is applied to simulations of the deformation and breakup of a particle-cluster aggregate in shear flows. In the simulations, the solid particle is modeled by a droplet with strong interfacial tension and large viscosity. The van der Waals attraction force is taken into account for the interaction between the particles. The ratio of the hydrodynamic drag force to cohesive force, I, is introduced, and the effect of I on the aggregate deformation and breakup in shear flows is investigated. It is found that the aggregate is easier to deform and to be dispersed when I is over 100.     

Emulsion droplet deformation and breakup with Lattice Boltzmann model

In this paper we have performed an extensive study of the effects of various dimensionless numerical parameters used in the Lattice Boltzmann implementation of the diffuse interface model describing deformation and breakup of an emulsion droplet in 2D. Such an extensive study on these parameter is absent in scientific literature of diffuse interface models. We have found that parameters like the dimensionless interface thickness and the Peclet number have to be within certain ranges for correct physical behavior. Outside these ranges droplets either dissolve, show incorrect Laplace pressures, or do not deform to stable shapes at subcritical capillary numbers. Furthermore, we have found that droplet breakup is sensitive to these parameters.     

Decidable and undecidable logics with a binary modality

We give an overview of decidability results for modal logics having a binary modality. We put an emphasis on the demonstration of proof-techniques, and hope that this will also help in finding the borderlines between decidable and undecidable fragments of usual first-order logic.Research supported by the Hungarian National Foundation for Scientific Research grants no. T16448, F17452, T7255. Research of the first author is also supported by a grant of Logic Graduate School of Eötvös Loránd University Budapest     

Analysis of single droplet dynamics on striped surface domains using a lattice Boltzmann method

In this paper, the behavior of a micron-scale fluid droplet on a heterogeneous surface is investigated using a two-phase lattice Boltzmann method (LBM). The two-phase LBM permits the simulation of the time dependent three-dimensional motion of a liquid droplet on solid surface patterned with hydrophobic and hydrophilic strips. A nearest-neighbor molecular interaction force is used to model the adhesive forces between the fluid and solid walls. The solid heterogeneous wall is a uniform hydrophilic substrate painted with hydrophobic strips. The model is validated by demonstrating the consistency of the simulation results with an exact solution for capillary rise and through qualitative comparison of computed dynamic contact line behavior with experimentally measured surface properties and observed surface shapes of a droplet on a heterogeneous surface. The dependence of spreading behavior on wettability, the width of hydrophobic strip, initial location of the droplet relative to the strips, and gravity is investigated. A decrease in contact angle of the liquid on a hydrophilic surface may lead to breakup of the droplet for certain substrate patterns. The simulations suggest that the present lattice Boltzmann (LB) model can be used as a reliable way to study fluidic control on heterogeneous surfaces and other wetting related subjects.     

Better than $l/Mflops sustained: a scalable PC-based parallel computer for lattice QCD

We study the feasibility of a PC-based parallel computer for medium to large scale lattice QCD simulations. The Eötvös Univ., Inst. Theor. Phys. cluster consists of 137 Intel P4-1.7GHz nodes with 512 MB RDRAM. The 32-bit, single precision sustained performance for dynamical QCD without communication is 1510 Mflops/node with Wilson and 970 Mflops/node with staggered fermions. This gives a total performance of 208 Gflops for Wilson and 133 Gflops for staggered QCD, respectively (for 64-bit applications the performance is approximately halved). The novel feature of our system is its communication architecture. In order to have a scalable, cost-effective machine we use Gigabit Ethernet cards for nearest-neighbor communications in a two-dimensional mesh. This type of communication is cost effective (only 30% of the hardware costs is spent on the communication). According to our benchmark measurements this type of communication results in around 40% communication time fraction for lattices upto 48³·96 in full QCD simulations. The price/sustained-performance ratio for full QCD is better than $l/Mflops for Wilson (and around $1.5/Mflops for staggered) quarks for practically any lattice size, which can fit in our parallel computer. The communication software is freely available upon request for non-profit organizations.     

Bistability in the hydrodynamic resistance of a drop trapped at a microcavity junction

We investigate the flow resistance of a droplet trapped at a constriction in a microcavity located at a microchannel bifurcation as a function of system parameters including capillary number, drop confinement, and viscosity ratio. Using a combination of experiments and volume-of-fluid numerical simulations, we measure the hydrodynamic resistance of the trapped drop and connect it to drop deformation in the microcavity. For drop sizes smaller than the microcavity, we observe a bistable behavior in terms of the resistance of the trapped drop as a function of capillary number. For these underfilled drops, we find that the resistance is low at small capillary number (Ca < 10^?3) and jumps to high resistance at a threshold capillary number. For drops equal to the microcavity size, we observe that the bistability vanishes and the drop resistance is of similar magnitude as that of underfilled drops at large capillary number. To explain these findings, we use confocal microscopy and simulations to obtain three-dimensional views of the drop deformation and continuous phase fluid in the microcavity. We observe that the low resistance is due to negligible drop deformation and unobstructed flow of continuous phase through the constriction. The high resistance is due to the drop interface protruding into the constriction restricting the flow of continuous phase through the gutters. Taken together, our results indicate that a trapped drop at a bifurcation can act as a nonlinear resistor and could be potentially used as a soft switch to control droplet trajectories in microfluidic devices.     

Droplet impingement and breakup on a dry surface

In this work, new results of droplet impingement and breakup have been obtained using three-dimensional lattice Boltzmann method. All four phases after impingement, the kinematic, spreading, relaxation and equilibrium phases, leading to breakup have been obtained for a range of Weber number, Reynolds number and density ratio. Conditions have been chosen such that for comparison with available data in the literature. The maximum spread factor compares well with experiments as well as the theoretical value of 0.5 Re^0.25. At Oh < 0.15 and Capillary number, Ca < 1.0, the relaxation phase is marked by the presence of strong oscillations in the spreading diameter. An analytical solution for breakup based on the conservation of energy is provided. Criteria for three-dimensional droplet breakup have been developed as functions of Re and We.     

Numerical prediction of three-dimensional time-dependent viscoelastic extrudate swell using differential and algebraic models

The dynamic behavior of a droplet on a solid surface is simulated by the lattice Boltzmann method (LBM) for two-phase fluids with large density differences; the wetting boundary condition on solid walls is incorporated in this simulation. By using the method, the dynamic behavior of a droplet impinging on a horizontal wall is investigated in terms of various Weber numbers. The dynamic contact angle, the contact line velocity, and the wet length are calculated, and found to be in good agreement with available experimental data. In addition, the method is applied to simulations of the collision of a falling droplet with a stationary droplet on a solid surface. The behavior of the droplets and the mixing process during their collision are simulated in terms of various impact velocities and several static contact angles on the solid surface. It is seen that mixing occurs around the rim of the coalescent droplet due to the circular flows. Also, the relationship between the mixing rate of the primary coalescent droplet and Weber number is investigated.     

Numerical modeling of multiphase flows in microfluidics and micro process engineering: a review of methods and applications

This article presents a comprehensive review of numerical methods and models for interface resolving simulations of multiphase flows in microfluidics and micro process engineering. The focus of the paper is on continuum methods where it covers the three common approaches in the sharp interface limit, namely the volume-of-fluid method with interface reconstruction, the level set method and the front tracking method, as well as methods with finite interface thickness such as color-function based methods and the phase-field method. Variants of the mesoscopic lattice Boltzmann method for two-fluid flows are also discussed, as well as various hybrid approaches. The mathematical foundation of each method is given and its specific advantages and limitations are highlighted. For continuum methods, the coupling of the interface evolution equation with the single-field Navier–Stokes equations and related issues are discussed. Methods and models for surface tension forces, contact lines, heat and mass transfer and phase change are presented. In the second part of this article applications of the methods in microfluidics and micro process engineering are reviewed, including flow hydrodynamics (separated and segmented flow, bubble and drop formation, breakup and coalescence), heat and mass transfer (with and without chemical reactions), mixing and dispersion, Marangoni flows and surfactants, and boiling.     

A Long-step barrier method for convex quadratic programming

In this paper we propose a long-step logarithmic barrier function method for convex quadratic programming with linear equality constraints. After a reduction of the barrier parameter, a series of long steps along projected Newton directions are taken until the iterate is in the vicinity of the center associated with the current value of the barrier parameter. We prove that the total number of iterations isO(nL) orO(nL), depending on how the barrier parameter is updated.On leave from Eötvös University, Budapest and partially supported by OTKA 2116.     

Critical conditions and breakup of non-squashed microconfined droplets: effects of fluid viscoelasticity

Droplet breakup in systems with either a viscoelastic matrix or a viscoelastic droplet is studied microscopically in bulk and confined shear flow, using a parallel plate counter rotating shear flow cell. The ratio of droplet diameter to gap spacing is systematically varied between 0.1 and 0.85. In bulk shear flow, the effects of matrix and droplet viscoelasticity on the critical capillary number for breakup are very moderate under the studied conditions. However, in confined conditions a profoundly different behaviour is observed: the critical capillary numbers of a viscoelastic droplet are similar to those of a Newtonian droplet, whereas matrix viscoelasticity causes breakup at a much lower capillary number. The critical capillary numbers are compared with the predictions of a phenomenological model by Minale et al. (Langmuir 26:126–132, 2010); the model results are in qualitative disagreement with the experimental data. It is also found that the critical dimensionless droplet length, the critical capillary number, and the dimensionless droplet length at breakup show a similar dependency on confinement ratio. As a result, confined droplets in a viscoelastic matrix have a smaller dimensionless length at breakup than droplets in a Newtonian matrix, which affects the breakup mode. Whereas confined droplets in a Newtonian matrix can break up into multiple parts, only two daughter droplets are obtained after breakup in a viscoelastic matrix, up to very large confinement ratios.     

Lattice Boltzmann simulations of the motion induced by variable surface tension

Methods for implementing variable surface tension in the multiphase Lattice Boltzmann model with the color model and Shan-Chen scheme are tested by analyzing the models’ abilities to reproduce a theoretical result by Levich and Kuznetzov. If the surface tension around a droplet is asymmetrical, the droplet moves towards the side where the surface tension is lower. The droplet’s velocity is proportional to the surface tension gradient, the droplet’s radius, and the inverse of the viscosity. The model is tested to determine whether the simulated droplets move in the manner predicted by theory. Although the discreteness of the underlying lattice causes a spurious oscillation to the velocity, the numerical results concerning the average velocity show a good correspondence between theory and the model in regards to the surface tension gradient and droplet size. The color model also produces good simulations in the scenarios with different viscosities, while the diffusive properties and unknown relationships between the parameters and surface tension in the Shan-Chen model make the numerical results of that model more dubious, even though several of the results are qualitatively in agreement.     

Lattice Boltzmann modeling of microchannel flows in the transition flow regime

Owing to its kinetic nature and distinctive computational features, the lattice Boltzmann method for simulating rarefied gas flows has attracted significant research interest in recent years. In this article, a lattice Boltzmann (LB) model is presented to study microchannel flows in the transition flow regime, which have gained much attention because of fundamental scientific issues and technological applications in various micro-electro-mechanical system (MEMS) devices. In the model, a Bosanquet-type effective viscosity is used to account for the rarefaction effect on gas viscosity. To match the introduced effective viscosity and to gain an accurate simulation, a modified second-order slip boundary condition with a new set of slip coefficients is proposed. Numerical investigations demonstrate that the results, including the velocity profile, the non-linear pressure distribution along the channel, and the mass flow rate, are in good agreement with the solution of the linearized Boltzmann equation, the direct simulation Monte Carlo (DSMC) results, and the experimental results over a broad range of Knudsen numbers. It is shown that taking the rarefaction effect on gas viscosity into consideration and employing an appropriate slip boundary condition can lead to a significant improvement in the modeling of rarefied gas flows with moderate Knudsen numbers in the transition flow regime.     

Inkjet droplet deposition dynamics into square microcavities for OLEDs manufacturing

The dynamics of inkjet deposition in square microcavities are investigated utilizing a three-dimensional multi-relaxation-time pseudopotential lattice Boltzmann (LB) model with large density ratios. A geometric scheme is considered within the pseudopotential LBM framework to obtain the desired contact angles. The effects of wettability, density ratios, droplet viscosity and impact velocity are explored to reveal the droplet–microcavity interactions. With the contact angles of microcavity increasing, the physical outcomes including the crown-like shape with a small round dot, circular hollow core, uniform film and convex film are identified and analyzed. At a lower density ratio ρ_r?=?11.6, the surrounding denser gas resists the droplet recoiling flow resulting in an increasing hollow core. The appropriate higher droplet viscosity and decreasing impact velocity are preferred which could eliminate the hollow core in the recoiling phase and accelerate the inkjet deposition process straightforward. The revelation of droplet-microcavity dynamics is beneficial for optimizing inkjet deposition process and fabricating uniform OLEDs panels.     

Numerical simulation of coalescence and breakup of rising droplets

Rising droplets with coalescence and breakup are numerically simulated using the lattice BGK method. It is shown for single droplet that the rising velocities are in good agreement with those obtained by two types of empirical correlations. The coalescence of droplets is shown when two droplets are placed vertically in line at different elevations. The breakup of droplet is observed in some cases after the coalescence. It is found that the breakup of coalesced droplet occurs when the Weber number at the coalescence exceeds a critical value, and the critical Weber number agrees well with that given by the empirical correlation.     

A Finite-volume/Boundary-element Method for Flow Past Interfaces in the Presence of Surfactants, with Application to Shear Flow Past a Viscous Drop

A finite-volume method is developed for solving the convection-diffusion equation governing the transport of an insoluble surfactant over a generally evolving fluid interface, using an unstructured triangular grid. The unstructured grid has significant advantages compared with a structured grid based on global curvilinear coordinates, concerning adaptability and ability to conserve the total amount of the surfactant. The finite-volume method is combined with a boundary-element method for Stokes flow to yield an integrated procedure that is capable of describing the evolution of an interface from a specified initial state. Several series of simulations of the deformation of a neutrally buoyant viscous drop suspended in an infinite simple shear flow, or a semi-infinite shear flow bounded by a plane wall are performed. The results for the infinite flow extend those presented previously for the particular case where the ratio of the drop viscosity to the ambient fluid viscosity, λ, is equal to unity. It is shown that the effect of surfactant transport on the drop deformation and on the effective rheological properties of a dilute suspension becomes increasingly more important as λ becomes smaller and the drop reduces to an inviscid bubble. For semi-infinite flow past a drop above a plane wall, it is found that interfacial stresses due to variations in surface tension facilitate the drop migration away from the wall.     

Droplet generation in a microchannel with a controllable deformable wall

We report the droplet generation behavior of a microfluidic droplet generator with a controllable deformable membrane wall using experiments and analytical model. The confinement at the droplet generation junction is controlled by using external pressure, which acts on the membrane, to generate droplets smaller than junction size (with other parameters fixed) and stable and monodispersed droplets even at higher capillary numbers. A non-dimensional parameter, i.e., controlling parameter K _p, is used to represent the membrane deformation characteristics due to the external pressure. We investigate the effect of the controlled membrane deformation (in terms of K _p), viscosity ratio λ and flow rate ratio r on the droplet size and mobility. A correlation is developed to predict droplet size in the controllable deformable microchannel in terms of the controlling parameter K _p, viscosity ratio λ and flow rate ratio r. Due to the deflection of the membrane wall, we demonstrate that the transition from the stable dripping regime to the unstable jetting regime is delayed to a higher capillary number Ca (as compared to rigid droplet generators), thus pushing the high throughput limit. The droplet generator also enables generation of droplets of sizes smaller than the junction size by adjusting the controlling parameter.     

Inertia effect on the transient deformation of elastic capsules in simple shear flow

The transient deformation of cylindrical liquid-filled capsules with elastic membranes is studied in simple shear flow at small and moderate Reynolds numbers. The aim of the study is to investigate the inertia effect on the deformation of elastic capsules and the flow structure around them. The simulation is based on a hybrid method which introduces the immersed boundary concept in the framework of the multi-block lattice Boltzmann model. The deformation of capsules with circular and elliptical resting shapes is studied; the membrane constitutive model is Hooke’s law. However, the present model can be implemented to capsules with arbitrary resting configurations and constitutive laws. The simulation results show that inertia has important effect on the transient deformation process, steady configuration and tank treading frequency of a capsule in simple shear flow; Inertia also significantly affects the flow structure and vorticity field around and inside a capsule.     

Application of lattice Boltzmann method in free surface flow simulation of micro injection molding

The filling flow in micro injection molding was simulated by using the lattice Boltzmann method (LBM). A tracking algorithm for free surface to handle the complex interaction between gas and liquid phases in LBM was used for the free surface advancement. The temperature field in the filling flow is also analyzed by combining the thermal lattice Boltzmann model and the free surface method. To simulate the fluid flow of polymer melt with a high Prandtl number and high viscosity, a modified lattice Boltzmann scheme was adopted by introducing a free parameter in the thermal diffusion equation to overcome the restriction of the thermal relaxation time. The filling flow simulation of micro injection molding was successfully performed in the study.     

液丝破裂的研究进展和展望

总结有关液丝破裂研究的实验工作,分析Weber数、流体粘度及初始扰动对液丝破裂的影响。简要介绍牛顿流体和非牛顿流体的一维、二维数学模型,并指出该研究的实际应用和展望。一维模型在最近几年被广泛使用,极大地增强了人们对液滴形成过程中界面破裂的理解,但不能同时得到精确的宏观特征和微观特征;三维模型的计算量庞大。为了研究的可行性和结果的精确性,应对二维模型进行更多研究。