An Efficient Hybrid Incompressible SPH Solver with Interface Handling for Boundary Conditions

We propose a hybrid smoothed particle hydrodynamics solver for efficientlysimulating incompressible fluids using an interface handling method for boundary conditions in the pressure Poisson equation. We blend particle density computed with one smooth and one spiky kernel to improve the robustness against both fluid–fluid and fluid–solid collisions. To further improve the robustness and efficiency, we present a new interface handling method consisting of two components: free surface handling for Dirichlet boundary conditions and solid boundary handling for Neumann boundary conditions. Our free surface handling appropriately determines particles for Dirichlet boundary conditions using Jacobi‐based pressure prediction while our solid boundary handling introduces a new term to ensure the solvability of the linear system. We demonstrate that our method outperforms the state‐of‐the‐art particle‐based fluid solvers.     

固体入水的边界压力处理及表面粒子位置的修正

基于传统光滑粒子流体动力学(SPH)方法的边界力法、虚粒子法或耦合力法处理固体入水时,流体与固体交互界面的粒子密度不连续、压力不稳定、固体边界处会发生部分流体粒子穿透或分离等现象,而流体表面因为受到力的作用,表面破碎后,液面较粗糙.针对上述问题,结合边界力和虚粒子的优点,对耦合力法进行改进,处理运动固体边界,阻止流体粒...     

Boundary geometric control of a linear Stefan problem

This paper addresses the geometric control of the position of a liquid–solid interface in a melting process of a material known as Stefan problem. The system model is hybrid, i.e. the dynamical behavior of the liquid-phase temperature is modeled by a heat equation while the motion of the moving boundary is described by an ordinary differential equation. The control is applied at one boundary as a heat flux and the second moving boundary represents the liquid–solid interface whose position is the controlled variable. The control objective is to ensure a desired position of the liquid–solid interface. The control law is designed using the concept of characteristic index, from geometric control theory, directly issued from the hybrid model without any reduction of the partial differential equation. It is shown by use of Lyapunov stability test that the control law yields an exponentially stable closed-loop system. The performance of the developed control law is evaluated through simulation by considering zinc melting.     

Simulation of floating bodies with the lattice Boltzmann method

This paper is devoted to the simulation of floating rigid bodies in free surface flows. For that, a lattice Boltzmann based model for liquid–gas–solid flows is presented. The approach is built upon previous work for the simulation of liquid–solid particle suspensions on the one hand, and on an interface-capturing technique for liquid–gas free surface flows on the other. The incompressible liquid flow is approximated by a lattice Boltzmann scheme, while the dynamics of the compressible gas are neglected. We show how the particle model and the interface capturing technique can be combined by a novel set of dynamic cell conversion rules. We also evaluate the behaviour of the free surface–particle interaction in simulations. One test case is the rotational stability of non-spherical rigid bodies floating on a plane water surface–a classical hydrostatic problem known from naval architecture. We show the consistency of our method in this kind of flows and obtain convergence towards the ideal solution for the heeling stability of a floating box.     

Liquid bridge instability applied to microfluidics

This paper presents a new way of combining and mixing reagents within one droplet, which may then be used as a microfluidic biochemical reactor. This is made possible by coalescing aqueous droplets on opposing microcapillary tips immersed in density-matched silicone oil. It was found that there are two possible outcomes from a binary capillary-suspended droplet interaction. The droplets may coalesce to form a stable fluid bridge between opposing capillary tips. The droplets may, however, coalesce to form an unstable liquid bridge that quickly ruptures resulting in the two fluid volumes combining into one droplet suspended from a single capillary tip. The stability boundary that determines one outcome or the other was found to be related to a number of variables that describe the equilibrium shape of the liquid bridge interface. Suspending the host droplet from a larger diameter microcapillary dramatically increases the range of volumes that the system can combine by shifting the stability boundary. This ensures the desired effect of pinch-off near the tip of the finer microcapillary thereby dispensing microfluidic samples in one direction.     

Separation of particles using acoustic streaming and radiation forces in an open microfluidic channel

In this study, a method to separate particles, within a small sample, based on size is demonstrated using ultrasonic actuation. This is achieved in a fluid, which has been deposited on a flat surface and is contained by a channel, such that it has a rectangular wetted area. The system utilises acoustic radiation forces (ARFs) and acoustic streaming. The force field generates two types of stable collection locations, a lower one within the liquid suspension medium and an upper one at the liquid–air interface. Acoustic streaming selectively delivers smaller particles from the lower locations to the upper ones. Experimental data demonstrate the ability to separate two sets of polystyrene microparticles, with diameters of 3 and 10 μm, into different stable locations. Methods to reduce migration of larger particles to the free surface are also investigated, thereby maximising the efficiency of the separation. Extraction of one set of 99 % pure particles at the liquid–air interface from the initial particle mixture using a manual pipette is demonstrated here. In addition, computational modelling performed suggests the critical separation size can be tuned by scaling the size of the system to alter which of ARFs and acoustic streaming-induced drag forces is dominant for given particle sizes, therefore presenting an approach to tunable particle separation system based on size.     

An immersed interface method for the Vortex-In-Cell algorithm

The paper presents a two-dimensional immersed interface technique for the Vortex-In-Cell (VIC) method for simulation of flows past bodies of complex geometry. The particle–mesh VIC algorithm is augmented by a local particle–particle correction term in a Particle–Particle Particle–Mesh (P³M) context to resolve sub-grid scales incurred by the presence of the immersed interface. The particle–particle correction furthermore allows to disjoin mesh and particle resolution by explicitly resolving sub-grid scales on the particles. This P³M algorithm uses an influence matrix technique to annihilate the anisotropic sub-grid scales and adds an exact particle–particle correction term. Free-space boundary conditions are satisfied through the use of modified Green’s functions in the solution of the Poisson equation for the streamfunction. The concept is extended such as to provide exact velocity predictions on the mesh with free-space boundary conditions.The random walk technique is employed for the diffusion in order to relax the need for a remeshing of the computational elements close to solid boundaries. A novel partial remeshing technique is introduced which only performs remeshing of the vortex elements which are located sufficiently distant from the immersed interfaces, thus maintaining a sufficient spatial representation of the vorticity field.Convergence of the present P³M algorithm is demonstrated for a circular patch of vorticity. The immersed interface technique is applied to the flow past a circular cylinder at a Reynolds number of 3000 and the convergence of the method is demonstrated by a systematic refinement of the spatial parameters. Finally, the flow past a cactus-like geometry is considered to demonstrate the efficient handling of complex bluff body geometries. The simulations offer an insight into physically interesting flow behavior involving a temporarily negative total drag force on the section.     

On the degree of boundary slip over nonplanar surfaces

The breakdown of the no-slip boundary condition at a fluid–solid interface has been recognized in micro/nanofluidics for many years. However, the relationship between the curvature of the surface and the degree of boundary slip has not been understood sufficiently well. The present study reveals that the degree of slip depends effectively on the surface curvature, which is having an opposing effect over rotating concave and convex surfaces. The results show that as surface curvature increases, the boundary slip becomes negligible over a concave surface, while it becomes increasingly important over a convex surface. In addition, boundary slip formulae are proposed that can accurately predict the boundary slips over convex and concave surfaces. These formulae are found to be in very good agreement with DSMC data for a range of accommodation coefficients and boundary curvatures. The present study then explains the mechanism of the intriguing phenomenon of velocity inversion which has, until the present study, often been mistakenly attributed solely to the effects of boundary curvature.     

Stable and Fast Fluid–Solid Coupling for Incompressible SPH

The solid boundary handling has been a research focus in physically based fluid animation. In this paper, we propose a novel stable and fast particle method to couple predictive–corrective incompressible smoothed particle hydrodynamics and geometric lattice shape matching (LSM), which animates the visually realistic interaction of fluids and deformable solids allowing larger time steps or velocity differences. By combining the boundary particles sampled from solids with a momentum‐conserving velocity‐position correction scheme, our approach can alleviate the particle deficiency issues and prevent the penetration artefacts at the fluid–solid interfaces simultaneously. We further simulate the stable deformation and melting of solid objects coupled to smoothed particle hydrodynamics fluids based on a highly extended LSM model. In order to improve the time performance of each time step, we entirely implement the unified particle framework on GPUs using compute unified device architecture. The advantages of our two‐way fluid–solid coupling method in computer animation are demonstrated via several virtual scenarios.     

Boundary Geometric Control of a Nonlinear Diffusion System with Time‐Dependent Spatial Domain

A Stefan problem represents a distributed parameter system with a time‐dependent spatial domain. This paper addresses the boundary control of the position of the moving liquid–solid interface in the case of nonlinear Stefan problem with Neumann actuation. The main idea consists in deriving an equivalent linear model by means of Cole‐Hopf tangent transformation, i.e. under a certain physical assumption, the original nonlinear Stefan problem is converted to a linear one. Then, the geometric control law is deduced directly from that developed, by the authors of the present paper, for the linear Stefan problem. Based on the fact that the Cole‐Hopf transformation is bijective, it is shown that the developed control law yields a stable closed‐loop system. The performance of the controller is evaluated through numerical simulation in the case of stainless steel melting characterized by a temperature‐dependent thermal conductivity, which is nonlinear. The objective is to control the position of the liquid–solid interface by manipulating a heat flux at the boundary.     

Examination of dendritic growth and microsegregation during solidification of Al–Li binary alloy using the phase-field simulation coupling CALPHAD data

Dendritic growth is one of the most important phenomena during the solidification of alloys. However, solute redistribution on the front of solid-liquid interface may result in nonuniform distribution of concentration between dendrite branches. This often causes microscopic segregation and undermines the properties of materials. In order to control the solidification microstructure of Al–Li alloy, we firstly need to understand in depth the morphological and concentration evolution during dendrite growth. Here, the KKS (S.G. Kim, W.T. Kim, T. Suzuki) phase-field model coupling CALPHAD data is employed. The dependences of the dendrite morphologies and growth kinetics on undercooling or initial solute concentration are qualitatively analyzed. Dendrite growth rate increases slowly when undercooling ΔT is approximately less than 25 °C, and steeply when ΔT>40 °C corresponding to the transition from diffusional dendrite growth into rapid solidification. Accordingly, the obtained morphologies change from dendrite into seaweed crystal. The increase of supersaturation influences dendrite growth similarly in terms of growth rate and morphology. Moreover, through simulation of columnar dendrites growth, we find that the microscopic segregation becomes more severely with decreasing undercooling, or increasing supersaturation. These results demonstrate the capability of the technology---phase-field simulation coupling to CALPHAD in the modelling of microstructure evolution during solidification of alloys.     

Three-dimensional deformation analyses of the ultra-thin liquid film surface (linearized analyses for the steady state)

Long wave theory, which is the time evolution equation for the shape and deformation of thin liquid films and includes surface tension and surface forces such as van der Waals forces, was used to examine steady and three-dimensional deformations of ultra-thin but continuous liquid films. As liquid film deformations caused by gas pressures and shear stresses at the gas–liquid interface are usually very small, the linearized long wave equation, which is obtained for infinitesimal deformations, was employed to predict the steady-state liquid surface deformations produced by gas pressures and shear stresses. As the velocity of the solid increases and the liquid film thickness decreases, the deformation decreases and is nearly constant along solid running direction almost everywhere except at the applied position of the pressure and shearing stresses. The results obtained using the linearized equation agrees well with those obtained using the nonlinear equation and the calculation time is greatly reduced.     

Lattice Boltzmann modeling of dendritic growth in forced and natural convection

A two-dimensional (2D) coupled model is developed for the simulation of dendritic growth during alloy solidification in the presence of forced and natural convection. Instead of conventional continuum-based Navier–Stokes (NS) solvers, the present model adopts a kinetic-based lattice Boltzmann method (LBM), which describes flow dynamics by the evolution of distribution functions of moving pseudo-particles, for the numerical computations of flow dynamics as well as thermal and solutal transport. The dendritic growth is modeled using a solutal equilibrium approach previously proposed by Zhu and Stefanescu (ZS), in which the evolution of the solid/liquid interface is driven by the difference between the local equilibrium composition and the local actual liquid composition. The local equilibrium composition is calculated from the local temperature and curvature. The local temperature and actual liquid composition, controlled by both diffusion and convection, are obtained by solving the LB equations using the lattice Bhatnagar–Gross–Krook (LBGK) scheme. Detailed model validation is performed by comparing the simulations with analytical predictions, which demonstrates the quantitative capability of the proposed model. Furthermore, the convective dendritic growth features predicted by the present model are compared with those obtained from the Zhu–Stefanescu and Navier–Stokes (ZS–NS) model, in which the fluid flow is calculated using an NS solver. It is found that the evolution of the solid fraction of dendritic growth calculated by both models coincides well. However, the present model has the significant advantages of numerical stability and computational efficiency for the simulation of dendritic growth with melt convection.     

改进的流体模拟固体边界处理算法

流体模拟是计算机图形学的一个重要研究分支,流体的固体边界处理一直是流体 模拟的研究重点,光滑粒子流体动力学(SPH)方法中的镜像粒子法是处理固体边界的一个重要方 法。镜像粒子法通过靠近边界的流体粒子在边界外动态生成对应的镜像粒子来处理固体边界问 题,但随着边界复杂程度的提高,传统的镜像粒子法生成镜像粒子的复杂度也随之提高,模拟 效率随之降低。为此,文章对镜像粒子法进行改进,提出一种新的镜像粒子场量求值方法,有 效地降低了复杂边界情况下生成镜像粒子的复杂度,且使靠近边界的流体粒子场量更加均匀。 仿真实验结果表明,随着流体模拟粒子数的增加以及边界复杂程度的提高,该方法比传统镜像 粒子法效率高的优势也更加明显。     

Selective particle and cell clustering at air–liquid interfaces within ultrasonic microfluidic systems

In this study, we demonstrate particle and cell clustering in distinct patterns on the free surface of microfluidic volumes. Employing ultrasonic actuation, submersed microparticles are forced to two principal positions: nodal lines (pressure minima) of a standing wave within the liquid bulk, and distinct locations on the air–liquid interface (free surface); the latter of which has not been previously demonstrated using ultrasonic standing waves. As such, we unravel the fundamental mechanisms behind such patterns, showing that the contribution of fluid particle velocity variations on the free surface (acoustic radiation force) results in patterned particle clustering. In addition, by varying the size and density of the microparticles (3.5–31 μm polystyrene and 1–5 μm silica), acoustic streaming is found to increase the tendency for a smaller and lighter particle to cluster at the air–liquid interface. This selectivity is exploited for the isolation of multiple microparticle and cell types on the free surface from their nodally aligned counterparts. Free surface clustering is demonstrated in both an open microfluidic chamber and a sessile droplet, as well as using a range of biological species Escherichia coli, blood cells, Ragweed pollen and Paper Mulberry pollen). The ability to selectively cluster submersed microparticles and cells in distinct patterns on the free surface showcases the excellent suitability of this method to lab-on-a-chip systems.     

Rotational motion and lateral migration of an elliptical magnetic particle in a microchannel under a uniform magnetic field

We have numerically investigated the motion of an elliptical magnetic particle in a microfluidic channel subjected to an external uniform magnetic field. By using the direct numerical simulation method and an arbitrary Lagrangian–Eulerian technique, the involved particle–fluid-magnetic field problem can be solved in a fully coupled manner. The numerical predictions of the particle trajectory and orientation with and without a uniform magnetic field are in qualitative agreement with the existing experimental results, and numerical results have revealed the impacts of key parameters such as inlet flow velocity, magnetic field direction, and particle shape on the rotational motion and lateral migration of the elliptical particle. Meanwhile, the shape-based particle separation in a low Reynolds number flow with the aid of an applied uniform magnetic field has also been numerically demonstrated.     

Numerical modeling of microscale droplet dispensing in parallel-plate electrowetting-on-dielectric (EWOD) devices with various reservoir designs

Water droplet dispensing in microfluidic parallel-plate electrowetting-on-dielectric (EWOD) devices with various reservoir designs has been numerically studied. The Navier–Stokes equations are solved using a finite-volume formulation with a two-step projection method on a fixed grid. The free surface of the liquid is tracked by a coupled level set and volume-of-fluid method with the surface tension force determined by the continuum surface force model. Contact angle hysteresis which is an indispensible element in EWOD modeling has been implemented. A simplified model is adopted for the viscous stresses exerted by the parallel plates at the solid–liquid interface. Good agreement has been achieved between the numerical results and the corresponding experimental data. The dispensing mechanism has been carefully examined, and droplet volume inconsistency for each design has been investigated. It has been discovered that the pressure distribution on the cutting electrode at the beginning of the cutting stage is of considerable significance for the inconsistency of droplet volumes. Several key elements which directly affect the pressure distribution and volume inconsistency have been identified.     

Numerical investigation of polygonal particle separation in microfluidic channels

We numerically investigate the separation of polygonal particles through an array of solid obstacles in microfluidic devices. Particle–fluid, particle–particle and particle–wall interactions are all considered in our numerical method. Firstly, the separation of circular particles based on size is simulated and the relationship of the migration angle and forcing angle by our simulations is coincided with the experimental results. Then, the simulations of polygon particle separation based on shape are carried out. The results show that the shape of particles can be used for particle separation through an array of solid obstacles. Through reasonable design of the shape of obstacles, separation of polygon particles can be achieved. In addition, the results indicate that our numerical method has the potential to substantially improve the design and optimization of microfluidic devices for the separation of particles.     

Molecular dynamics-based prediction of boundary slip of fluids in nanochannels

Computational modeling and simulation can provide an effective predictive capability for flow properties of the confined fluids in micro/nanoscales. In this paper, considering the boundary slip at the fluid–solid interface, the motion property of fluids confined in parallel-plate nanochannels are investigated to couple the atomistic regime to continuum. The corrected second-order slip boundary condition is used to solve the Navier–Stokes equations for confined fluids. Molecular dynamics simulations for Poiseuille flows are performed to study the influences of the strength of the solid–fluid coupling, the fluid temperature, and the density of the solid wall on the velocity slip at the fluid boundary. For weak solid–fluid coupling strength, high temperature of the confined fluid and high density of the solid wall, the large velocity slip at the fluid boundary can be obviously observed. The effectiveness of the corrected second-order slip boundary condition is demonstrated by comparing the velocity profiles of Poiseuille flows from MD simulations with that from continuum.