Numerical simulations of particle migration in a viscoelastic fluid subjected to Poiseuille flow

In this work we present 2D numerical simulations on the migration of a particle suspended in a viscoelastic fluid under Poiseuille flow. A Giesekus model is chosen as constitutive equation of the suspending liquid. In order to study the sole effect of the fluid viscoelasticity, both fluid and particle inertia are neglected.The governing equations are solved through the finite element method with proper stabilization techniques to get convergent solutions at relatively large flow rates. An Arbitrary Lagrangian–Eulerian (ALE) formulation is adopted to manage the particle motion. The mesh grid is moved along the flow so as to limit particle motion only in the gradient direction to substantially reduce mesh distortion and remeshing.Viscoelasticity of the suspending fluid induces particle cross-streamline migration. Both large Deborah number and shear thinning speed up the migration velocity. When the particle is small compared to the gap (small confinement), the particle migrates towards the channel centerline or the wall depending on its initial position. Above a critical confinement (large particles), the channel centerline is no longer attracting, and the particle is predicted to migrate towards the closest wall when its initial position is not on the channel centerline. As the particle approaches the wall, the translational velocity in the flow direction is found to become equal to the linear velocity corresponding to the rolling motion over the wall without slip.     

An efficient and robust method for Lagrangian magnetic particle tracking in fluid flow simulations on unstructured grids

In this paper we report on a newly developed particle tracking scheme for fluid flow simulations on 3D unstructured grids, aiming to provide detailed insights in the particle behaviour in complex geometries. A possible field of applications is the magnetic drug targeting (MDT) technique, on which this paper will be focused. MDT is a promising medical technique that uses locally applied magnetic fields to capture magnetic drug carriers at the desired locations in the human body, strongly increasing the efficiency of medical drugs. The new particle tracking scheme combines the advantages of existing methods and is easy for implementation in a generic numerical code. The scheme is tested and validated for simple MDT cases that include effects of a non-homogeneous magnetic field on deposition of magnetic particles in laminar flow. The first test case is a validation study of the magnetic particle trajectories released in a horizontal circular pipe flow with a current-carrying wire parallel to the flow, for which analytical solutions are reported in literature. The second test case involves particle capture efficiencies in a 90° bent tube for different configurations of the imposed magnetic field. This configuration corresponds more closely to the conditions inside blood vessels, because of the presence of secondary motions. These results are compared with numerical studies from literature too. The obtained results demonstrate that the developed particle tracking scheme is a very robust, efficient and accurate method, which can give detailed insights in particle behaviour in complex geometries. As such it is a good candidate for future applications and optimisations of MDT technique for loco-regional cancer treatment or treatment of cardiovascular diseases.     

Effect of particle migration on heat transfer in suspensions of nanoparticles flowing through minichannels

Recent work has shown that suspensions of highly thermally conducting nanoparticles with a size considerably smaller than 100 nm have great potential as a high-energy carrier for small channel systems. However, it is also known that particles in a suspension under certain conditions may migrate. This indicates that the efficiency of heat transfer in the small channels may not be as superior as expected, which bears significance to the system design and operation. This work aims at addressing this issue by examining the effect of particle migration on heat transfer under a fully developed laminar flow regime in small channels. This involves the development of both flow and heat transfer models, and a numerical solution to the models. The flow model takes into account the effects of the shear-induced and viscosity-gradient-induced particle migration, as well as self-diffusion due to Brownian motion, which is coupled with an energy equation. The results suggest a significant non-uniformity in particle concentration and, hence, thermal conductivity over the tube cross-section due to particle migration, particularly for large particles at high concentrations. Compared with the constant thermal conductivity assumption, the non-uniform distribution due to particle migration leads to a higher Nusselt number, which depends on the Peclet number and the mean particle concentration. Further improvement of the model is needed to take into account other factors such as entrance effects, as well as the dynamics of particles and particle–wall interactions.     

Dissipative particle dynamics simulations of electroosmotic flow in nano-fluidic devices

When modeling the hydrodynamics of nanofluidic systems, it is often essential to include molecular-level information such as molecular fluctuations. To this effect, we present a mesoscopic approach which combines a fluctuating hydrodynamics formulation with an efficient implementation of Electroosmotic flow (EOF) in the small Debye length limit. The resulting approach, whose major ingredient is Dissipative Particle Dynamics, is sufficiently coarse-grained to allow efficient simulation of the hydrodynamics of micro/nanofluidic devices of sizes that are too large to be simulated by ab initio methods such as Molecular Dynamics. Within our formulation, EOF is efficiently generated using the recently proven similitude between velocity and electric field under appropriate conditions. More specifically, EOF is generated using an effective boundary condition, akin to a moving wall, thus avoiding evaluation of the computationally expensive electrostatic forces. Our method is used for simulating EOFs and DNA molecular sieving in simple and complex two-dimensional (2D) and 3D geometries frequently used in nano-fluidic devices. The numerical data obtained from our model are in very good agreement with theoretical results.     

Numerical analysis and simulations of contact problem with wear

This paper presents a quasistatic problem of an elastic body in frictional contact with a moving foundation. The model takes into account wear of the contact surface of the body caused by the friction. We recall existence and uniqueness results obtained in Sofonea et al. (2017). The main aim of this paper is to present a fully discrete scheme for numerical approximation together with an error estimation of a solution to this problem. Finally, computational simulations are performed to illustrate the mathematical model.     

Inertial effects on cylindrical particle migration in linear shear flow near a wall

Micro-/nanoparticle-based systems are regarded as one of the possible candidates due to the engineerability and multifunctionality to maximize the accumulation of the nano-/microparticle-based drug delivery system on the target. Recent advances in nanotechnology enable the fabrication of diverse particle shapes from simple spherical particles to more complex shapes. The particle dynamics in blood flow and endocytosis characteristics of non-spherical particles change as the non-sphericity effect increases. We used a numerical approach to investigate the particle dynamics in linear shear flow near a wall. We examined the dynamics of slender cylindrical particles with aspect ratio γ = 5.0 in terms of particle trajectory, velocity, and force variation for different Stokes numbers over time. We identified the rotating inertia of particle near a wall as the source of inertial migration toward the wall. The drift velocity of slender cylindrical particles is comparable to that of discoidal particles. We discuss the possibilities and limitations of using slender cylindrical particles as a drug delivery system.     

Numerical simulations of shear dependent viscoelastic flows with a combined finite element–finite volume method

A hybrid combined finite element–finite volume method has been developed for the numerical simulation of shear-dependent viscoelastic flow problems governed by a generalized Oldroyd-B model with a non-constant viscosity function. The method is applied to the 4:1 planar contraction benchmark problem, to investigate the influence of the viscosity effects on the flow and results are compared with those found in the literature for creeping Oldroyd-B flows, for a range of Weissenberg numbers. The method is also applied to flow in a smooth stenosed channel. It is shown that the qualitative behavior of the flow is influenced by the rheological properties of the fluid, namely its viscoelastic and inertial effects, as well as the shear-thinning viscosity.These results appear in the framework of a preliminary study of the numerical simulation of steady and pulsatile blood flows in two-dimensional stenotic vessels, using this hybrid finite element–finite volume method.     

行星式搅拌釜内高黏固液两相流的数值研究

行星式搅拌装置适用于固体颗粒与高黏度聚合物熔体的混合,搅拌釜内高黏度流体的流动状况非常复杂,实验方法很难获得搅拌釜内流场细节.利用FLUENT软件数值模拟了新型行星式搅拌釜内高黏固液两相流的流场,分析了不同转速条件下搅拌釜不同截面的速度场和浓度场.计算中采用欧拉模型,使用动网格技术,利用FLUENT的用户自定义函数确定...     

Numerical simulations of laser wakefield accelerators in optimal Lorentz frames

The simulation of laser wakefield accelerators with particle-in-cell codes in relativistic reference frames is described, with emphasis on the computational speed-ups, which may potentially exceed three orders of magnitude in comparison with laboratory frame configurations. The initialization of laboratory quantities in a relativistically moving frame is depicted, and the method for result comparison with the plasma rest frame is described. Benchmarks with laboratory frame simulations and experimental data where gains of ∼20 times were obtained are discussed, and potential numerical issues are analyzed. This method enables numerical simulations with shorter turnaround times required for parameter scanning, and for one-to-one three-dimensional experimental modeling of current and next generation laser wakefield experiments.     

Axial particle displacements in fluid slugs after passing a simple serpentiform microchannel

In this work, we designed a simple microchannel to separate particles in fluids by size. We found that mixtures of polystyrene 2 and 0.5 μm particles in a fluid slug can be differentiated by size after passing a long serpentiform microchannel. In contrast to the tubular pinch effect, which separates the particle in radial direction, we found that the particle suspensions in fluid slugs are displaced along the flow directions. The separation performance increases with the increasing flow velocity. The feature of differentiation along the flow directions in our device leads to the result that the separation process can be easily improved by stretching the slug before cutting the slug into pieces. Furthermore, the alternative air slugs between working fluid slugs can also prevent clogging inside the microchannels.     

Lateral migration of particles suspended in viscoelastic fluids in a microchannel flow

In this work, we investigated the lateral migration of microparticles suspended in two different viscoelastic fluids with or without the second normal stress difference. For the viscoelastic fluid without the second normal stress difference, competing forces existed between microfluidic inertia and the first normal stress difference (N ₁), which resulted in a synergetic effect of particle focusing. For the fluid with the second normal stress difference (N ₂), particles were greatly affected by a N ₂-induced secondary flow, and the competition among the inertia, N ₁, and N ₂ determined the lateral migration trajectories of the particles. The obtained results were delineated with the blockage ratio, which showed good agreement with the results of a recent numerical study (Villone et al. in J Non Newton Fluid Mech 195:1–8, 2013). The present study also examined the possibility of particle separation in a size-dependent manner using the N ₂-induced secondary flow in microchannel flow.     

Application of continuum mechanics to fluid flow in nanochannels

A fundamental understanding of the transport phenomena in nanofluidic channels is critical for systematic design and precise control of such miniaturized devices towards the integration and automation of Lab-on-a-chip devices. The goal of this study is to develop a theoretical model of electroosmotic flow in nano channels to gain a better understanding of transport phenomena in nanofluidic channels. Instead of using the Boltzmann distribution, the conservation condition of ion number and the Nernst equation are used in this new model to find the ionic concentration field of an electrolyte solution in nano channels. Correct boundary conditions for the potential field at the center of the nanochannel and the concentration field at the wall of the channel are developed and applied to this model. It is found that the traditional plug-like velocity profile is distorted in the center of the channel due to the presence of net charges in this region opposite to that in the electrical double layer region. The developed model predicted a trend similar to that observed in experiments reported in the literature for the area-average velocity versus the ratio of Debye length to the channel height.     

Direct numerical simulations of localized disturbances in pipe Poiseuille flow

We consider pipe Poiseuille flow subjected to a disturbance which is highly localized in space. Experiments by Peixinho and Mullin have shown this disturbance to be efficient in triggering turbulence, yielding a threshold dependence on the required amplitude as R^-1.5 on the Reynolds number, R. The experiments also indicate an initial formation of hairpin vortices, with each hairpin having a length of approximately one pipe radius, independent of the Reynolds number in the range of R=2000-3000. We perform direct numerical simulations for R=5000. The results show a packet of hairpin vortices traveling downstream, each having a length of approximately one pipe radius. The perturbation remains highly localized in space while being advected downstream for approximately 10 pipe diameters. Beyond that distance from the disturbance origin, the flow becomes severely disordered.     

Dissipative particle dynamics simulation of shear flow in a microchannel with a deformable membrane

Thin deformable membranes are encountered in a number of microfluidics-based applications. These are often employed for enhancing sorting, mixing, cross-diffusion transport, etc. Microfluidic systems with deformable membranes can be better understood by employing simple models and efficient computational procedures. In this paper, we present a dissipative particle dynamics model to simulate the interaction between a deformable membrane and fluid flow in a two-dimensional microchannel. The membrane is modeled as a bead-spring system with both extensional and torsional springs to simulate extensional stiffness and bending rigidity, respectively. By performing detailed simulations on a membrane pinned at both ends and oriented parallel to the flow, we observe different steady state conformations. These membrane deflections are found to be relatively large for low bending stiffnesses and small for high stiffnesses. The membrane was found to exhibit a simple bowing out mode for high stiffness values and more complex conformations at lower stiffnesses.     

Application of the phase space action principle to finite-size particle plasma simulations in the drift-kinetic approximation

We formulate a finite-size particle numerical model of strongly magnetized plasmas in the drift-kinetic approximation. We use the phase space action as an alternative to previous variational formulations based on Low’s Lagrangian or on a Hamiltonian with a non-canonical Poisson bracket. The useful property of this variational principle is that it allows independent transformations of particle coordinates and velocities, i.e., transformations in particle phase space. With such transformations, a finite degree-of-freedom drift-kinetic action is obtained through time-averaging of the finite degree-of-freedom fully-kinetic action. Variation of the drift-kinetic Lagrangian density leads to a self-consistent, macro-particles and fields numerical model. Since the computational particles utilize only guiding center coordinates and velocities, there is a large computational advantage in the time integration part of the algorithm. Numerical comparison between the time-averaged fully-kinetic and drift-kinetic charge and current, deposited on a computational grid, offers insight into the range of validity of the model. Being based on a variational principle, the algorithm respects the energy conserving property of the underlying continuous system. The development in this paper serves to further emphasize the advantages of using variational approaches in plasma particle simulations.     

Numerical analysis of history-dependent hemivariational inequalities and applications to viscoelastic contact problems with normal penetration

In this paper numerical approximation of history-dependent hemivariational inequalities with constraint is considered, and corresponding Céa’s type inequality is derived for error estimate. For a viscoelastic contact problem with normal penetration, an optimal order error estimate is obtained for the linear element method. A numerical experiment for the contact problem is reported which provides numerical evidence of the convergence order predicted by the theoretical analysis.     

Reconsidering simulations in science education at a distance: features of effective use

Abstract  This paper proposes a reconsideration of use of computer simulations in science education. We discuss three studies of the use of science simulations for undergraduate distance learning students. The first one, The Driven Pendulum simulation is a computer-based experiment on the behaviour of a pendulum. The second simulation, Evolve is concerned with natural selection in a hypothetical species of a flowering plant. The third simulation, The Double Slit Experiment deals with electron diffraction and students are provided with an experimental setup to investigate electron diffraction for double and single slit arrangements. We evaluated each simulation, with 30 students each for The Driven Pendulum and Evolve simulations and about 100 students for The Double Slit Experiment . From these evaluations we have developed a set of the features for the effective use of simulations in distance learning. The features include student support, multiple representations and tailorability.