Modeling electrokinetic flows by the smoothed profile method

We propose an efficient modeling method for electrokinetic flows based on the smoothed profile method (SPM) 1, 2, 3 and 4 and spectral element discretizations. The new method allows for arbitrary differences in the electrical conductivities between the charged surfaces and the surrounding electrolyte solution. The electrokinetic forces are included into the flow equations so that the Poisson–Boltzmann and electric charge continuity equations are cast into forms suitable for SPM. The method is validated by benchmark problems of electroosmotic flow in straight channels and electrophoresis of charged cylinders. We also present simulation results of electrophoresis of charged microtubules, and show that the simulated electrophoretic mobility and anisotropy agree with the experimental values.     

具有聚电解质层圆柱形纳米通道中的电动能量转换效率

柔性纳米通道是在刚性纳米通道壁面处添加一层带某种电荷的聚电解质层或固定电荷层的纳米通道. 本文在低Zeta势近似下, 通过解析求解电势满足的线性化Poisson-Boltzmann方程和速度满足的Cauchy动量方程, 给出了圆柱形柔性纳米通道中电解质溶液的流向势和电动能量转换效率的解析解. 在表面Zeta势取值相同, 且管径相同(聚电解质层厚度远小于管径前提下)的情形下, 将圆柱形柔性纳米通道和刚性纳米通道中电解质溶液的流向势和电动转换效率进行了比较. 结果表明, 柔性纳米通道中的流向势和转换效率明显高于刚性通道中的流向势和转换效率. 在本文选取的参数范围内, 柔性纳米通道中的电动转换效率比刚性纳米通道中的转换效率提高1.5-3倍.     

Modeling electrokinetic flows in microchannels using coupled lattice Boltzmann methods

We present a numerical framework to solve the dynamic model for electrokinetic flows in microchannels using coupled lattice Boltzmann methods. The governing equation for each transport process is solved by a lattice Boltzmann model and the entire process is simulated through an iteration procedure. After validation, the present method is used to study the applicability of the Poisson–Boltzmann model for electrokinetic flows in microchannels. Our results show that for homogeneously charged long channels, the Poisson–Boltzmann model is applicable for a wide range of electric double layer thickness. For the electric potential distribution, the Poisson–Boltzmann model can provide good predictions until the electric double layers fully overlap, meaning that the thickness of the double layer equals the channel width. For the electroosmotic velocity, the Poisson–Boltzmann model is valid even when the thickness of the double layer is 10 times of the channel width. For heterogeneously charged microchannels, a higher zeta potential and an enhanced velocity field may cause the Poisson–Boltzmann model to fail to provide accurate predictions. The ionic diffusion coefficients have little effect on the steady flows for either homogeneously or heterogeneously charged channels. However the ionic valence of solvent has remarkable influences on both the electric potential distribution and the flow velocity even in homogeneously charged microchannels. Both theoretical analyses and numerical results indicate that the valence and the concentration of the counter-ions dominate the Debye length, the electrical potential distribution, and the ions transport. The present results may improve the understanding of the electrokinetic transport characteristics in microchannels.     

Suppression of electro-osmotic flow by surface roughness

We show that nanoscale surface roughness, which commonly occurs on microfabricated metal electrodes, can significantly suppress electro-osmotic flows when excess surface conductivity is appreciable. We demonstrate the physical mechanism for electro-osmotic flow suppression due to surface curvature, compute the effects of varying surface conductivity and roughness amplitudes on the slip velocities of a model system, and identify scalings for flow suppression in different regimes of surface conduction. We suggest that roughness may be one factor that contributes to large discrepancies observed between classical electrokinetic theory and modern microfluidic experiments.     

Characterization of the channel walls roughness in photonic crystal fibers

We present electron microscope (FEI NanoSEM) and atomic force microscopy measurements of surface roughness in nanochannels in photonic crystal fibers (PCF). A method was invented to cleave the PCF along the axis without damaging the surface structure in the nanochannels allowing us to characterize the morphology of the nanochannels in the PCF. A multi-wall carbon nanotube mounted onto commercial AFM probes and super sharp silicon non-contact mode AFM probes were used to characterize the wall roughness in the nanochannels. The roughness is shown to have a Gaussian distribution, and has an amplitude smaller than 0.5 nm. The height–height correlation function is an exponential correlation function with an autocorrelation length of 13 nm, and 27 nm corresponding with scan sizes of 200×100 nm², and 1600×200 nm², respectively.     

A front-tracking/ghost-fluid method for fluid interfaces in compressible flows

A front-tracking/ghost-fluid method is introduced for simulations of fluid interfaces in compressible flows. The new method captures fluid interfaces using explicit front-tracking and defines interface conditions with the ghost-fluid method. Several examples of multiphase flow simulations, including a shock–bubble interaction, the Richtmyer–Meshkov instability, the Rayleigh–Taylor instability, the collapse of an air bubble in water and the breakup of a water drop in air, using the Euler or the Navier–Stokes equations, are performed in order to demonstrate the accuracy and capability of the new method. The computational results are compared with experiments and earlier computational studies. The results show that the new method can simulate interface dynamics accurately, including the effect of surface tension. Results for compressible gas–water systems show that the new method can be used for simulations of fluid interface with large density differences.     

壁面粗糙度对水平后台阶气粒两相流动影响的PDPA实验研究

用相位多普勒颗粒测速仪(PDPA)测量了颗粒的平均与脉动速度,研究了壁面粗糙度对水平后台阶气粒两相流动的影响。研究结果表明,壁面粗糙度减小颗粒纵向平均速度,增大颗粒纵向和横向脉动速度。壁面粗糙度对流场中不同位置处颗粒运动影响的强弱不同,其中逆流区处较弱,下游处较强。壁面粗糙度对不同粒径颗粒运动影响的强弱不同,其中对细颗粒的影响较弱且被局限在壁面附近,对粗颗粒的影响较强且扩散到整个流场。     

The effect of surface roughness on rarefied gas flows by lattice Boltzmann method

This paper studies the roughness effect combining with effects of rarefaction and compressibility by a lattice Boltzmann model for rarefied gas flows at high Knudsen numbers. By discussing the effect of the tangential momentum accommodation coefficient on the rough boundary condition, the lattice Boltzmann simulations of nitrogen and helium flows are performed in a two-dimensional microchannel with rough boundaries. The surface roughness effects in the microchannel on the velocity field, the mass flow rate and the friction coefficient are studied and analysed. Numerical results for the two gases in micro scale show different characteristics from macroscopic flows and demonstrate the feasibility of the lattice Boltzmann model in rarefied gas dynamics.     

A direct-forcing embedded-boundary method with adaptive mesh refinement for fluid–structure interaction problems

In the present work we developed a structured adaptive mesh refinement (S-AMR) strategy for fluid–structure interaction problems in laminar and turbulent incompressible flows. The computational grid consists of a number of nested grid blocks at different refinement levels. The coarsest grid blocks always cover the entire computational domain, and local refinement is achieved by the bisection of selected blocks in every coordinate direction. The grid topology and data-structure is managed using the Paramesh toolkit. The filtered Navier–Stokes equations for incompressible flow are advanced in time using an explicit second-order projection scheme, where all spatial derivatives are approximated using second-order central differences on a staggered grid. For transitional and turbulent flow regimes the large-eddy simulation (LES) approach is used, where special attention is paid on the discontinuities introduced by the local refinement. For all the fluid–structure interaction problems reported in this study the complete set of equations governing the dynamics of the flow and the structure are simultaneously advanced in time using a predictor–corrector strategy. An embedded-boundary method is utilized to enforce the boundary conditions on a complex moving body which is not aligned with the grid lines. Several examples of increasing complexity are given to demonstrate the robustness and accuracy of the proposed formulation.     

Energy law preserving C finite element schemes for phase field models in two-phase flow computations

We use the idea in [33] to develop the energy law preserving method and compute the diffusive interface (phase-field) models of Allen–Cahn and Cahn–Hilliard type, respectively, governing the motion of two-phase incompressible flows. We discretize these two models using a C⁰ finite element in space and a modified midpoint scheme in time. To increase the stability in the pressure variable we treat the divergence free condition by a penalty formulation, under which the discrete energy law can still be derived for these diffusive interface models. Through an example we demonstrate that the energy law preserving method is beneficial for computing these multi-phase flow models. We also demonstrate that when applying the energy law preserving method to the model of Cahn–Hilliard type, un-physical interfacial oscillations may occur. We examine the source of such oscillations and a remedy is presented to eliminate the oscillations. A few two-phase incompressible flow examples are computed to show the good performance of our method.     

A Fourier spectral method for the Navier–Stokes equations with volume penalization for moving solid obstacles

An efficient numerical scheme to compute flows past rigid solid bodies moving through viscous incompressible fluid is presented. Solid obstacles of arbitrary shape are taken into account using the volume penalization method to impose no-slip boundary condition. The 2D Navier–Stokes equations, written in the vorticity-streamfunction formulation, are discretized using a Fourier pseudo-spectral scheme. Four different time discretization schemes of the penalization term are proposed and compared. The originality of the present work lies in the implementation of time-dependent penalization, which makes the above method capable of solving problems where the obstacle follows an arbitrary motion. Fluid–solid coupling for freely falling bodies is also implemented. The numerical method is validated for different test cases: the flow past a cylinder, Couette flow between rotating cylinders, sedimentation of a cylinder and a falling leaf with elliptical shape.     

Influence of surface heterogeneity in electroosmotic flows—Implications in chromatography, fluid mixing, and chemical reactions in microdevices

We analyze the influence of surface heterogeneity, inducing a random ζ-potential at the walls in electroosmotic incompressible flows. Specifically, we focus on how surface heterogeneity modifies the physico-chemical processes (transport, chemical reaction, mixing) occurring in microchannel and microreactors. While the macroscopic short-time features associated with solute transport (e.g. chromatographic patterns) do not depend significantly on ζ-potential heterogeneity, spatial randomness in the surface ζ-potential modifies the spectral properties of the advection-diffusion operator, determining different long-term properties of transport/reaction phenomena compared to the homogeneous case. Examples of physical relevance (chromatography, infinitely fast reactions) are addressed.     

Nested Cartesian grid method in incompressible viscous fluid flow

In this work, the local grid refinement procedure is focused by using a nested Cartesian grid formulation. The method is developed for simulating unsteady viscous incompressible flows with complex immersed boundaries. A finite-volume formulation based on globally second-order accurate central-difference schemes is adopted here in conjunction with a two-step fractional-step procedure. The key aspects that needed to be considered in developing such a nested grid solver are proper imposition of interface conditions on the nested-block boundaries, and accurate discretization of the governing equations in cells that are with block-interface as a control-surface. The interpolation procedure adopted in the study allows systematic development of a discretization scheme that preserves global second-order spatial accuracy of the underlying solver, and as a result high efficiency/accuracy nested grid discretization method is developed. Herein the proposed nested grid method has been widely tested through effective simulation of four different classes of unsteady incompressible viscous flows, thereby demonstrating its performance in the solution of various complex flow–structure interactions. The numerical examples include a lid-driven cavity flow and Pearson vortex problems, flow past a circular cylinder symmetrically installed in a channel, flow past an elliptic cylinder at an angle of attack, and flow past two tandem circular cylinders of unequal diameters. For the numerical simulations of flows past bluff bodies an immersed boundary (IB) method has been implemented in which the solid object is represented by a distributed body force in the Navier–Stokes equations. The main advantages of the implemented immersed boundary method are that the simulations could be performed on a regular Cartesian grid and applied to multiple nested-block (Cartesian) structured grids without any difficulty. Through the numerical experiments the strength of the solver in effectively/accurately simulating various complex flows past different forms of immersed boundaries is extensively demonstrated, in which the nested Cartesian grid method was suitably combined together with the fractional-step algorithm to speed up the solution procedure.     

Surface-charge-governed ion transport in nanofluidic channels

A study of ion transport in aqueous-filled silica channels as thin as 70 nm reveals a remarkable degree of conduction at low salt concentrations that departs strongly from bulk behavior: In the dilute limit, the electrical conductances of channels saturate at a value that is independent of both the salt concentration and the channel height. Our data are well described by an electrokinetic model parametrized only by the surface-charge density. Using chemical surface modifications, we further demonstrate that at low salt concentrations, ion transport in nanochannels is governed by the surface charge.     

Inner–outer interactions in rough-wall turbulence

Here we revisit the inner–outer interaction model (IOIM) of Marusic et al. (Science, vol. 329, 2010, pp. 193–196) that enables the prediction of statistics of the fluctuating streamwise velocity in the inner region of wall-bounded turbulent flows from a large-scale velocity signature measured in the outer region of the flow. The model is characterised by two empirically observed inner–outer interactions: superposition of energy from outer region large-scale motions; and amplitude modulation by these large-scale motions of a small-scale ‘universal’ signal (u^*), which in smooth-wall flows is Reynolds number invariant. In the present study, the inner–outer interactions in rough-wall turbulent boundary layers are examined within the framework of the IOIM. Simultaneous two-point hot-wire anemometry measurements enable quantification, via the model parameters, of the strengths of superposition and amplitude modulation effects in a rough-wall flow, and these are compared to a smooth-wall flow. It is shown that the present rough-wall significantly reduces the effects of superposition, while increasing the amplitude modulation effect. The former is true even in flows that exhibit outer region similarity. Using the model parameters obtained from the two-point measurements, predictions of inner region streamwise velocity statistics and spectra are compared to measurements over a range of friction and roughness Reynolds numbers. These results indicate that the u^* signal does depend on roughness Reynolds number (k⁺_s), but is robust to changes in friction Reynolds number (δ⁺). Additionally, the superposition strength is shown to be relatively independent of both roughness and friction Reynolds number. The implications of the present results on the suitability of the IOIM as a predictive tool in rough-wall turbulence are discussed.     

Development of a new correlation to calculate permeability for flows with high Knudsen number

Flows with high Knudsen number play a prominent role in many engineering applications. The present study is an effort toward the simulation of flow with high Knudsen number using modified lattice Boltzmann method(LBM) through a porous medium in a channel. The effect of collision between molecules and solid walls, which is required to accurately simulate transition flow regime, is taken into account using a modified relaxation time. Slip velocity on the wall, which is another significant difficulty in simulating transition flow regime, is captured using the slip reflection boundary condition(SRBC). The geometry of porous medium is considered as in-line and staggered. The results are in good agreement with previous works. A new correlation is obtained between permeability, Knudsen number and porosity for flows in transition flow regimes.     

Density waves and the effect of wall roughness in granular Poiseuille flow: Simulationand linear stability

The formation of density waves and the effect of wall roughness on them are studied using molecular dynamics simulations of gravity-driven granular Poiseuille flow. Three basic types of structures are found in moderately dense flows: a plug, a sinuous wave and a slug; a new varicose wave mode has been identified in dense flows with channels of large widths at moderate dissipations; only clump-like structures appear in dilute flows. The simulation results are contrasted with the predictions of a linear stability analysis of the kinetic-theory continuum equations for granular Poiseuille flow. The theoretical predictions on the form of density waves are in qualitative agreement with simulations in denser flows, however, there are discrepancies between simulation and theory in dilute flows.     

Eulerian simulation of sedimentation flows in vertical and inclined vessels

Sedimentation of particles in inclined and vertical vessels is numerically simulated using a finite volume method where the Eulerian multiphase model is applied. The particulate phase as well as the fluid phase is regarded as a continuum while the viscosity and solid stress of the particulate phase are modelled by the kinetic theory of granular flows. The numerical results show an interesting phenomenon of the emergence of two circulation vortices of the sedimentation flow in a vertical vessel but only one in the inclined vessel. Several sensitivity tests are simulated to understand the factors that influence the dual-vortex flow structure in vertical sedimentation. Results show that a larger fluid viscosity makes the two vortex centres much closer to each other and the boundary layer effect at lateral walls is the key factor to induce this phenomenon. In the fluid boundary layer particles settle down more rapidly and drag the local carrier fluid to flow downward near the lateral walls and thus form the dual-vortex flow pattern.