Compact model for a MEM perforation cell with viscous, spring, and inertial forces

A compact model for calculating damping, inertial, and spring forces in a perforated squeeze-film damper is reported. The repetitive pressure patterns around each perforation are utilized by analyzing the visco-acoustic wave transmission around the hole in a cylindrical volume, called perforation cell. The model is needed in applications where the acoustic wavelength of the oscillation is comparable with the dimensions of the perforation cell. The model is constructed of acoustic impedance two-ports. A novel model is derived for the air gap region, and a published two-port model is used for the hole. The impedances for these two-ports are derived from the low reduced frequency model that is equivalent with linearized, harmonic Navier–Stokes equations for acoustic wave propagation in thin channels. This model considers also the transition from the isothermal conditions at low frequencies to the adiabatic ones at high frequencies. The dimensions of MEMS structures are considered using slip conditions for velocities and temperatures. Also, an easy-to-use simplified model for frequencies where the squeeze number and the Reynolds numbers are below unity is derived. The analytical compact model is verified with FEM simulations using a harmonic solver for linearized Navier–Stokes equations with slip boundary conditions in a wide range of perforation ratios. The maximum relative error in the damping coefficient in the simulated cases was 20% upto the first resonant frequency.     

Second-order gaseous slip flow models in long circular and noncircular microchannels and nanochannels

This paper significantly extends previous studies to the transition regime by employing the second-order slip boundary conditions. A simple analytical model with second-order slip boundary conditions for a normalized Poiseuille number is proposed. The model can be applied to either rarefied gas flows or apparent liquid slip flows. The developed simple models can be used to predict the Poiseuille number, mass flow rate, tangential momentum accommodation coefficient, pressure distribution of gaseous flow in noncircular microchannels and nanochannels by the research community for the practical engineering design of microchannels and nanochannels. The developed second-order models are preferable since the difficulty and “investment” is negligible compared with the cost of alternative methods such as molecular simulations or solutions of Boltzmann equation. Navier–Stokes equations with second-order slip models can be used to predict quantities of engineering interest such as the Poiseuille number, tangential momentum accommodation coefficient, mass flow rate, pressure distribution, and pressure drop beyond its typically acknowledged limit of application. The appropriate or effective second-order slip coefficients include the contribution of the Knudsen layers in order to capture the complete solution of the Boltzmann equation for the Poiseuille number, mass flow rate, and pressure distribution. It could be reasonable that various researchers proposed different second-order slip coefficients because the values are naturally different in different Knudsen number regimes. It is analytically shown that the Knudsen’s minimum can be predicted with the second-order model and the Knudsen value of the occurrence of Knudsen’s minimum depends on inlet and outlet pressure ratio. The compressibility and rarefaction effects on mass flow rate and the curvature of the pressure distribution by employing first-order and second-order slip flow models are analyzed and compared. The condition of linear pressure distribution is given.     

Analytic damping model for an MEM perforation cell

The concept of the perforation cell is specified for compact modelling of perforated gas dampers with micromechanical dimensions. Both, analytic expressions and FEM simulations, are used to derive its flow resistance. An extensive set of FEM simulations is performed to characterize the flow resistance of the cell, and to derive approximations for different flow regions by fitting simple functions to them. Sinusoidal small-amplitude velocities are assumed, and micromechanical dimensions are considered with rare gas effects in the slip flow regime (Knudsen number <0.1). The model is capable of modelling all practical combinations of the perforation cell dimensions in a wide range of perforation ratios (1,...,90%). Its validity is verified with a Navier–Stokes solver, and it is shown to be accurate (relative error <4.5%) in the continuum and slip flow regimes. Estimates for cut-off frequencies due to inertial and compressibility effects are specified in a way that the maximum operation frequency of the model can be easily tested. Using a harmonic FEM solver, these estimates are verified. The perforation cell model is also applied to estimate the damping in a perforated rectangular damper (4,...,64 square holes). The damping predicted by the simple model is in moderate agreement with that obtained with 3D FEM simulations.     

Equivalent electrical network for performance characterization of piezoelectric peristaltic micropump

Utilizing an electronic–hydraulic analogy, this study develops an equivalent electrical network of a piezoelectric peristaltic micropump which has not been modeled the whole system operation completely by computational fluid dynamics (CFD) or equivalent electrical network so far due to its excessive complicated structure. The validity of the proposed model is verified by comparing the simulation results obtained using the SPICE (simulation program with integrated circuit emphasis) software package for flow rate spectrum and its maximum state of a typical micropump with the experimental observations for two working fluids, namely DI water and blood. The simulation results predict a maximum flow rate frequency and flow rate of 280 Hz and 43.23 μL/min, respectively, for water, and 210 Hz and 24.12 μL/min for blood. The corresponding experimental results are found to be 300 Hz and 41.58 μL/min for water and 250 Hz and 23.75 μL/min for blood. The relatively poorer agreement between the two sets of results when using blood as the working fluid is thought to be the result of the non-Newtonian nature of blood, which induces a more complex, non-linear flow behavior within the micropump. Having validated the proposed model, the equivalent network is used to perform a systematic analysis of the correlation between the principal micropump design parameters and operating conditions and the micropump performance. The results confirm the validity of the equivalent electrical network model as the first microfluidic modeling tool for optimizing the design of peristaltic micropumps and for predicting their performance.     

Effects of surface roughness and interface wettability on nanoscale flow in a nanochannel

Non-equilibrium molecular dynamics simulations have been carried out to investigate the effect of surface roughness and interface wettability on the nanorheology and slip boundary condition of simple fluids in a nanochannel of several atomic diameters width. The solid surfaces decorated with periodic nanostrips are considered as the rough surface in this study. The simulation results showed that the interface wettability and the surface roughness are important in determining the nanorheology of the nanochannel and fluid slip at solid–fluid interface. It is observed that the presence of surface roughness always suppresses the fluid slip for hydrophilic and hydrophobic surface nanochannels. For fluids over smooth and hydrophobic surfaces, the snapshots of fluid molecules show that an air gap or nanobubble exists at the fluid–solid interface, resulting in the apparent slip velocity. For a given surface with fixed interface wettability, the fluid velocities increase by increasing the driving force, while the driving force has no significant influence on the density structure of fluid molecules. The fluid slip and the flow rate are measured for hydrophilic and hydrophobic nanochannels. The flow rates in rough surface nanochannels are smaller than those of smooth surface walls due to the increase of drag resistance at the solid–fluid interface. The dependence between fluid slip and flow rate showed that the slip length increases approximately linearly with the flow rate for both the hydrophobic and hydrophilic surface nanochannels.     

字典神经网络方法快速湍流烟雾合成

目的 基于物理的烟雾模拟是计算机图形学的重要组成部分,渲染具有细小结构的高分辨率烟雾,需要大量的计算资源和高精度的数值求解方法。针对目前高精度湍流烟雾模拟速度慢,仿真困难的现状,提出了基于字典神经网络的方法,能够快速合成湍流烟雾,使得合成的结果增加细节的同时,保持高分辨率烟雾结果的重要结构信息。方法 使用高精度的数值仿真求解方法获得高分辨率和低分辨率的湍流烟雾数据,通过采集速度场局部块及相应的空间位置信息和时间特征生成数据集, 设计字典神经网络的网络架构,训练烟雾高频成分字典预测器,在GPU（graphic processing unit）上实现并行化,快速合成高分辨率的湍流烟雾结果。结果 实验表明,基于字典神经网络的方法能够在非常低分辨率的烟雾数据下合成空间和时间上连续的高分辨率湍流烟雾结果,效率比通过在GPU平台上直接仿真得到高分辨率湍流烟雾的结果快了一个数量级,且合成的烟雾结果与数值仿真方法得到的高分辨率湍流烟雾结果足够接近。结论 本文方法解决了烟雾的上采样问题,能够从非常低分辨率的烟雾仿真结果,通过设计基于字典神经网络结构以及特征描述符编码烟雾速度场的局部和全局信息,快速合成高分辨率湍流烟雾结果,且保持高精度烟雾的细节,与数值仿真方法的对比表明了本文方法的有效性。     

Hybrid molecular dynamics-continuum simulation for nano/mesoscale channel flows

The present study deals with multiscale simulation of the fluid flows in nano/mesoscale channels. A hybrid molecular dynamics (MD)-continuum simulation with the principle of crude constrained Lagrangian dynamics for data exchange between continuum and MD regions is performed to resolve the Couette and Poiseuille flows. Unlike the smaller channel heights, H < 50σ (σ is the molecular length scale, σ ≈ 0.34 nm for liquid Ar), considered in the previous works, this study deals with nano/mesoscale channels with height falling into the range of 44σ ≤ H ≤ 400σ, i.e., O(10)–O(10²) nm. The major concerns are: (1) to alleviate statistic fluctuations so as to improve convergence characteristics of the hybrid simulation—a novel treatment for evaluation of force exerted on individual particle is proposed and its effectiveness is demonstrated; (2) to explore the appropriate sizes of the pure MD region and the overlap region for hybrid MD-continuum simulations—the results disclosed that, the pure MD region of at least 12σ and the overlap region of the height 10σ have to be used in this class of hybrid MD-continuum simulations; and (3) to investigate the influences of channel height on the predictions of the flow field and the slip length—a slip length correlation is formulated and the effects of channel size on the flow field and the slip length are discussed. An erratum to this article can be found at     

Thermal interactions in nanoscale fluid flow: molecular dynamics simulations with solid–liquid interfaces

Molecular dynamics (MD) simulations of nano-scale flows typically utilize fixed lattice crystal interactions between the fluid and stationary wall molecules. This approach cannot properly model interactions and thermal exchange at the wall–fluid interface. We present a new interactive thermal wall model that can properly simulate the flow and heat transfer in nano-scale channels. The new model utilizes fluid molecules freely interacting with the thermally oscillating wall molecules, which are connected to the lattice positions with “bonds”. Thermostats are applied separately to each layer of the walls to keep the wall temperature constant, while temperature of the fluid is sustained without the application of a thermostat. Two-dimensional MD simulation results for shear driven nano-channel flow shows parabolic temperature distribution within the domain, induced by viscous heating due to a constant shear rate. As a result of the Kapitza resistance, temperature profiles exhibit jumps at the fluid–wall interface. Time dependent simulation results for freezing of liquid argon in a nano-channel are also presented.     

Micro-droplet formation in non-Newtonian fluid in a microchannel

Micro-droplet formation from an aperture with a diameter of micrometers is numerically investigated under the cross-flow conditions of an experimental microchannel emulsification process. The process involves dispersing an oil phase into continuous phase fluid through a microchannel wall made of apertured substrate. Cross-flow in the microchannel is of non-Newtonian nature, which is included in the simulations. Micro-droplets of diameter 0.76–30 μm are obtained from the simulations for the apertures of diameter 0.1–10.0 μm. The simulation results show that rheology of the bulk liquid flow greatly affects the formation and size of droplets and that dispersed micro-droplets are formed by two different breakup mechanisms: in dripping regime and in jetting regime characterized by capillary number Ca. Relations between droplet size, aperture opening size, interfacial tension, bulk flow rheology, and disperse phase flow rate are discussed based on the simulation and the experimental results. Data and models from literature on membrane emulsification and T-junction droplet formation processes are discussed and compared with the present results. Detailed force balance models are discussed. Scaling factor for predicting droplet size is suggested.     

An artificial neural network-based multiscale method for hybrid atomistic-continuum simulations

This paper presents an artificial neural network-based multiscale method for coupling continuum and molecular simulations. Molecular dynamics modelling is employed as a local “high resolution” refinement of computational data required by the continuum computational fluid dynamics solver. The coupling between atomistic and continuum simulations is obtained by an artificial neural network (ANN) methodology. The ANN aims to optimise the transfer of information through minimisation of (1) the computational cost by avoiding repetitive atomistic simulations of nearly identical states, and (2) the fluctuation strength of the atomistic outputs that are fed back to the continuum solver. Results are presented for prototype flows such as the isothermal Couette flow with slip boundary conditions and the slip Couette flow with heat transfer.     

A Faster Algorithm for Computing the Principal Sequence of Partitions of a Graph

We consider the following problem: given an undirected weighted graph G=(V,E,c) with nonnegative weights, minimize function c(δ(Π))−λ|Π| for all values of parameter λ. Here Π is a partition of the set of nodes, the first term is the cost of edges whose endpoints belong to different components of the partition, and |Π| is the number of components. The current best known algorithm for this problem has complexity O(|V|²) maximum flow computations. We improve it to |V| parametric maximum flow computations. We observe that the complexity can be improved further for families of graphs which admit a good separator, e.g. for planar graphs.     

Consistency Property of Finite FC-Normal Logic Programs

Marek＇s forward-chaining construction is one of the important techniques for investigating the non-monotonic reasoning. By introduction of consistency property over a logic program, they proposed a class of logic programs, FC-normal programs, each of which has at least one stable model. However, it is not clear how to choose one appropriate consistency property for deciding whether or not a logic program is FC-normal. In this paper, we firstly discover that, for any finite logic programⅡ, there exists the least consistency property LCon（Ⅱ） overⅡ, which just depends onⅡitself, such that, Ⅱ is FC-normal if and only ifⅡ is FC-normal with respect to （w.r.t.） LCon（Ⅱ）. Actually, in order to determine the FC-normality of a logic program, it is sufficient to check the monotonic closed sets in LCon（Ⅱ） for all non-monotonic rules, that is LFC（Ⅱ）. Secondly, we present an algorithm for computing LFC（Ⅱ）. Finally, we reveal that the brave reasoning task and cautious reasoning task for FC-normal logic programs are of the same difficulty as that of normal logic programs.     

Orthonormal Basis Functions for Continuous-Time Systems and Lp Convergence

In this paper, model sets for linear-time-invariant continuous-time systems that are spanned by fixed pole orthonormal bases are investigated. These bases generalize the well-known Laguerre and two-parameter Kautz cases. It is shown that the obtained model sets are everywhere dense in the Hardy space H ₁(Π) under the same condition as previously derived by the authors for the denseness in the (Π is the open right half plane) Hardy spaces H _p(Π), 1<p<∞. As a further extension, the paper shows how orthonormal model sets, that are everywhere dense in H _p(Π), 1≤p<∞, and which have a prescribed asymptotic order, may be constructed. Finally, it is established that the Fourier series formed by orthonormal basis functions converge in all spaces H _p(Π) and (D is the open unit disk) H _p(D), 1<p<∞. The results in this paper have application in system identification, model reduction, and control system synthesis. Date received: June 16, 1998. Date revised February 4, 1999.     

Multi-scale study of liquid flow in micro/nanochannels: effects of surface wettability and topology

The paper reports parametric study, using a molecular dynamics–continuum hybrid simulation method, of liquid flow in micro/nanochannels with surface nanostructures. The effects of channel height, shape of roughening element, ratio of pitch to length of roughening element and liquid–solid bonding strengths (representing surface wettability) on the velocity and temperature boundary conditions are investigated. The velocity boundary condition is found to shift from significant slip to locking due to the blocking of the surface nanostructure. The blocking appears weak for small pitch ratio and weak liquid–solid bonding. Distorted streamlines, small random eddies and appreciable density oscillations are seen in the vicinity of the wall for small pitch ratio and strong liquid–solid bonding. On the other hand, smooth streamlines and weak density oscillations are seen for large pitch ratio and weak liquid–solid bonding. Results also reveals that: relative slip length, relative Kapitza length and minus pressure gradient vary with channel height and pitch ratio in functions of power law and approximately linear, respectively; relative slip and Kapitza lengths vary with liquid–solid bonding strength as approximately decreasing power functions (except for the strongest case), whereas minus pressure gradient varies with liquid–solid bonding strength as approximately a logarithm-like function. The effect of shape of roughening element is found to be much less significant compared with the other factors studied.     

Reconsideration of Low Reynolds Number Flow-Through Constriction Microchannels Using the DSMC Method

Gaseous flow through a microchannel is treated numerically and analytically in order to assess pressure and mass flow losses due to a constriction of a finite length. Numerical modeling of two-dimensional (2-D) microchannel flow in the slip and transitional regimes is carried out using the direct simulation Monte Carlo (DSMC) method. The prediction of pressure losses and mass flow based on a simple analytic model for constriction microchannel flow are found to be in excellent agreement with DSMC simulations. Constriction has a dramatic effect on pressure loss and mass flow rate for the considered cases. The DSMC results indicate that the flow in the constriction microchannel separates in the transition section, but the separation does not significantly impact pressure distributions.hfillhbox[1189]     

Large-eddy simulation of vortex breakdown in compressible swirling jet flow

Vortex breakdown in a compressible swirling jet flow is investigated by large-eddy simulation (LES) using the approximate deconvolution model. Conditions are chosen similar to recent experimental investigations by Liang and Maxworthy [Liang H, Maxworthy T. An experimental investigation of swirling jets. J Fluid Mech 2005;525:115] for incompressible flow. LES results are presented for two simulations of a swirling jet at Mach number Ma = 0.6 with and without inflow forcing by imposed linear instability disturbances. Both the forced and the self-excited jet show three-dimensional helical waves developing in the jet breakdown zone. The features observed in the two simulations are compared to each other as well as to the experiments with respect to flow statistics and instability behaviour. Both simulations show favourable qualitative agreement with the experiment.     

Pi-sigma-pi threshold formulas

We present lower and upper bounds on the size of pi-sigma-pi (Π ∑ Π) formulas computing threshold functions for small thresholds. Our results show that the limitations of Π ∑ Π formulas for computing threshold functions for small thresholds are more pronounced than suggested by the lower bounds for small depth circuits computing the majority function.     

Convergence Analysis of Batch Gradient Algorithm for Three Classes of Sigma-Pi Neural Networks

Sigma-Pi (Σ-Π) neural networks (SPNNs) are known to provide more powerful mapping capability than traditional feed-forward neural networks. A unified convergence analysis for the batch gradient algorithm for SPNN learning is presented, covering three classes of SPNNs: Σ-Π-Σ, Σ-Σ-Π and Σ-Π-Σ-Π. The monotonicity of the error function in the iteration is also guaranteed.

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Determination of the effective diffusion coefficient in porous media including Knudsen effects

A 3-D bond pore network model is presented and used to evaluate the effect of pore size and connectivity on the effective diffusion coefficient in random porous media. The control equations of the system are set up and the simulation method is discussed. The simulation results show that when the average pore size d _m < 1 μm, the effective diffusion coefficient is strongly dependent on pore size. The analysis shows that Knudsen and bulk diffusion effects can be decoupled, and for any given diffusion conditions, the effect coefficient accounting for Knudsen diffusion can be obtained. Thus, the effect of pore size can been readily accounted for by correcting the bulk effective diffusivity with the Knudsen effect coefficient. The simulations also show that the percolation threshold in random porous materials decreases with increased pore network connectivity.     

Numerical simulation of the motion of red blood cells and vesicles in microfluidic flows

We study the mathematical modeling and numerical simulation of the motion of red blood cells (RBC) and vesicles subject to an external incompressible flow in a microchannel. RBC and vesicles are viscoelastic bodies consisting of a deformable elastic membrane enclosing an incompressible fluid. We provide an extension of the finite element immersed boundary method by Boffi and Gastaldi (Comput Struct 81:491–501, 2003), Boffi et al. (Math Mod Meth Appl Sci 17:1479–1505, 2007), Boffi et al. (Comput Struct 85:775–783, 2007) based on a model for the membrane that additionally accounts for bending energy and also consider inflow/outflow conditions for the external fluid flow. The stability analysis requires both the approximation of the membrane by cubic splines (instead of linear splines without bending energy) and an upper bound on the inflow velocity. In the fully discrete case, the resulting CFL-type condition on the time step size is also more restrictive. We perform numerical simulations for various scenarios including the tank treading motion of vesicles in microchannels, the behavior of ‘healthy’ and ‘sick’ RBC which differ by their stiffness, and the motion of RBC through thin capillaries. The simulation results are in very good agreement with experimentally available data.