Dynamics of rotating paramagnetic particles simulated by lattice Boltzmann and particle dynamics methods

Novel biochemical sensors consisting of rotating chains of microscale paramagnetic particles have been proposed that would enable convenient, sensitive analyte detection. Predicting the dynamics of these particles is required to optimise their design. The results of lattice Boltzmann (LB) and particle dynamics (PD) simulations are reported, where the LB approach provides a verified solution of the complete Navier-Stokes equations, including the hydrodynamic interactions among the particles. On the other hand, the simpler PD approach neglects hydrodynamic interactions, and does not compute the fluid motion. It is shown that macroscopic properties, like the number of aggregated particles, depend only on the drag force and not on the total hydrodynamic force, making PD simulations yield reasonably accurate predictions. Relatively good agreement between the LB and PD simulations, and qualitative agreement with experimental data, are found for the number of aggregated particles as a function of the Mason number. The drag force on a rotating cylinder is significantly different from that on particle chains calculated from both simulations, demonstrating the different dynamics between the two cases. For microscopic quantities like the detailed force distributions on each particle, the complete Navier-Stokes solution, here represented by the LB simulation, is required.     

A lattice Boltzmann approach for solving scalar transport equations

A lattice Boltzmann (LB) approach is presented for solving scalar transport equations. In addition to the standard LB for fluid flow, a second set of distribution functions is introduced for transport scalars. This LB approach fully recovers the macroscopic scalar transport equation satisfying an exact conservation law. It is numerically stable and scalar diffusivity does not have a Courant-Friedrichs-Lewy-like stability upper limit. With a sufficient lattice isotropy, numerical solutions are independent of grid orientations. A generalized boundary condition for scalars on arbitrary geometry is also realized by a precise control of surface scalar flux. Numerical results of various benchmarks are presented to demonstrate the accuracy, efficiency and robustness of the approach.     

Efficient lattice Boltzmann algorithm for Brownian suspensions

A lattice Boltzmann (LB)-based hybrid method is developed to simulate suspensions of Brownian particles. The method uses conventional LB discretization (without fluid- level fluctuations) for suspending fluid, and treats Brownian particles as point masses with a stochastic thermal noise. LB equations are used to compute the velocity perturbations induced by the particle motion. It is shown that this method correctly reproduces the short-time and long-time diffusive behaviour of a Brownian particle. Unlike the earlier hybrid methods that use thermal fluctuations in the fluid, this method correctly reproduces the temperature of the particle and does not require an empirical rescaling of the bare friction coefficient to obtain the correct diffusive behaviour. It is observed that the present method is at least twice as fast as the earlier method. This method is best suited for flows of polymers and Brownian suspensions in microfluidic devices.     

Computation of higher‐order moments of generalized polynomial chaos expansions

Because of the complexity of fluid flow solvers, non‐intrusive uncertainty quantification techniques have been developed in aerodynamic simulations in order to compute the quantities of interest required in an optimization process, for example. The objective function is commonly expressed in terms of moments of these quantities, such as the mean, standard deviation, or even higher‐order moments. Polynomial surrogate models based on polynomial chaos expansions have often been implemented in this respect. The original approach of uncertainty quantification using polynomial chaos is however intrusive. It is based on a Galerkin‐type formulation of the model equations to derive the governing equations for the polynomial expansion coefficients. Third‐order, indeed fourth‐order moments of the polynomials are needed in this analysis. Besides, both intrusive and non‐intrusive approaches call for their computation provided that higher‐order moments of the quantities of interest need to be post‐processed. In most applications, they are evaluated by Gauss quadratures and eventually stored for use throughout the computations. In this paper, analytical formulas are rather considered for the moments of the continuous polynomials of the Askey scheme, so that they can be evaluated by quadrature‐free procedures instead. Matlab^© codes have been developed for this purpose and tested by comparisons with Gauss quadratures. Copyright © 2017 John Wiley & Sons, Ltd.     

On time integration of viscoplastic constitutive models suitable for creep

Creep of critical components such as electrical solder connections may occur over long periods of time. Efficient numerical simulations of such problems generally require the use of quasi‐static formulations with conjugate‐gradient techniques for solving the large number of algebraic equations. Implicit in the approach is the need to solve the constitutive equation several times for large time steps and for loading directions that may have no resemblance to the actual solution. Therefore, an unconditionally stable and efficient algorithm for solving the constitutive equation is essential for the overall efficiency of the solution procedure. Unfortunately, constitutive equations suitable for simulating the materials of interest are notoriously difficult to solve numerically and most existing algorithms have a stability limit on the time step which may be several orders of magnitude smaller than the desired time step. Here an algorithm is proposed which is a combination of the use of a trapezoidal rule and an iterative Newton–Raphson method for solving implicitly the non‐linear equations. The key to the success of the proposed approach is to always use an initial guess based on the steady‐state solution to the constitutive equation. A representative viscoplastic constitutive equation is used as a model for illustrating the approach. The algorithm is developed and typical numerical results are provided to substantiate the claim that stability has been achieved. Copyright © 2001 John Wiley & Sons, Ltd.     

Multi-domain dual reciprocity for the solution of inelastic non-Newtonian flow problems at low Reynolds number

An efficient boundary element solution of the motion of inelastic non-Newtonian fluids at low Reynolds number is presented in this paper. For the numerical solution all the domain integrals of the boundary element formulation have been transformed into equivalent boundary integrals by means of the dual reciprocity method (DRM). To achieve an accurate approximation of the non-linear and non-Newtonian terms two major improvements have been made to the DRM, namely the use of augmented thin plate splines as interpolation functions, and the partition of the entire domain into smaller subregions or domain decomposition. In each subregion or domain element the DRM was applied together with some additional equations that ensure continuity on the interfaces between adjacent subdomains. After applying the boundary conditions the final systems of equations will be sparse and the approximation of the nonlinear terms will be more localised than in the traditional DRM. This new method known as multidomain dual reciprocity (MD-DRM) has been used to solve several non-Newtonian problems including the pressure driven flow of a power law fluid, the Couette flow and two simulations of industrial polymer mixers. Received 7 February 2001     

Unified fractional step method for Lagrangian analysis of quasi‐incompressible fluid and nonlinear structure interaction using the PFEM

The fractional step method (FSM) is an efficient solution technique for the particle finite element method, a Lagrangian‐based approach to simulate fluid–structure interaction (FSI). Despite various refinements, the applicability of the FSM has been limited to low viscosity flow and FSI simulations with a small number of equations along the fluid–structure interface. To overcome these limitations, while incorporating nonlinear response in the structural domain, an FSM that unifies structural and fluid response in the discrete governing equations is developed using the quasi‐incompressible formulation. With this approach, fluid and structural particles do not need to be treated separately, and both domains are unified in the same system of equations. Thus, the equations along the fluid–structure interface do not need to be segregated from the fluid and structural domains. Numerical examples compare the unified FSM with the non‐unified FSM and show that the computational cost of the proposed method overcomes the slow convergence of the non‐unified FSM for high values of viscosity. As opposed to the non‐unified FSM, the number of iterations required for convergence with the unified FSM becomes independent of viscosity and time step, and the simulation run time does not depend on the size of the FSI interface. Copyright © 2016 John Wiley & Sons, Ltd.     

Lattice Boltzmann method for adiabatic acoustics

The lattice Boltzmann method (LBM) has been proved to be a useful tool in many areas of computational fluid dynamics, including computational aero-acoustics (CAA). However, for historical reasons, its applications in CAA have been largely restricted to simulations of isothermal (Newtonian) sound waves. As the recent kinetic theory-based reformulation establishes a theoretical framework in which LBM can be extended to recover the full Navier-Stokes-Fourier (NS) equations and beyond, in this paper, we show that, at least at the low-frequency limit (sound frequency much less than molecular collision frequency), adiabatic sound waves can be accurately simulated by the LBM provided that the lattice and the distribution function ensure adequate recovery of the full NS equations.     

Mixed Convection of Non-Newtonian Erying Powell Fluid with TemperatureDependent Viscosity over a Vertically Stretched Surface

The viscosity of a substance or material is intensely influenced by the temperature, especially in the field of lubricant engineering where the changeable temperature is well executed. In this paper, the problem of temperature-dependent viscosity on mixed convection flow of Eyring Powell fluid was studied together with Newtonian heating thermal boundary condition. The flow was assumed to move over a vertical stretching sheet. The model of the problem, which is in partial differential equations, was first transformed to ordinary differential equations using appropriate transformations. This approach was considered to reduce the complexity of the equations. Then, the transformed equations were solved using the Keller box method under the finite difference scheme approach. The validation process of the results was performed, and it was found to be in an excellent agreement. The results on the present computation are shown in tabular form and also graphical illustration. The major finding was observed where the skin friction and Nusselt number were boosted in the strong viscosity.     

The Prediction of Permeability with the Aid of Computer Simulations

The particular area of focus for this study is the use of theory to predict the permeability of a material through the use of the Ergun equation and the Kozeny-Carman equation along with computer simulations. The Ergun equation is well known for estimating permeability, and the Kozeny-Carman equation has also been used to a lesser extent. Existing literature extensively covers the use of these equations with homogeneous materials containing mono-size particles. In this study, an alternative way is sought to characterize mixtures that is based on the structure of the porosity, or void size, rather than the traditional method of using mean particle diameter. In doing so, this allows the Ergun and Kozeny-Carman equations to be rewritten to provide for an expansion in the type of mixtures that they can be applied to. Results are presented in this article on the application of these equations to mixtures including mono-size particles, then modified to include binary and distributed mixtures.     

The Prediction of Permeability with the Aid of Computer Simulations

The particular area of focus for this study is the use of theory to predict the permeability of a material through the use of the Ergun equation and the Kozeny-Carman equation along with computer simulations. The Ergun equation is well known for estimating permeability, and the Kozeny-Carman equation has also been used to a lesser extent. Existing literature extensively covers the use of these equations with homogeneous materials containing mono-size particles. In this study, an alternative way is sought to characterize mixtures that is based on the structure of the porosity, or void size, rather than the traditional method of using mean particle diameter. In doing so, this allows the Ergun and Kozeny-Carman equations to be rewritten to provide for an expansion in the type of mixtures that they can be applied to. Results are presented in this article on the application of these equations to mixtures including mono-size particles, then modified to include binary and distributed mixtures.     

Finite element simulation of internal flows with heat transfer using a velocity correction approach

This paper enumerates finite-element based prediction of internal flow problems, with heat transfer. The present numerical simulations employ a velocity correction algorithm, with a Galerkin weighted residual formulation. Two problems each in laminar and turbulent flow regimes are investigated, by solving full Navier-Stokes equations. Flow over a backward-facing step is studied with extensive validations. The robustness of the algorithm is demonstrated by solving a very complex problem viz. a disk and doughnut baffled heat exchanger, which has several obstructions in its flow path. The effect of wall conductivity in turbulent heat transfer is also studied by performing a conjugate analysis. Temporal evolution of flow in a channel due to circular, square and elliptic obstructions is investigated, to simulate the vortex dynamics. Flow past an in-line tube bank of a heat exchanger shell is numerically studied. Resulting heat and fluid flow patterns are analysed. Important design parameters of interest such as the Nusselt number, Strouhal number, skin friction coefficient, pressure drop etc. are obtained. It is successfully demonstrated that the velocity correction approach with a Galerkin weighted residual formulation is able to effectively simulate a wide range of fluid flow features.     

Metabolic fingerprinting of biofluids by infrared spectroscopy: modeling and optimization of flow rates for laminar fluid diffusion interface sample preconditioning

The laminar fluid diffusion interface (LFDI) is a microfluidic tool that manipulates the composition of liquid mixtures by exploiting differences among diffusion coefficients of the dissolved components. One application is the preprocessing of (bio)fluids prior to spectroscopic characterization. For example, in the case of infrared (IR) spectroscopy, the technique can improve sensitivity to low-concentration serum metabolites. The practical benefit is "metabolic fingerprinting" measurements that are more sensitive to low-concentration metabolites than are the counterpart measurements for the original serum sample. Optimal use of the LFDI technique has proven elusive, since the composition of the product of interest is very sensitive to the choice of flow rates for the liquid streams entering and emerging from the LFDI channel. To provide the basis for optimal use, this study had the objective of developing a simulation package that predicts the composition of the LFDI product, given the LFDI structural and operating parameters. To demonstrate the utility of the simulations, composition of the LFDI products predicted for two illustrative sets of trials were compared with experimental data. The flow rates thus derived provided a LFDI product that is relatively rich in serum metabolites, while largely depleted of protein, and very well suited for subsequent IR spectroscopic characterization.     

Langmuir-Blodgett films as chemical sensors

This review covers the fundamental scheme of chemical sensors, fields of major interest in chemical sensors with Langmuir-Blodgett (LB) films, and new and future trends in LB sensor studies. The topics discussed are the relation between sensor characteristics and LB film structure, the biomimetic approach to sensor developments, proposals for transducer improvements, and the possibility of fabricating molecular filters by LB techniques.     

Impact of Artificial Compressibility on the Numerical Solution of Incompressible Nanofluid Flow

The numerical solution of compressible flows has become more prevalent than that of incompressible flows. With the help of the artificial compressibility approach, incompressible flows can be solved numerically using the same methods as compressible ones. The artificial compressibility scheme is thus widely used to numerically solve incompressible Navier-Stokes equations. Any numerical method highly depends on its accuracy and speed of convergence. Although the artificial compressibility approach is utilized in several numerical simulations, the effect of the compressibility factor on the accuracy of results and convergence speed has not been investigated for nanofluid flows in previous studies. Therefore, this paper assesses the effect of this factor on the convergence speed and accuracy of results for various types of thermo-flow. To improve the stability and convergence speed of time discretizations, the fifth-order Runge-Kutta method is applied. A computer program has been written in FORTRAN to solve the discretized equations in different Reynolds and Grashof numbers for various grids. The results demonstrate that the artificial compressibility factor has a noticeable effect on the accuracy and convergence rate of the simulation. The optimum artificial compressibility is found to be between 1 and 5. These findings can be utilized to enhance the performance of commercial numerical simulation tools, including ANSYS and COMSOL.     

Vortex core identification in viscous hydrodynamics

We describe a software package designed for the investigation of topological fluid dynamics with a novel algorithm for locating and tracking vortex cores. The package is equipped with modules for generating desired vortex knots and links and evolving them according to the Navier-Stokes equations, while tracking and visualizing them. The package is parallelized using a message passing interface for a multiprocessor environment and makes use of a computational steering library for dynamic user intervention.     

Evaluation of a grid based molecular dynamics approach for polypeptide simulations

Molecular dynamics is very important for biomedical research because it makes possible simulation of the behavior of a biological macromolecule in silico. However, molecular dynamics is computationally rather expensive: the simulation of some nanoseconds of dynamics for a large macromolecule such as a protein takes very long time, due to the high number of operations that are needed for solving the Newton's equations in the case of a system of thousands of atoms. In order to obtain biologically significant data, it is desirable to use high-performance computation resources to perform these simulations. Recently, a distributed computing approach based on replacing a single long simulation with many independent short trajectories has been introduced, which in many cases provides valuable results. This study concerns the development of an infrastructure to run molecular dynamics simulations on a grid platform in a distributed way. The implemented software allows the parallel submission of different simulations that are singularly short but together bring important biological information. Moreover, each simulation is divided into a chain of jobs to avoid data loss in case of system failure and to contain the dimension of each data transfer from the grid. The results confirm that the distributed approach on grid computing is particularly suitable for molecular dynamics simulations thanks to the elevated scalability.     

Physical and computational scaling issues in lattice Boltzmann simulations of binary fluid mixtures

We describe some scaling issues that arise when using lattice Boltzmann (LB) methods to simulate binary fluid mixtures--both in the presence and absence of colloidal particles. Two types of scaling problem arise: physical and computational. Physical scaling concerns how to relate simulation parameters to those of the real world. To do this effectively requires careful physics, because (in common with other methods) LB cannot fully resolve the hierarchy of length, energy and time-scales that arise in typical flows of complex fluids. Care is needed in deciding what physics to resolve and what to leave unresolved, particularly when colloidal particles are present in one or both of two fluid phases. This influences steering of simulation parameters such as fluid viscosity and interfacial tension. When the physics is anisotropic (for example, in systems under shear) careful adaptation of the geometry of the simulation box may be needed; an example of this, relating to our study of the effect of colloidal particles on the Rayleigh-Plateau instability of a fluid cylinder, is described. The second and closely related set of scaling issues are computational in nature: how do you scale-up simulations to very large lattice sizes? The problem is acute for systems undergoing shear flow. Here one requires a set of blockwise co-moving frames to the fluid, each connected to the next by a Lees-Edwards like boundary condition. These matching planes lead to small numerical errors whose cumulative effects can become severe; strategies for minimizing such effects are discussed.     

Quantitative insight into dislocation nucleation from high-temperature nanoindentation experiments

Nanoindentation has become ubiquitous for the measurement of mechanical properties at ever-decreasing scales of interest, including some studies that have explored the atomic-level origins of plasticity in perfect crystals. With substantial guidance from atomistic simulations, the onset of plasticity during nanoindentation is now widely believed to be associated with homogeneous dislocation nucleation. However, to date there has been no compelling quantitative experimental support for the atomic-scale mechanisms predicted by atomistic simulations. Our purpose here is to significantly advance the quantitative potential of nanoindentation experiments for the study of dislocation nucleation. This is accomplished through the development and application of high-temperature nanoindentation testing, and the introduction of statistical methods to quantitatively evaluate data. The combined use of these techniques suggests an unexpected picture of incipient plasticity that involves heterogeneous nucleation sites, and which has not been anticipated by atomistic simulations.