Numerical Simulation of Flow Field and Ion Transport for Different Ion Source Sampling Interfaces of a Mass Spectrometer.

Understanding ion transport mechanisms in the flow expansion section of the first vacuum region of a mass spectrometer (MS) with an atmospheric pressure ionization source is essential for optimizing the MS sampling interface design. In this study, numerical simulations of three types of ions in two different MS interface designs have been carried out. In contrast to previously reported numerical studies, nonequilibrium gas dynamics due to rarefied gas effects has been considered in modeling the flow expansion and a realistic space charge effect has been considered in a continuous ion injection mode. Numerical simulations reveal that a flat plate interface has a higher peak buffer gas velocity but a narrower zone of silence compared to the conical interface. Shock wave structures are clearly captured, and the Knudsen number distribution is displayed. Simulation results show that in the axial direction the buffer gas effect is much stronger than the electric force effect in the current configuration. The conical interface leads to both a strong ion acceleration in the zone of silence and a strong ion deceleration downstream. In the radial direction, both the electric force and buffer gas drag force play an important role. The conical interface introduces a relatively stronger ion focusing effect from the radial buffer gas effect and a stronger ion dispersion from the radial electric force than the flat plate interface. The net effect for the current configuration is an increase in ion losses for the conical interface. Nanoelectrospray ionization experiments were carried out to validate the ion transmission efficiency.

Modelling Thermally Induced Non-Equilibrium Gas Flows by Coupling Kinetic and Extended Thermodynamic Methods.

Thermally induced non-equilibrium gas flows have been simulated in the present study by coupling kinetic and extended thermodynamic methods. Three different types of thermally induced gas flows, including temperature-discontinuity- and temperature-gradient-induced flows and radiometric flow, have been explored in the transition regime. The temperature-discontinuity-induced flow case has shown that as the Knudsen number increases, the regularised 26 (R26) moment equation system will gradually loss its accuracy and validation. A coupling macro- and microscopic approach is employed to overcome these problems. The R26 moment equations are used at the macroscopic level for the bulk flow region, while the kinetic equation associated with the discrete velocity method (DVM) is applied to describe the gas close to the wall at the microscopic level, which yields a hybrid DVM/R26 approach. The numerical results have shown that the hybrid DVM/R26 method can be faithfully used for the thermally induced non-equilibrium flows. The proposed scheme not only improves the accuracy of the results in comparison with the R26 equations, but also extends their capability with a wider range of Knudsen numbers. In addition, the hybrid scheme is able to reduce the computational memory and time cost compared to the DVM.

Lattice Boltzmann modeling of fluid-particle interaction based on a two-phase mixture representation.

In this work, we derive a lattice Boltzmann model for fluid-particle interaction by considering the system as a two-phase mixture. A partially saturated type scheme is achieved rigorously without any viscosity-dependent weight parameter. The scheme is of second-order accuracy in both space and time including the body-force term. Moreover, we devise a scheme suitable for the scenario where two or more particles intersect a single computational cell, typically occurring for particles in contact or close to contact. Good performance is found when the present scheme is validated against three classic problems, namely the flow past a stationary cylinder, a cylindrical particle settling in a channel under gravity, and the flow around two impacting cylinders.

Numerical Simulation of Ion Transport in a Nano-Electrospray Ion Source at Atmospheric Pressure.

Understanding ion transport properties from the ion source to the mass spectrometer (MS) is essential for optimizing device performance. Numerical simulation helps in understanding of ion transport properties and, furthermore, facilitates instrument design. In contrast to previously reported numerical studies, ion transport simulations in a continuous injection mode whilst considering realistic space-charge effects have been carried out. The flow field was solved using Reynolds-averaged Navier-Stokes (RANS) equations, and a particle-in-cell (PIC) method was applied to solve a time-dependent electric field with local charge density. A series of ion transport simulations were carried out at different cone gas flow rates, ion source currents, and capillary voltages. A force evaluation analysis reveals that the electric force, the drag force, and the Brownian force are the three dominant forces acting on the ions. Both the experimental and simulation results indicate that cone gas flow rates of ≤250 slph (standard liter per hour) are important for high ion transmission efficiency, as higher cone gas flow rates reduce the ion signal significantly. The simulation results also show that the ion transmission efficiency reduces exponentially with an increased ion source current. Additionally, the ion loss due to space-charge effects has been found to be predominant at a higher ion source current, a lower capillary voltage, and a stronger cone gas counterflow. The interaction of the ion driving force, ion opposing force, and ion dispersion is discussed to illustrate ion transport mechanism in the ion source at atmospheric pressure. Graphical Abstract.

Linearized-moment analysis of the temperature jump and temperature defect in the Knudsen layer of a rarefied gas.

Understanding the thermal behavior of a rarefied gas remains a fundamental problem. In the present study, we investigate the predictive capabilities of the regularized 13 and 26 moment equations. In this paper, we consider low-speed problems with small gradients, and to simplify the analysis, a linearized set of moment equations is derived to explore a classic temperature problem. Analytical solutions obtained for the linearized 26 moment equations are compared with available kinetic models and can reliably capture all qualitative trends for the temperature-jump coefficient and the associated temperature defect in the thermal Knudsen layer. In contrast, the linearized 13 moment equations lack the necessary physics to capture these effects and consistently underpredict kinetic theory. The deviation from kinetic theory for the 13 moment equations increases significantly for specular reflection of gas molecules, whereas the 26 moment equations compare well with results from kinetic theory. To improve engineering analyses, expressions for the effective thermal conductivity and Prandtl number in the Knudsen layer are derived with the linearized 26 moment equations.

Nonequilibrium gaseous heat transfer in pressure-driven plane Poiseuille flow.

Nonequilibrium heat and mass transfer in a pressure-driven plane Poiseuille flow is investigated using the direct simulation Monte Carlo method from the early slip to the free molecular regime. Our investigations reveal several nonintuitive, nonequilibrium thermal flow patterns, including expansion cooling near the walls, a nonconstant pressure profile, and counter-gradient heat transfer along the channel center-line. A bimodal trend in the tangential heat flux is found in the slip and the early transition regime. In the upper transition and free molecular regime, the net heat flow in the entire channel is largely unidirectional and in the opposite direction of mass flow. However, in the slip and the early transition regime, a two-way heat flow is observed in the channel as the normal heat flux profile plays a key role in determining the net gaseous heat flow direction. Moreover, the heat flow rate profile exhibits a maximum value at an intermediate value of Knudsen number. The effects of incomplete surface accommodation on nonequilibrium heat flow are also investigated in this work. It is shown that for very low values of the accommodation coefficient, the gaseous heat flow direction is reversed and is consistently in the direction of mass flow.

Role of surface shape on boundary slip and velocity defect.

Although many gas-phase microfluidic devices contain curved surfaces, relatively little research has been conducted on the degree of slip over nonplanar surfaces. The present study demonstrates the influence of the surface shape (i.e., convex/concave) on the velocity slip and formation of the Knudsen layer. In addition, the study reveals that there is a simple relationship between the shear stress exerted on the surface and the velocity defect in the Knudsen layer.

Analysis of the slip coefficient and defect velocity in the Knudsen layer of a rarefied gas using the linearized moment equations.

The linearized R13 and R26 moment equations are used to study Kramers' problem. Analytical solutions for the defect velocity and slip coefficient are derived and compared with numerical results from the kinetic theory. It is found that the linearized R26 equations can capture the Knudsen layer fairly accurately in terms of the defect velocity and slip coefficient, while the linearized R13 equations underpredict the kinetic data. At the wall, however, the kinetic models predict a slightly higher value for the defect velocity than the linearized R26 equations. In general, the linearized R26 equations perform well for both specular and diffusive walls.

Recent advances in computational fluid dynamics relevant to the modelling of pesticide flow on leaf surfaces.

Increasing societal and governmental concern about the worldwide use of chemical pesticides is now providing strong drivers towards maximising the efficiency of pesticide utilisation and the development of alternative control techniques. There is growing recognition that the ultimate goal of achieving efficient and sustainable pesticide usage will require greater understanding of the fluid mechanical mechanisms governing the delivery to, and spreading of, pesticide droplets on target surfaces such as leaves. This has led to increasing use of computational fluid dynamics (CFD) as an important component of efficient process design with regard to pesticide delivery to the leaf surface. This perspective highlights recent advances in CFD methods for droplet spreading and film flows, which have the potential to provide accurate, predictive models for pesticide flow on leaf surfaces, and which can take account of each of the key influences of surface topography and chemistry, initial spray deposition conditions, evaporation and multiple droplet spreading interactions. The mathematical framework of these CFD methods is described briefly, and a series of new flow simulation results relevant to pesticide flows over foliage is provided. The potential benefits of employing CFD for practical process design are also discussed briefly.

Biomimetic design of artificial micro-vasculatures for tissue engineering.

Over the last decade, highly innovative micro-fabrication techniques have been developed that are set to revolutionise the biomedical industry. Fabrication processes, such as photolithography, wet and dry etching, moulding, embossing and lamination, have been developed for a range of biocompatible and biodegradable polymeric materials. One area where these fabrication techniques could play a significant role is in the development of artificial micro-vasculatures for the creation of tissue samples for drug screening and clinical applications. Despite the enormous technological advances in the field of tissue engineering, one of the major challenges is the creation of miniaturised fluid distribution networks to transport nutrients and waste products, in order to sustain the viability of the culture. In recent years, there has been considerable interest in the development of microfluidic manifolds that mimic the hierarchical vascular and parenchymal networks found in nature. This article provides an overview of microfluidic tissue constructs, and also reviews the hydrodynamic scaling laws that underpin the fluid mechanics of vascular systems. It shows how Murray's law, which governs the optimum ratio between the diameters of the parent and daughter branches in biological networks, can be used to design the microfluidic channels in artificial vasculatures. It is shown that it is possible to introduce precise control over the shear stress or residence time in a hierarchical network, in order to aid cell adhesion and enhance the diffusion of nutrients and waste products. Finally, the paper describes the hydrodynamic extensions that are necessary in order to apply Murray's law to the rectangular channels that are often employed in artificial micro-vasculatures.

Lattice Boltzmann models for nonequilibrium gas flows.

Due to its computational efficiency, the kinetic-based lattice Boltzmann method has recently been used to model nonequilibrium gas dynamics. With appropriate boundary conditions, lattice Boltzmann models have been able to capture both velocity slip and temperature jump at a solid surface. To enable these models to simulate flows in the transition regime, both high-order and modified lattice Boltzmann models have been proposed. In this paper, we demonstrate the advantages of the standard lattice Bhatnagar-Gross-Krook model in predicting high-order rarefaction phenomenon. In addition, we show that current high-order lattice Boltzmann models are not yet able to capture the nonlinear constitutive relation for the stress in the Knudsen layer, despite the improved predictions of the wall slip-velocity, especially for Poiseuille flow. By considering how the wall affects the gas mean free path, we present a simplified high-order lattice Boltzmann model that can predict flow in the transition regime and is also able to capture the essential characteristics of the Knudsen layer.

Capturing Knudsen layer phenomena using a lattice Boltzmann model.

In recent years, lattice Boltzmann methods have been increasingly used to simulate rarefied gas flows in microscale and nanoscale devices. This is partly due to the fact that the method is computationally efficient, particularly when compared to solution techniques such as the direct simulation Monte Carlo approach. However, lattice Boltzmann models developed for rarefied gas flows have difficulty in capturing the nonlinear relationship between the shear stress and strain rate within the Knudsen layer. As a consequence, these models are equivalent to slip-flow solutions of the Navier-Stokes equations. In this paper, we propose an effective mean-free path to address the Knudsen layer effect, so that the capabilities of lattice Boltzmann methods can be extended beyond the slip-flow regime. The model has been applied to rarefied shear-driven and pressure-driven flows between parallel plates at Knudsen numbers between 0.01 and 1. Our results show that the proposed approach significantly improves the near-wall accuracy of the lattice Boltzmann method and provides a computationally economic solution technique over a wide range of Knudsen numbers.

Biomimetic design of microfluidic manifolds based on a generalised Murray's law.

The relationship governing the optimum ratio between the diameters of the parent and daughter branches in vascular systems was first discovered by Murray using the principle of minimum work. This relationship is now known as Murray's law and states that the cube of the diameter of the parent vessel must equal the sum of the cubes of the daughter vessels. For symmetric bifurcations, an important consequence of this geometric rule is that the tangential shear stress at the wall remains constant throughout the vascular network. In the present paper, we extend this important hydrodynamic concept to arbitrary cross-sections and provide a framework for constructing a simple but elegant biomimetic design rule for hierarchical microfluidic networks. The paper focuses specifically on constant-depth rectangular and trapezoidal channels often employed in lab-on-a-chip systems. To validate our biomimetic design rule and demonstrate the application of Murray's law to microfluidic manifolds, a comprehensive series of computational fluid dynamics simulations have been performed. The numerical predictions are shown to be in very good agreement with the theoretical analysis, confirming that the generalised version of Murray's law can be successfully applied to the design of constant-depth microfluidic devices.

Lattice Boltzmann simulation of rarefied gas flows in microchannels.

For gas flows in microchannels, slip motion at the solid surface can occur even if the Mach number is negligibly small. Since the Knudsen number of the gas flow in a long microchannel can vary widely and the Navier-Stokes equations are not valid for Knudsen numbers beyond 0.1, an alternative method that can be applicable to continuum, slip and transition flow regimes is highly desirable. The lattice Boltzmann equation (LBE) approach has recently been expected to have such potential. However, some hurdles need to be overcome before it can be applied to simulate rarefied gas flows. The first major hurdle is to accurately model the gas molecule and wall surface interactions. In addition, the Knudsen number needs to be clearly defined in terms of LBE properties to ensure that the LBE simulation results can be checked against experimental measurements and other simulation results. In this paper, the Maxwellian scattering kernel is adopted to address the gas molecule and surface interactions with an accommodation coefficient (in addition to the Knudsen number) controlling the amount of slip motion. The Knudsen number is derived consistently with the macroscopic property based definition. The simulation results of the present LBE model are in quantitative agreement with the established theory in the slip flow regime. In the transition flow regime, the model captures the Knudsen minimum phenomenon qualitatively. Therefore, the LBE can be a competitive method for simulation of rarefied gas flows in microdevices.

Continuous cell washing and mixing driven by an ultrasound standing wave within a microfluidic channel.

Ultrasound standing wave radiation force and laminar flow have been used to transfer yeast cells from one liquid medium to another (washing) by a continuous field-flow fractionation (FFF) approach. Two co-flowing streams, a cell-free suspending phase (flow rate > 50% of the total flow-through volume) and a yeast suspension, were introduced parallel to the nodal plane of a 3 MHz standing wave resonator. The resonator was fabricated to have a single pressure nodal plane at the centre line of the chamber. Laminar flow ensured a stable interface was maintained as the two suspending phases flowed through the sound field. Initiation of the ultrasound transferred cells to the cell-free phase within 0.5 s. This particle transfer procedure circumvents the pellet formation and re-suspension steps of centrifuge based washing procedures. In addition, fluid mixing was demonstrated in the same chamber at higher sound pressures. The channel operates under negligible back-pressure (cross-section, 0.25 [times] 10 mm) and with only one flow convergence and one flow division step, the channel cannot be easily blocked. The force acting on the cells is small; less than that experienced in a centrifuge generating 100g. The acoustically-driven cell transfer and mixing procedures described may be particularly appropriate for the increasingly complex operations required in molecular biology and microbiology and especially for their conversion to continuous flow processes.

Velocity boundary condition at solid walls in rarefied gas calculations.

Maxwell's famous slip boundary condition is often misapplied in current rarefied gas flow calculations (e.g., in hypersonics, microfluidics). For simulations of gas flows over curved or moving surfaces, this means crucial physics can be lost. We give examples of such cases. We also propose a higher-order boundary condition based on Maxwell's general equation and the constitutive relations derived by Burnett. Unlike many other higher-order slip conditions these are applicable to any form of surface geometry. It is shown that these "Maxwell-Burnett" boundary conditions are in reasonable agreement with the limited experimental data available for Poiseuille flow and can also predict Sone's thermal-stress slip flow-a phenomenon which cannot be captured by conventional slip boundary conditions.

Effect of flow development region and fringing magnetic force field on annular split-flow thin fractionation.

Split-flow thin (SPLITT) fractionation devices have been widely used to separate macromolecules, colloids, cells and particles. Recently, the quadrupole magnetic flow sorter (QMS) has been reported in the literature as another family of SPLITT fractionation device. However, the separation performance observed in the experimental measurements is generally found to deviate from the ideal behaviour. Possible causes such as hydrodynamic lift force, high particle concentration and imperfect geometries have been extensively examined. However, the effects of flow development regions and fringing magnetic force field at the separation channel inlet and outlet, which are ignored by the theory, have not been investigated. The error introduced by ignoring these effects need to be rigorously studied so that the theory can be used to optimise operation flow rates with confidence. Indeed, we find in this paper that these ignored effects are responsible to the discrepancy between the experimental data and the theoretical predictions. A new theory has been proposed for optimisation of device operation.

An analysis of induced pressure fields in electroosmotic flows through microchannels.

Induced pressure gradients are found to cause band-broadening effects which are important to the performance of microfluidic devices, such as capillary electrophoresis and capillary chromatography. An improved understanding of the underlying mechanisms causing an induced pressure gradient in electroosmotic flows is presented. The analysis shows that the induced pressure distribution is the key to understanding the experimentally observed phenomena of leakage flows. A novel way of determining the static pressures at the inlet and outlet of microchannels is also presented that takes account of the pressure losses due to flow contraction and expansion. These commonly neglected pressure losses at the channel entrance and outlet are shown to be important in accurately describing the flow. The important parameters that define the effect of induced pressure on the flows are discussed, which may facilitate the design of improved microfluidic devices. The present model clearly identifies the mechanism behind the experimentally observed leakage flows, which is further confirmed by numerical simulations. Not only can the leakage flow occur from the electric-field-free side channel to the main channel, but also the fluid in the main channel can be attracted into the side channel by the induced pressure gradient.

General theory for flow optimisation of split-flow thin fractionation.

Recently, magnetic split-flow thin (SPLITT) fractionation has been developed to separate macromolecules, colloids, cells and particles. However, the previous theory, developed for an infinitely long channel, needs to be improved to consider the flow transit regimes at both inlet and outlet. In this paper, we describe a new approach to optimising flow-rates for particle separation which considers the effect of flow transit region. Surprisingly, the critical particle migration velocities derived by the present theory are identical to the previous simplified theory. Therefore, the previous simplified theory may have wider application than might have been expected. As a test of our theory, a numerical simulation based on solving Navier-Stokes equations has also been carried out for a magnetic SPLITT device. The trajectory of a particle with the critical migration velocity is exactly as expected by our theory. Following experimental validation, this work will facilitate the design of new SPLITT fractionation systems with smaller aspect ratio.