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The multiscale stochastic simulation method based on the marriage of the Brownian Configuration Field (BCF) and the Radial Basis Function mesh-free approximation for dilute fibre suspensions by our group, is further developed to simulate non-dilute fibre suspensions. For the present approach, the macro and micro processes proceeded at each time step are linked to each other by a fibre contributed stress formula associated with the used kinetic model. Due to the feature of non-dilute fibre suspensions, the interaction between fibres is introduced into the evolution equation to determine fibre configurations using the BCF method. The fibre stresses are then determined based on the fibre configuration fields using the Phan–Thien–Graham model. The efficiency of the simulation method is demonstrated by the analysis of the two challenging problems, the axisymmetric contraction and expansion flows, for a range of the fibre concentration from semi-dilute to concentrated regimes. Results evidenced by numerical experiments show that the present method would be potential in analysing and simulating various suspensions in food and medical industries.

Recently, wearable electronics for health monitoring have been demonstrated with considerable benefits for early-stage disease detection. This article reports a flexible, bending-insensitive, bio-compatible and lightweight respiration sensor. The sensor consists of highly oriented carbon nanotube (HO-CNT) films embedded between electro-spun polyacrylonitrile (PAN) layers. By aligning carbon nanotubes between the PAN layers, the sensor exhibits a high sensitivity towards airflow (340 mV/(m/s)) and excellent flexibility and robustness. In addition, the HO-CNT sensor is insensitive to mechanical bending, making it suitable for wearable applications. We successfully demonstrated the attachment of the sensor to the human philtrum for real-time monitoring of the respiration quality. These results indicate the potential of HO-CNT flow sensor for ubiquitous personal health care applications.

A valveless microfluidic pump using a lead zirconate titanate (PZT) diaphragm actuated synthetic jet is developed and fabricated. For this present design, a valveless pump structure is developed in which the pump chamber is sealed on one side and connected to an emitting nozzle at another side. The design is simulated using the multiphysics approach and then successfully investigated with a prototype produced by a low-cost additive fabrication technique. The device's parameters, including the liquid pumping characteristics and the size of the PZT membrane, are optimized based on its desired performance. The developed device can be applied over a wide range of applications from micromixing to fluidic controlling.

In forests and membranes, Carbon nano tubes (CNT) are not individual, instead they tend to be agglomerated into bundles because of the strong van der Waals interaction. CNTs usually form into bundles containing up to hundreds or thousands of parallel CNTs named as fibres which create networks within a CNT membrane. Recently, CNT based macrostructures (yarn and membrane) have increasingly been used in various applications in electronics, medical and bioengineering. Meanwhile the volume density of CNTs impacts on mechanical and physical properties of macrostructures, the controlling of the density of membranes is very complex. Thus, in this paper, an electric processing to dilate CNT membrane is sufficiently studied and investigated by both the experiment and particle based numerical simulation. Several initially potential applications of the method are also represented not only to control the density of CNTs but also to improve the CNTs’ alignment in macro-structures.

We present a multi-physics simulation associated with experimental investigation for an electrohydrodynamic gyroscope based on ion wind corona discharge. The present device consisting of multiple point-ring electrodes generates a synthetic jet flow of ions for inertial sensing applications. Meanwhile the residual charge of jet is neutralized by an external ring electrode to guarantee the ion wind stable while circulating inside the device's channels. The working principle including the generation and then circulation of jet flow within the present device is firstly demonstrated by a numerical simulation and the feasibility and stability of the device are then successfully investigated by experimental work. Results show owing to the ion wind corona discharge based approach associated with new configuration, the present device is robust and consumes low energy.

The development of a multimodal sensing platform with multiple layers for electronic skin (e-skin) sensing of temperature and pressure has attracted considerable interest to practical applications in soft robotics, human-machine interfaces, and wearable health monitoring. In this work, we demonstrated a new platform technology with multiple sandwiched layers of highly oriented carbon nanotube membrane and polyacrylonitrile for the integration of pressure and temperature sensory functionalities into a single platform that is thin, ultra-lightweight, flexible, and wearable. The key technology of in situ deposition of sensor platform on objects or in robot interface makes this a unique method for the development of e-skins for robotic applications, offering a new approach to wearable electronics and portable health care.

A novel gyroscope using circulatory electro-hydrodynamics flow in a confined space is presented for the first time. The configuration of the new gyroscope includes three point-ring corona discharge actuators that generate ion flows in three separated sub-channels. The three ion flows then merge together when going through a nozzle of the main chamber entrance and create a jet flow. In the new configuration, the residual charge of ion wind flow is removed by a master-ring electrode located at one end of the main chamber. Under the effect of the angular speed of gyroscope, the jet flow is deflected and this deflection is sensed using hotwires. The results, which are consistently acquired by both the numerical simulation and experiment on our prototypes, demonstrate the repeatability and stability of the new approach. Since the ion wind can be generated by a minimum power, the present configuration-based device does not require any vibrating component. Thus, the device is robust, cost, and energy-effective.

Electrohydrodynamic atomization has been emerging as a powerful approach for respiratory treatment, including the generation and delivery of micro/nanoparticles as carriers for drugs and antigens. In this work, we present a new conceptual design in which two nozzles facilitate dual electrospray coexisting with ionic wind at chamfered tips by a direct current power source. Experimental results by a prototype have demonstrated the capability of simultaneously generating-and-delivering a stream of charged reduced particles. The concept can be beneficial to pulmonary nano-medicine delivery since the mist of nanoparticles is migrated without any restriction of either the collector or the assistance of external flow, but is pretty simple in designing and manufacturing devices.

A new conceptual design of electrospray has been developed to generate neutralized micro-droplet using on-chip electro-hydrodynamic. A prototype of a bipolar electrostatic atomization with chambered nozzle tips has been carried out to demonstrate the capability of spaying viable, safe, neutral and alternative droplets which can be applied in micro/nano-encapsulation, bio-scaffold production and also the polymeric micro/nanoparticle fabrication over conventional fabrication techniques as well as the direct current electro-spraying/electrospinning. Several initially experimental results as presented through this work have shown the potential application of the present device in drug delivery.

We report for the first time a lightweight, flexible and wearable hot-film flow sensor for real-time monitoring of human respiration. The sensor was manufactured by spinning and electrospinning methods from spinnable carbon nanotube (CNT) forest grown on silicon wafers and polyacrylonitrile (PAN). The sensor exhibited high sensitivity of 340 mV/(m/s), excellent flexibility, wearability and stability under bending and other mechanical disturbances. We successfully demonstrated a CNT wearable patch affixed to human upper lip for real-time monitoring of human respiration. The results indicate that our sensor can be employed to monitor sleep quality, personal health care and other clinical evaluations.

The paper reports the development of a particle precipitation based aerosol sampler using bipolar corona discharge ion winds with collected particles of minimized net charge. For the new approach, neutralized particles move towards a sampler under the effect of electric field and dual ion winds. Since there is no electrode or sampling chip installed inside the air-flow channel, impediments to airborne particle flow or ion winds are removed along the flow direction. In addition, the isolation of ion winds, which generate circuit, allows using various materials for the sampling chip including non-conductors and also protecting collected particles from any discharge ignition on the chip. The device mechanism is numerically simulated in OpenFOAM to study the electrofluidodynamic interaction of charged particles and bipolar ion winds. The efficiency of the new approach has been investigated by experiment with a maximum efficiency of 94%. The effects of flow rate, discharge voltage and electrode distances on the method are also evaluated.

We report a unique alternating current (AC) driven corona based air-flow generator using symmetrically arranged electrodes. Unlike the conventional configuration where one electrode generates charged ions moving towards the reference electrode, this configuration allows both negative and positive charges to simultaneously move away from the device and generate ion wind in parallel with the electrodes. In comparison with the direct current (DC) driven corona generator, the time oscillating AC field allows the device a better stabilization owing to the independence of ion wind strength from the inter-electrode spacing. Our results by both simulation and experiment showed that when the AC frequency exceeds a threshold value of 1100 Hz, the electric field at the electrode tips is determined dominantly by the charge cloud created in the previous half-cycle, resulting in stronger net electric field and thus stronger ion wind. In addition, the electrode separation in the AC driven corona based generator is less critical above the frequency threshold, yielding a more robust design with minimized susceptibility to manufacturing tolerances and impurities on the electrodes. Moreover, lower voltage levels of the AC driven system allow simpler and more economical design in the high voltage circuit of the AC generator.

In this paper, we report a further study of flow-network generating four jet flows which circulate in a sealed device to experimentally investigate the feasibility and efficiency of a dual-axis gyroscope. The experiment is carried out successfully and the experimental results reasonably agreed with those obtained by numerical analysis using OpenFOAM. The flow rectifying coefficient is determined using the mathematical lump model for a vibrating system, which takes into account of the device geometry and resonant frequency. Experimental and numerical results demonstrate that the coefficient of the new system developed in this study is significantly higher than those of conventional designs. The hotwire-integrated device which can function as a dual-axis gyroscope is tested using a turntable with speeds up to 1900 rpm. The scale factor and cross-sensitivity of the system are 0.26 μV s/° and 1.2%, respectively. The cross-sensitivity and the effects of linear acceleration, actuating voltage on the diaphragm, heating power and position of hotwires are also investigated.

We report an application of ion wind in angular rate sensing. A new design of a jet flow gyroscope using ion wind corona discharge is developed by conducting a numerical simulation and then an experimental analysis with regard to the advantages of a corona-discharge-based jet flow. Ion wind is generated by applying a high–voltage between a pin, as the discharge electrode, and a ring, as the reference electrode. The current–voltage characteristics of the discharge process by experimental works is set up as the boundary condition to describe the ion wind flow in the numerical simulation. A jet flow of ion wind is observed through an experiment and a simulation. When the gyroscope is subjected to an angular rate, the induced Coriolis force deflects the ion wind. This deflection is detected using four hotwires installed downstream of the working chamber behind the reference electrode. The experimental result show that the angular rate can be detected with a sensitivity of 4.7 μV/o/s. Because ion wind can be generated with minimum power and does not require any vibrating components, the device is robust, consumes low power, and is cost-effective.

This paper develops a millimeter scale fully packaged device in which a vortex flow of high velocity is generated inside a chamber. Under the actuation by a lead zirconate titanate (PZT) diaphragm, a flow circulates with increasing velocity after each actuating circle to form a vortex in a cavity named as the vortex chamber. At each cycle, the vibration of the PZT diaphragm creates a small net air flow through a rectifying nozzle, generates a synthetic jet which propagates by a gradual circulation toward the vortex chamber and then backward the feedback chamber. The design of such device is firstly conducted by a numerical analysis whose results are considered as the base of our experimental set-up. A vortex flow generated in the votex chamber was observed by a high-speed camera. The present approach which was illustrated by both the simulation and experiment is potential in various applications related to the inertial sensing, fluidic amplifier and micro/nano particle trapping and mixing.

We present the study of a simple and efficient air-flow generator under the effect of ion winds which are created by corona discharge. Based on our recent research of ion wind with bipolar corona using parallel pins, this work reports an investigation and evaluation of the corona system in asymmetrical configurations, where the two electrodes have different tip shapes. The system of new configuration is investigated both experimentally and numerically. The numerical and experimental results are the base to establish a regime of stable operation by the measured I-V characteristics. The optimized set-up can generate an air flow up to 2.24 m/s at the atmospheric pressure. With the asymmetrical configuration of different pin tip shapes, the system can be used in many mixing applications such as mixing solvent and die where the generated vortices are also presented.

In this paper, we report the details and findings of a study on tri-axis convective accelerometer, which is designed with the closed-loop type heat source and thermal sensing hotwire elements. The closed-loop heat source enhances the convective flow to the central part where a hotwire is placed to measure the vertical component of acceleration. The simulation was conducted using numerical analysis, and the device was prototyped by additive manufacturing. The device, functioning as a tilt sensor and an accelerometer, was tested up to acceleration of 20 g. The experiments were successfully conducted and the experimental results agreed reasonably with those obtained by numerical analysis. The results demonstrated that the closed-loop heat source could reduce the cross effect between the acceleration components. The scale factor and cross-sensitivity had the values of 0.26 μV/g and 1.2%, respectively. The cross-sensitivity and the effects of heating power were also investigated in this study.

This letter reports on the impact of compressive pressure on the electrical properties of carbon nanotube (CNT) yarns fabricated by dry Web-spinning and heat-treatment processes. Under increasing applied compressive pressure in the radial direction of the yarn, the electrical resistance of CNT yarns gradually decreased by 2.8% at a threshold applied pressure of 60 kPa where the resistance change is saturated. The decrease of CNT resistance with increasing pressure is attributed to the increase in the volume fraction of CNT, resulting in the increase of the effective junctions between adjacent CNTs, and the reduction of the tunneling distance between single CNTs. CNT yarns embedded in elastomers show high potential as an advanced functional element for a wide range of mechanical sensing applications including flexible pressure and tactile sensing.

This paper applies our recent approach to generate a circulatory jet flow within a confined space using ionic wind by the corona discharge. A millimetre-scaled prototype with bipolar discharge configuration, which consists of two pin electrodes, nozzle, working chamber, two circulating channels and three hotwires, was designed, manufactured and investigated. A dielectric barrier of 1.0 mm thickness, installed between the parallel electrodes of opposite polarity, is utilized in order to possibly minimize the inter-electrode distance, provide a smooth current-voltage discharge characteristic and prevent electrical spark. The experimental results demonstrate that the jet flow circulates inside the device with a average velocity of 0.7 m/s. The characteristics of flow by experiment are in reasonable agreement with the numerical analysis using the finite-volume method. The device specifications were investigated with several parameters including the discharge voltage on the electrode and the heating power on hotwires. In addition, the dependence of packaging conditions on the discharge process and the effect of alternating current on the generation of ion wind are also presented. The device has low power consumption of 33 mW, and great versatility for applications in fluidic inertial sensors, fluidic amplifiers or gas mixing.

We report a highly stable electrical conductance of a compact and well-oriented carbon nanotube yarn under tensile strain. The gauge factor of the yarn was found to be extremely small of approximately 0.15 thanks to the improvements in the dry spinning process, including multi-web spinning and heat treatment. The threshold strain $\varepsilon _{s}$ , below which the yarn retains its electrical conductance stability, has also been determined to be approximately $15\times 10^{3}$ ppm. Owing to its highly stable resistance under mechanical strain, the yarn has a good potential as a wiring material for niche applications, where light weight and resistance stability are required.

A novel air-flow generator based on the effect of ion wind has been developed by the simultaneous generation of both positive and negative ions using two electrodes of opposite polarity placed in parallel. Unlike the conventional unipolar-generators, this bipolar configuration creates an ion wind, which moves away from both electrodes and yields a very low net charge on the device. The electro-hydrodynamic behavior of air-flow has been experimentally and numerically studied. The velocity of ion wind reaches values up to 1.25 m/s using low discharge current 5 μA with the kinetic conversion efficiency of 0.65% and the released net charge of −30 fA, 8 orders of magnitude smaller compared with the discharge current. Due to easy scalability and low net charge, the present configuration is beneficial to applications with space constraints and/or where neutralized discharge process is required, such as inertial fluidic units, circulatory flow heat transfer, electrospun polymer nanofiber to overcome the intrinsically instability of the process, or the formation of low charged aerosol.

A fully packaged convective vortex gyrometer actuated by a PZT diaphragm is reported. The flow circulates at higher velocity after each actuating circle to form a vortex in the desired chamber. The vortex is characterized by hotwire anemometry. The device is initially designed based on a numerical analysis whose results are used to set up the experiment. The angular rate sensing of the device is successfully tested using a turntable. The technique is a potential solution to various applications related to inertial sensing and fluidic amplifier.

In this paper, a PZT synthetic jet that can function as both an efficient pumping and mixing device is developed. Compare with the conventional design where the practice of controlling the internal flow is undertaken by microvalves structure, this approach promotes the durability and allows the device to work with different liquids at high Reynold number without losing of backflow from the diffuser, therefore provides efficient mixing. The pumping performance is applicable for commercialized counterparts while the homogeneous medium was obtained at downstream in the experiments, which was further confirmed by simulation. Notably, the chaotic mixing feature of the device is also applicable for immiscible liquids with the micro-droplet formation result at the outlet.

Carbon nanotubes (CNTs) are of high interest for sensing applications, owing to their superior mechanical strength, high Young’s modulus and low density. In this work, we report on a facile approach for the fabrication of carbon nanotube devices using a four terminal configuration. Oriented carbon nanotube films were pulled out from a CNT forest wafer and then twisted into a yarn. Both the CNT film and yarn were arranged on elastomer membranes/diaphragms which were arranged on a laser cut acrylic frame to form pressure sensors. The sensors were calibrated using a precisely controlled pressure system, showing a large change of the output voltage of approximately 50 mV at a constant supply current of 100 µA and under a low applied pressure of 15 mbar. The results indicate the high potential of using CNT films and yarns for pressure sensing applications.

In this paper, we propose a simple but effective preconditioning technique to improve the numerical stability of Integrated Radial Basis Function (IRBF) methods. The proposed preconditioner is simply the inverse of a well-conditioned matrix that is constructed using non-flat IRBFs. Much larger values of the free shape parameter of IRBFs can thus be employed and better accuracy for smooth solution problems can be achieved. Furthermore, to improve the accuracy of local IRBF methods, we propose a new stencil, namely Combined Compact IRBF (CCIRBF), in which (i) the starting point is the fourth-order derivative; and (ii) nodal values of first- and second-order derivatives at side nodes of the stencil are included in the computation of first- and second-order derivatives at the middle node in a natural way. The proposed stencil can be employed in uniform/nonuniform Cartesian grids. The preconditioning technique in combination with the CCIRBF scheme employed with large values of the shape parameter are tested with elliptic equations and then applied to simulate several fluid flow problems governed by Poisson, Burgers, convection–diffusion, and Navier–Stokes equations. Highly accurate and stable solutions are obtained. In some cases, the preconditioned schemes are shown to be several orders of magnitude more accurate than those without preconditioning.

In this study, we present a high-order numerical method based on a combined compact integrated RBF (IRBF) approximation for viscous flow and fluid structure interaction (FSI) problems. In the method, the fluid variables are locally approximated by using the combined compact IRBF, and the incompressible Navier-Stokes equations are solved by using the velocity-pressure formulation in a direct fully coupled approach. The fluid solver is verified through various problems including heat, Burgers, convection-diffusion equations, Taylor-Green vortex and lid driven cavity flows. It is then applied to simulate some FSI problems in which an elastic structure is immersed in a viscous incompressible fluid. For FSI simulations, we employ the immersed boundary framework using a regular Eulerian computational grid for the fluid mechanics together with a Lagrangian representation of the immersed boundary. For the immersed fibre/membrane FSI problems, although the order of accuracy of the present scheme is generally similar to FDM approaches reported in the literature, the present approach is nonetheless more accurate than FDM approaches at comparable grid spacings. The numerical results obtained by the present scheme are highly accurate or in good agreement with those reported in earlier studies of the same problems.

Flexible and stretchable electronics have a wide variety of wearable applications in portable sensors, flexible electrodes/heaters, flexible circuits and stretchable displays. Spinnable carbon nanotubes (CNTs) constructed on flexible substrates are potential materials for wearable sensing applications owing to their high thermal and electrical conductivity, low mass density and excellent mechanical properties. Here, we demonstrate a wearable thermal flow sensor for healthcare using lightweight, high strength, flexible CNT yarns as hotwires, pencil graphite as electrodes, and lightweight, recyclable and biodegradable paper as flexible substrates, without using any toxic chemicals. The CNT-based sensor which could be utilized to monitor respiratory diseases is comfortably affixed to human skin and detects real-time human respiration. We also successfully demonstrate the temperature detecting functionality integrated in the same sensor, which can measure body temperature using a non-contact mode. The results indicate that the CNT yarn can be used to develop a wide range of environment-friendly, low-cost and lightweight paper-based flexible devices for wearable applications in temperature and respiratory monitoring, and personal healthcare.

Recent advances in assembling Carbon NanoTubes (CNTs) into macrostructures with outstanding properties, such as high tensile strength, high conductivity and porosity, and strong corrosive resistance, have underpinned potentially novel applications. For example, in advanced electronics, bioengineering and nanomechanics. This paper focuses on the development of (i) the piezoresistive polydimethylsiloxane–CNT (PDMS–CNT) composite membrane, and (ii) the thermo-resistive CNT hotwire using a technique of producing highly aligned CNT yarns and films. Our experimental results show that while PDMS–CNT films possess an outperformed gauge factor (10.7) compared with ones of CNT films in recent publications and several metals, a clear linear relationship of the resistance versus the temperature for a hotwire using CNT yarn is observed. Hence, the work supplies valuable evidence in the use of CNT films and yarns in several potential applications as thermal sensing elements and anemometric hotwires, respectively.

Synthetic jet pump is a potential technique to improve the pumping performance by introducing a smart structure which can enhance counter-rotating vortexes. Aligning with this approach, a new structure of valveless micro-pump is developed in this work. The mechanism of the present micro-pump is based on the combination of the nozzle and a tesla element to rectify the synthetic jet. The new structure of “ace of spades” nozzle, named Tesla coupled nozzle, creates series of vortexes at the orifice of the pump chamber that allows to attenuate the reversed flows while fluid is drawn through the pump. The present micro-pump is simple but robust and can perform at rather low voltages.

A novel configuration of gyroscope using an electro-hydrodynamics flow circulating in a confined space is developed. The configuration includes three corona discharge based actuators to generate ionic flows inside three separated sub-channels which are connected to the main chamber. Ionic flows are merged together while they move through a nozzle installed at the main chamber entrance. After the merging phase, the conflated flow is diverged to move back to sub-channels where each accelerates at the discharge actuator. A master ring is installed at the end of the nozzle to remove any residual charge of the conflated ion flow. The ion flow velocity is measured using several hotwires installed in the main chamber. Since the configuration does not require any vibrating components, the present device is robust, cost-effective and consumes low power, hence, very potential in application of inertial sensing.

This paper reports for the first time a millimeter scale fully packaged device which generates a vortex flow of high velocity. The flow which is simply actuated by a PZT diaphragm circulates with a higher velocity after each actuating circle to form a vortex in a desired chamber. The design of such device is firstly conducted by a numerical analysis using OpenFOAM. Several numerical results are considered as the base of our experiment where a flow vortex is observed by a high speed camera. The present device is potential in various applications related to the inertial sensing, fluidic amplifier and micro/nano particle trapping and mixing.

We propose a novel numerical approach based on incompressible smoothed particle hydrodynamics and moving integrated radial basis function networks method, namely ISPH-MIRBFN, for solving incompressible viscous flow problems. In the ISPH method, the pressure is acquired from solving Poisson equation. In the present approach, the pressure Poisson equation is solved on a set of MIRBFN nodal points and the obtained results are then transferred to the SPH particles. The performance of the present method is investigated through several numerical examples including spin-down vortex, flows in a lid-driven closed-cavity and a lid-driven open-cavity with a prescribed bottom wall motion. Numerical results show that the proposed method reduces the spurious pressure fluctuations, yields a smoother pressure-field solution and maintains the computational efficiency when compared to the ISPH.

Developing flexible pressure sensors is of high interest in soft skin and tactile sensing applications. Here we demonstrate a simple approach to fabricating a sensitive resistive pressure sensor using carbon nanotube (CNT) micro-yarns as a pressure sensing element which is constructed on a stretchable acrylic elastomer. The sensor showed a high sensitivity of −0.86 Ω/kPa and a fast response time of 100 ms. Different to the longitudinal piezoresistive effect of micro-yarns, the high pressure sensitivity of the sensor was achieved owing to the compressibility of the micro-yarn in the direction perpendicular to the yarn axis. The sensor was also able to monitor finger pressure in real-time, demonstrating its potential for tactile sensing applications.

In this paper, an efficient electrostatic particle sampling system is developed based on the neutralized ion wind. Compare with the conventional schemes where unipolar ion is used to charge the airborne sample and the sampling stage is fixed as a part of high voltage circuit, the new approach allows sampling stage to be electrically floated and adds insignificant charge to the bioaerosol, thus reduces damages to the microorganisms while provides design flexibility and good collecting efficiency. The approach is suitable for the combination with a microfluidic interface to develop complex aerosol-to-hydrosol bio-samplers.

In this study, we present a numerical discretisation scheme, based on a fully coupled approach and compact local integrated radial basis function (CIRBF) approximations, to solve the Navier-Stokes equation in rectangular/non-rectangular domains. The velocity and pressure fields are simulated in a fully coupled manner [1] with Cartesian grids. The field variables are locally approximated in each direction by using CIRBF approximations defined over 3-node stencils, where nodal values of the first-and second-order derivatives of the field variables are also included [2, 3]. The present scheme, whose system matrix is sparse, is verified through the solutions of several test problems including Taylor-Green vortices. Highly accurate solutions are obtained.

This paper presents a numerical method for the Fokker-Planck Equation (FPE) based on mesoscopic modelling of dilute polymer solutions using Radial Basis Function (RBF) approaches. The stress is determined by the solution of a FPE while the velocity field is locally calculated via the solution of conservation Differential Equations (DEs) [1,2]. The FPE and PDEs are approximated separately by two different Integrated RBF methods. The time implicit discretisation of both FPE and PDEs is carried out using collocation methods where the high order RBF approximants improve significantly the accuracy of the numerical solutions and the convergence rate. As an illustration of the method, the time evolution of a start-up flow is studied for the Finitely Extensible Nonlinear Elastic (FENE) dumbbell model.

The analytic expressions of the mean nearest neighbour distance, the free energy, the absolute stabilizing temperature of alloy state and the melting temperature for substitution alloy AB with interstitial atom C and body-cantered cubic structure under pressure are derived by the statistical moment method. The theoretical results are applied to alloy FeCrC. Our calculated results are compared with other calculations and experimental data.