Hydrodynamics of gas–liquid Taylor flow in rectangular microchannels

The effect of fluid properties and operating conditions on the generation of gas–liquid Taylor flow in microchannels has been investigated experimentally and numerically. Visualisation experiments and 2D numerical simulations have been performed to study bubble and slug lengths, liquid film hold-up and bubble velocities. The results show that the bubble and slug lengths increase as a function of the gas and liquid flow rate ratios. The bubble and slug lengths follow the model developed by Garstecki et?al. (Lab chip 6:437–446, 2006) and van Steijn et?al. (Chem Eng Sci 62:7505–7514, 2007), however, the model coefficients appear to be dependent on the liquid properties and flow conditions in some cases. The ratio of the bubble velocity to superficial two-phase velocity is close to unity, which confirms a thin liquid film under the assumption of a stagnant liquid film. Numerical simulations confirm the hypothesis of a stagnant liquid film and provide information on the thickness of the liquid film.     

Pressure drop of three-phase liquid–liquid–gas slug flow in round microchannels

In this paper we present a model for the calculation of pressure drop of three-phase liquid–liquid–gas slug flow in microcapillaries of a circular cross section. Introduced models consist of terms attributing for frictional and interfacial pressure drop, incorporating the presence of a stagnant thin film at the wall of the channel. Different formulations of the interfacial pressure drop equation were employed, using expressions developed by Bretherton (J Fluid Mech 10:166–188, 1961), Warnier et al. (Microfluid Nanofluid 8:33–45, 2010) or Ratulowski and Chang (Phys Fluids A 1:1642–1655, 1989). Models were validated experimentally using oleic acid–water–nitrogen and heptane–water–nitrogen three-phase flows in round Teflon or Radel R microchannels of 254- and 508-µm nominal inner diameter, for capillary numbers Ca _b between 10^?4 and 4.9 × 10^?1 and Reynolds numbers Re between 0.095 and 300. Best agreement between measured and calculated values of pressure drop, with relative error between ?22 and 19 % or ?20 and 16 %, is reached for Warnier’s or Ratulowski and Chang’s interfacial pressure drop equation, respectively. The results prove that three-phase slug flow pressure drop can be successfully predicted by extending existing two-phase slug flow correlations. Good agreement of Bretherton’s equation was reached only at lower Ca numbers, indicating that an extension of the interfacial pressure drop equation as performed by Warnier et al. (Microfluid Nanofluid 8:33–45, 2010) or Ratulowski and Chang (Phys Fluids A 1:1642–1655, 1989) for higher capillary numbers is necessary. Additionally it was demonstrated that pressure drop increases substantially if dry slug flow occurs or if microchannels with significant surface roughness are employed. Those influences were not accounted for in the models presented.     

Flow-induced deformation of compliant microchannels and its effect on pressure–flow characteristics

We report theoretical and experimental investigations of flow through compliant microchannels in which one of the walls is a thin PDMS membrane. A theoretical model is derived that provides an insight into the physics of the coupled fluid–structure interaction. For a fixed channel size, flow rate and fluid viscosity, a compliance parameter \(f_{\text{p}}\) is identified, which controls the pressure–flow characteristics. The pressure and deflection profiles and pressure–flow characteristics of the compliant microchannels are predicted using the model and compared with experimental data, which show good agreement. The pressure–flow characteristics of the compliant microchannel are compared with that obtained for an identical conventional (rigid) microchannel. For a fixed channel size and flow rate, the effect of fluid viscosity and compliance parameter \(f_{\text{p}}\) on the pressure drop is predicted using the theoretical model, which successfully confront experimental data. The pressure–flow characteristics of a non-Newtonian fluid (0.1 % polyethylene oxide solution) through the compliant and conventional (rigid) microchannels are experimentally measured and compared. The results reveal that for a given change in the flow rate, the corresponding modification in the viscosity due to the shear thinning effect determines the change in the pressure drop in such microchannels.     

Numerical simulation of gas flow in rough microchannels: hybrid kinetic–continuum approach versus Navier–Stokes

The flow field in a rough microchannel is numerically analyzed using a hybrid solver, dynamically coupling kinetic and Navier–Stokes solutions computed in rarefied and continuum subareas of the flow field, respectively, and a full Navier–Stokes solver. The rough surface is configured with triangular roughness elements, with a maximum relative roughness of 5 % of the channel height. The effects of Mach number, Knudsen number (or Reynolds number) and roughness height are investigated and discussed in terms of Poiseuille number and mass flow rate. Discrepancies between full Navier–Stokes and hybrid solutions are analyzed, assessing the range of validity of Navier–Stokes equations provided with first-order slip boundary conditions for modeling gas flow along a rough surface. Results indicate that the roughness increases Poiseuille number and decreases mass flux in comparison with those for the smooth microchannel. Increasing rarefaction results in further enhancement of roughness effect. At the same time, the compressibility effect is more noticeable than the roughness one, although the compressibility effect is alleviated by increase in the rarefaction. It was found that, although the Navier–Stokes solution of the flow in a smooth channel is accurate up to Kn = 0.1, when relative roughness height is higher than 1.25 % significant errors already appear at Kn = 0.02.     

Prediction of flow pattern of gas–liquid flow through circular microchannel using probabilistic neural network

The present study attempts to develop a flow pattern indicator for gas–liquid flow in microchannel with the help of artificial neural network (ANN). Out of many neural networks present in literature, probabilistic neural network (PNN) has been chosen for the present study due to its speed in operation and accuracy in pattern recognition. The inbuilt code in MATLAB R2008a has been used to develop the PNN. During training, superficial velocity of gas and liquid phase, channel diameter, angle of inclination and fluid properties such as density, viscosity and surface tension have been considered as the governing parameters of the flow pattern. Data has been collected from the literature for air–water and nitrogen–water flow through different circular microchannel diameters (0.53, 0.25, 0.100 and 0.050 mm for nitrogen–water and 0.53, 0.22 mm for air–water). For the convenience of the study, the flow patterns available in literature have been classified into six categories namely; bubbly, slug, annular, churn, liquid ring and liquid lump flow. Single PNN model is unable to predict the flow pattern for the whole range (0.53 mm–0.050 mm) of microchannel diameter. That is why two separate PNN models has been developed to predict the flow patterns of gas–liquid flow through different channel diameter, one for diameter ranging from 0.53 mm to 0.22 mm and another for 0.100 mm–0.05 mm. The predicted map and their transition boundaries have been compared with the corresponding experimental data and have been found to be in good agreement. Whereas accuracy in prediction of transition boundary obtained from available analytical models used for conventional channel is less for all diameter of channel as compared to the present work. The percentage accuracy of PNN (～94% for 0.53 mm ID and ～73% for 0.100 mm ID channel) has also been found to be higher than the model based on Weber number (～86% for 0.53 mm ID and ～36% for 0.05 mm ID channel).     

Enhancement of heat transfer in a convergent/divergent channel by using carbon nanotubes in the presence of a Darcy–Forchheimer medium

This article explores the influence of thermal radiation on the flow and heat transfer of single-walled carbon nanotubes over both a convergent and divergent channel. Flow is induced due to a Darcy–Forchheimer medium. Further, the heat transfer mechanism is analyzed in the presence of a thermal radiation process. Guided by some appropriate similarity transformations, the fundamental PDEs are converted into a self-similar system of coupled non-linear ODEs. The findings are obtained with the help of the Runge–Kutta-45-based shooting method. The roles of the Reynolds number, porosity parameter, inertia coefficient parameter, Prandtl number and radiation parameter are presented graphically. Results are displayed and show that the rate of heat transfer is higher in a divergent channel as compared to a convergent channel.

     

Transient simulations of the electrophoretic motion of a cylindrical particle through a 90° corner

The trajectory of a cylindrical particle driven by electrophoresis was transiently simulated as the particle moves through a 90° corner. A variety of system parameters were tested to determine their impact on the particle motion. The zeta potential, channel width, and particle aspect ratio were shown to have a minimal effect on the particle motion. Conversely, the initial vertical position of the particle and initial angle with respect to the horizontal had a significant impact on the particle motion. The presence of the 90° corner acts to reduce the initial distribution of angles to the vertical of 90° to less than 30°, demonstrating the possibility of using a corner as a passive control element as part of a larger microfluidic system. However, the reduction in angle is limited to the area near the corner posing a limitation on this means of control.     

QoE–aware optimization of multimedia flow scheduling

This paper deals with the subjective quality maximization problem when scheduling multimedia traffic flows in a shared channel. In order to quantify such user satisfaction a utility function dependent on flow transfer delay is used. In this context, we formulate the Quality of Experience aware resource allocation optimization problem as a Markov Decision Process. This model is analytically unsolvable in general, and as an approximate solution we develop a simple and tractable index rule based on Gittins approach, originally aimed just at minimizing mean flow delay. As concluded from simulation results, when evaluating subjective quality performance this novel index rule proposal outperforms the most relevant existing scheduling disciplines.     

Transient performance of flow over a rotating object placed eccentrically inside a microchannel—numerical study

Industrial applications today are demanding the implementation of microelectromechanical systems (MEMS) into their products. These are mechanical devices that are able to perform work, and yet have characteristic lengths less than 1 mm. As a result, the Reynolds number is typically low, which indicates the dominance of viscous forces. When a cylinder is placed eccentrically inside a microchannel, where the rotor axis is perpendicular to the channel axis, a net force is transferred to the fluid as a result of the unequal shear stresses on the upper and lower surfaces of the rotor. Consequently, this causes the surrounding fluid in the channel to displace towards the microchannel outlet. The present numerical investigation is a comparative study of transient flow behavior in a microchannel with rotating cylinders with different cross-sectional geometries. The effects of channel height, eccentricity, Reynolds number, and pump load were studied, as well as the development of their respective streamlines and pressure contours. The steady state results were compared with existing numerical and experimental results, and the comparisons showed very good agreement.List of symbols C_D cylinder drag coefficient - C_L cylinder lift coefficient - C_M cylinder moment coefficient - d diagonal length of rotor (m) - F_L lift force on cylinder per unit length (N/m) - F_D drag force on cylinder per unit length (N/m) - h channel height (m) - L perimeter of rotor (m) - M moment on cylinder (N m) - ṁ mass flow rate (kg/s) - P_in inlet pressure (Pa) - P_out outlet pressure (Pa) - P* non-dimensional pressure - P channel pressure rise (Pa) - P* non-dimensional pressure rise - Q non-dimensional volume flow rate - Re Reynolds number - R normal distribution ratio - S curve length (m) - S non-dimensional channel height - t time (s) - t* non-dimensional time - t time step size (s) - ū average velocity inside microchannel (m/s) - u* non-dimensional average velocity - U cylinder surface velocity (m/s) - fluid velocity vector (m/s) - y_c distance from channel axis to cylinder center (m)Greek letters body forces per unit mass (m/s²) - rotor eccentricity - fluid dynamic viscosity (Pa s) - fluid kinematic viscosity (m²/s) - angle sweep over surface, =s/L (rad) - fluid density (kg/m³) - fluid shear stress (Pa) - * non-dimensional fluid shear stress - rotor angular velocity     

Numerical predictions of backward-facing step flows in microchannels using extended Navier–Stokes equations

Flows in microchannels were successfully predicted, in the past, both analytically and numerically, employing the extended Navier–Stokes equations (ENSE). In ENSE, the self-diffusion transport of mass, together with the resulting momentum and heat transport, is taken into account properly and the same is omitted in the classical Navier–Stokes equations. The ENSE have been employed here to numerically predict backward-facing step flows in microchannels, and the predictions are summarized in this paper. The results obtained by employing ENSE are compared with the available literature data computed by both direct simulation Monte Carlo and slip-velocity-based simulations. The good agreement of the present results with those given in the literature evidently points out that the ENSE can be applied to gas flows through complex microchannel geometries.     

Optimal power flow of HVDC system using teaching–learning-based optimization algorithm

In this paper, a solution to the optimal power flow (OPF) problem in electrical power networks is presented considering high voltage direct current (HVDC) link. Furthermore, the effect of HVDC link converters on the active and reactive power is evaluated. An objective function is developed for minimizing power loss and improving voltage profile. Gradient-based optimization techniques are not viable due to high number of OPF equations, their complexity and equality and inequality constraints. Hence, an efficient global optimization method is used based on teaching–learning-based optimization (TLBO) algorithm. The performance of the suggested method is evaluated on a 5-bus PJM network and compared with other algorithms such as particle swarm optimization, shuffled frog-leaping algorithm and nonlinear programming. The results are promising and show the effectiveness and robustness of TLBO method.

     

Study of subsonic�Csupersonic gas flow through micro/nanoscale nozzles using unstructured DSMC solver

We use an extended direct simulation Monte Carlo (DSMC) method, applicable to unstructured meshes, to numerically simulate a wide range of rarefaction regimes from subsonic to supersonic flows through micro/nanoscale converging–diverging nozzles. Our unstructured DSMC method considers a uniform distribution of particles, employs proper subcell geometry, and follows an appropriate particle tracking algorithm. Using the unstructured DSMC, we study the effects of back pressure, gas/surface interactions (diffuse/specular reflections), and Knudsen number on the flow field in micro/nanoscale nozzles. If we apply the back pressure at the nozzle outlet, a boundary layer separation occurs before the outlet and a region with reverse flow appears inside the boundary layer. Meanwhile, the core region of inviscid flow experiences multiple shock-expansion waves. In order to accurately simulate the outflow, we extend a buffer zone at the nozzle outlet. We show that a high viscous force creation in the wall boundary layer prevents any supersonic flow formation in the divergent part of the nozzle if the Knudsen number exceeds a moderate magnitude. We also show that the wall boundary layer prevents forming any normal shock in the divergent part. In reality, Mach cores would appear at the nozzle center followed by bow shocks and expansion region. We compare the current DSMC results with the solution of the Navier–Stokes equations subject to the velocity slip and temperature jump boundary conditions. We use OpenFOAM as a compressible flow solver to treat the Navier–Stokes equations.     

On the class of λ-statistically convergent difference sequences of fuzzy numbers

In this study, we introduce the sets $\left[ V,\lambda ,p\right] _{\Updelta }^{{\mathcal{F}}},\left[ C,1,p\right] _{\Updelta }^{{\mathcal{F}}}$ and examine their relations with the classes of $ S_{\lambda }\left( \Updelta ,{\mathcal{F}}\right)$ and $ S_{\mu }\left( \Updelta ,{\mathcal{F}}\right)$ of sequences for the sequences $\left( \lambda _{n}\right)$ and $\left( \mu _{n}\right) , 0<p<\infty $ and difference sequences of fuzzy numbers.