MHD channel flow control in 2D: Mixing enhancement by boundary feedback

A nonlinear Lyapunov-based boundary feedback control law is proposed for mixing enhancement in a 2D magnetohydrodynamic (MHD) channel flow, also known as Hartmann flow, which is electrically conducting, incompressible, and subject to an external transverse magnetic field. The MHD model is a combination of the Navier-Stokes PDE and the Magnetic Induction PDE, which is derived from the Maxwell equations. Pressure sensors, magnetic field sensors, and micro-jets embedded into the walls of the flow domain are employed for mixing enhancement feedback. The proposed control law, designed using passivity ideas, is optimal in the sense that it maximizes a measure related to mixing (which incorporates stretching and folding of material elements), while at the same time minimizing the control and sensing efforts. A DNS code is developed, based on a hybrid Fourier pseudospectral-finite difference discretization and the fractional step technique, to numerically assess the controller.     

Magnetohydrodynamic state estimation with boundary sensors

We present a PDE observer that estimates the velocity, pressure, electric potential and current fields in a magnetohydrodynamic (MHD) channel flow, also known as Hartmann flow. This flow is characterized by an electrically conducting fluid moving between parallel plates in the presence of an externally imposed transverse magnetic field. The system is described by the inductionless MHD equations, a combination of the Navier-Stokes equations and a Poisson equation for the electric potential under the so-called inductionless MHD approximation in a low magnetic Reynolds number regime. We identify physical quantities (measurable on the wall of the channel) that are sufficient to generate convergent estimates of the velocity, pressure, and electric potential field away from the walls. Our observer consists of a copy of the linearized MHD equations, combined with linear injection of output estimation error, with observer gains designed using backstepping. Pressure, skin friction and current measurements from one of the walls are used for output injection. For zero magnetic field or nonconducting fluid, the design reduces to an observer for the Navier-Stokes Poiseuille flow, a benchmark for flow control and turbulence estimation. We show that for the linearized MHD model the estimation error converges to zero in the L² norm. Despite being a subject of practical interest, the problem of observer design for nondiscretized 3-D MHD or Navier-Stokes channel flow has so far been an open problem.     

Thermal radiation effects on flow of Jeffery fluid in converging and diverging stretchable channels

Neural Computing and Applications - This paper investigates the flow of Jeffery fluid between converging and diverging channels. The walls of the channel are assumed to be capable for stretching or...     

Numerical analysis on electroosmotic flows in a microchannel with rectangle-waved surface roughness using the Poisson–Nernst–Planck model

The present study has numerically investigated two-dimensional electroosmotic flows in a microchannel with dielectric walls of rectangle-waved surface roughness to understand the roughness effect. For the study, numerical simulations are performed by employing the Nernst–Planck equation for the ionic species and the Poisson equation for the electric potential, together with the traditional Navier–Stokes equation. Results show that the steady electroosmotic flow and ionic-species transport in a microscale channel are well predicted by the Poisson–Nernst–Planck model and depend significantly on the shape of surface roughness such as the amplitude and periodic length of wall wave. It is found that the fluid flows along the surface of waved wall without involving any flow separation because of the very strong normal component of EDL (electric double layer) electric field. The flow rate decreases exponentially with the amplitude of wall wave, whereas it increases linearly with the periodic length. It is mainly due to the fact that the external electric-potential distribution plays a crucial role in driving the electroosmotic flow through a microscale channel with surface roughness. Finally, the present results using the Poisson–Nernst–Planck model are compared with those using the traditional Poisson–Boltzmann model which may be valid in these scales.     

Aggregate growth and breakup in particulate suspension flow through a micro-nozzle

A computational study is reported on the growth of aggregates in flow of a particulate suspension through a micro-nozzle. The study employs a soft-sphere discrete element method (DEM) with van der Waals adhesion force between the particles in two-dimensional, incompressible channel flow. A new computational approach for particle transport in complex domains is developed which uses a background Cartesian grid for efficient flow field interpolation at the particle locations, together with a level-set method to represent the nozzle boundaries in the particle computation. Three mechanisms for the growth or breakup of particulate aggregates in the micro-nozzle are examined: (1) enhanced particle collision due to lateral compression as fluid elements pass through the nozzle, (2) stretching of aggregates due to axial stretching of fluid elements, and (3) collision and intermittent adhesion of particles to the nozzle wall. The first of these mechanisms leads to aggregate growth, and the second to aggregate breakup. The wall collision and adhesion mechanism can enhance either aggregate growth or breakup, but it is found in most cases to be a primary agent in the breakup of incident aggregates as part of the aggregate attaches to the nozzle wall and is torn from the remainder of the aggregate due to the high shear near the walls. Simplified models for these processes are developed and used to interpret the trends observed in the DEM simulations. The effects of particle adhesion parameter, particle size and density, particle concentration, and nozzle geometry are examined. It is found that passage of a particulate suspension through a nozzle can lead to either a substantial decrease in aggregate size or a modest increase under different conditions, depending in part on the size of the incident aggregates.     

Mathematical modelling for pulsatile flow of Casson fluid along with magnetic nanoparticles in a stenosed artery under external magnetic field and body acceleration

In the present paper, the magnetohydrodynamics effects on flow parameters of blood carrying magnetic nanoparticles flowing through a stenosed artery under the influence of periodic body acceleration are investigated. Blood is assumed to behave as a Casson fluid. The governing equations are nonlinear and solved numerically using finite difference schemes. The effects of stenotic height, yield stress, magnetic field, particle concentration and mass parameters on wall shear stress, flow resistance and velocity distribution are analysed. It is found that wall shear stress and flow resistance values are considerably enhanced when an external magnetic field is applied. The velocity values of fluid and particles are appreciably reduced when a magnetic field is applied on the model. It is significant to note that the presence of nanoparticles, magnetic field and yield stress tend to increase the plug core radius. Increased wall shear stress and flow resistance affects the circulation of blood in the human cardiovascular system. The results obtained from the study can be used in normalizing the values of the model parameters and hence can be used for medical applications. The presence of magnetic field helps to slow down the flow of fluid and magnetic particles associated with it. The magnetic particles of nanosize developed in recent days are biodegradable and used in biomedical applications. Biomagnetic principles and biomagnetic particles as drug carriers are used in cancer treatments.

     

Numerical study of unsteady hydromagnetic Generalized Couette flow of a reactive third-grade fluid with asymmetric convective cooling

Unsteady hydromagnetic Generalized Couette flow and heat transfer characteristics of a reactive variable viscosity incompressible electrically conducting third grade fluid in a channel with asymmetric convective cooling at the walls in the presence of uniform transverse magnetic field is studied. It is assumed that the chemical kinetics in the flow system is exothermic and the convective heat transfer at the channel surface with the surrounding environment follow the Newton’s law of cooling. The coupled nonlinear partial differential equations governing the problem are derived and solved numerically using an unconditionally stable and convergent semi-implicit finite difference scheme. Both numerical and graphical results are presented and physical aspects of the problem are discussed with respect to various parameters embedded in the system.     

Microfluidic separation of magnetic particles with soft magnetic microstructures

This paper demonstrates simple and cost-effective microfluidic devices for enhanced separation of magnetic particles by using soft magnetic microstructures. By injecting a mixture of iron powder and polydimethylsiloxane (PDMS) into a prefabricated channel, an iron–PDMS microstructure was fabricated next to a microfluidic channel. Placed between two external permanent magnets, the magnetized iron–PDMS microstructure induces localized and strong forces on the magnetic particles in the direction perpendicular to the fluid flow. Due to the small distance between the microstructure and the fluid channel, the localized large magnetic field gradients result a vertical force on the magnetic particles, leading to enhanced separation of the particles. Numerical simulations were developed to compute the particle trajectories and agreed well with experimental data. Systematic experiments and numerical simulation were conducted to study the effect of relevant factors on the transport of superparamagnetic particles, including the shape of iron–PDMS microstructure, mass ratio of iron–PDMS composite, width of the microfluidic channel, and average flow velocity.     

Numerical simulation of free surface flows on a fish bypass

A computational fluid dynamics (CFD) model is developed to better understand the complex flow field inside a free surface fish bypass constructed at Rocky Reach Dam. This facility consists of two identical parallel channels, with fish screens on the side walls of each channel, and a pump station recirculating 96% of incoming flows into the forebay. The model is based on the Reynolds-averaged Navier-Stokes (RANS) equations, with a standard κ-ε turbulence model. The volume of fluid (VOF) method is used to predict free surface elevations. A proportional controller is implemented in the model to achieve a target flow rate at the pump exits. The pressure drop in the fish screens is modeled using porous media. Quantitative validation and visualization of the flow field characteristics indicate that CFD modeling may be a useful tool for fish passage design.     

Numerical study of asymmetric laminar flow of micropolar fluids in a porous channel

A numerical study is presented for the two-dimensional flow of a micropolar fluid in a porous channel. The channel walls are of different permeability. The fluid motion is superimposed by the large injection at the two walls and is assumed to be steady, laminar and incompressible. The micropolar model due to Eringen is used to describe the working fluid. The governing equations of motion are reduced to a set of non-linear coupled ordinary differential equations (ODEs) in dimensionless form by using an extension of Berman’s similarity transformations. A numerical algorithm based on finite difference discretization is employed to solve these ODEs. The results obtained are further improved by Richardson’s extrapolation for higher order accuracy. Comparisons with the previously published work are performed and are found to be in a good agreement. It has been observed that the velocity and microrotation profiles change from the most asymmetric shape to the symmetric shape across the channel as the parameter R or the permeability parameter A are varied between their extreme values. The results indicate that larger the injection velocity at a wall relative to the other is, smaller will be the shear stress at it than that at the other. The position of viscous layer has been found to be more sensitive to the permeability parameter A than to the parameter R. The micropolar fluids reduce shear stress and increase couple stress at the walls as compared to the Newtonian fluids.     

Induced mixing electrokinetics in a charged corrugated nano-channel: towards a controlled ionic transport

To perform a fluid analysis for electroosmotic flows in micro- and nano-channels, it is necessary to mix various fluid contents in micro- and nano-scales. It is observed that fluids in electroosmotic flow exhibits Reynolds number effect as the flow exerts very weak inertial force and it requires long channel for mixing of different layers and species through diffusion process. Hence, if the desired length scale of mixing is large, an enormous time is needed for the molecules to be thoroughly mixed by diffusion. The theory of dynamic equations on time scale is used to study the stability of these systems. It is found that such a system may exhibits an unstable nature for overlapping electric double layer field with fluctuating velocities and stability is preserved for zero linear growth coefficient. To obtain an improved understanding of mixing performance, a numerical study is performed with the variation of channel height when more than one ionic species with channels patterned with heterogeneity is considered. The wall heterogeneity may be created by placing some blocks of unequal size (with or without charged) close to the channel wall or some external potential patches. The analytical results for the transport characteristics of electroosmotic flow obtained are compared with the direct numerical simulation of the Navier–Stokes equation, Nernst–Plank equation, and Poisson equation, simultaneously. It is shown that heterogeneous potential could generate complex flow structures and the increment of species layers at different levels of the channel cross section from inlet to outlet significantly improve the mixing rate.     

Magnetically controlled valve for flow manipulation in polymer microfluidic devices

A simple, external in-line valve for use in microfluidic devices constructed of polydimethylsiloxane (PDMS) is described. The actuation of the valve is based on the principle that flexible polymer walls of a liquid channel can be pressed together by the aid of a permanent magnet and a small metal bar. In the presence of a small NdFeB magnet lying below the channel of interest, the metal bar is pulled downward simultaneously pushing the thin layer of PDMS down thereby closing the channel stopping any flow of fluid. The operation of the valve is dependent on the thickness of the PDMS layer, the height of the channel, the gap between the chip and the magnet and the strength of the magnet. The microfluidic channels are completely closed to fluid flows ranging from 0.1 to 1.0 μL/min commonly used in microfluidic applications.     

A chaotic mixer for magnetic bead-based micro cell sorter

An efficient magnetic force driven mixer with simple configuration is designed, fabricated, and tested. It is designed to facilitate the mixing of magnetic beads and biomolecules in a microchannel, where mixing is unavoidably inefficient due to its low Reynolds number. With appropriate temporal variations of the force field, chaotic mixing is achieved, hence the mixing becomes effective. The mixing device consists of embedded microconductors as a magnetic field source and a microchannel that guides the streams of working fluid. It is demonstrated that a pair of integrated micro conductors provides a local magnetic field strong enough to attract nearby magnetic beads. Mixing of magnetic beads is accomplished by applying a time-dependent control signal to a row of conductors, at the Reynolds number of as low as 10/sup -2/. Two-dimensional numerical simulation has been performed to design the configuration of the channel and electrodes, which creates chaotic motion of beads. It is found that a simple two-dimensional serpentine channel geometry with the transverse electrodes is able to create the stretching and folding of material lines, which is a manifestation of chaos. The mixing pattern predicted by the simulation has been confirmed by both flow visualization and PTV (particle tracking velocimetry) in the chaotic mixer fabricated, which should greatly increase the attachment of beads onto the target biomolecules. The optimum frequency of applied control signal is searched by evaluating the Lyapunov exponent in both numerical and experimental particle tracking. It is found that the range of optimum Strouhal number is 5相似文献   

Diffusion of a chemically reactive species of a power-law fluid past a stretching surface

A numerical solution for the steady magnetohydrodynamic (MHD) non-Newtonian power-law fluid flow over a continuously moving surface with species concentration and chemical reaction has been obtained. The viscous flow is driven solely by the linearly stretching sheet, and the reactive species emitted from this sheet undergoes an isothermal and homogeneous one-stage reaction as it diffuses into the surrounding fluid. Using a similarity transformation, the governing non-linear partial differential equations are transformed into coupled nonlinear ordinary differential equations. The governing equations of the mathematical model show that the flow and mass transfer characteristics depend on six parameters, namely, the power-law index, the magnetic parameter, the local Grashof number with respect to species diffusion, the modified Schmidt number, the reaction rate parameter, and the wall concentration parameter. Numerical solutions for these coupled equations are obtained by the Keller-Box method, and the solutions obtained are presented through graphs and tables. The numerical results obtained reveal that the magnetic field significantly increases the magnitude of the skin friction, but slightly reduces the mass transfer rate. However, the surface mass transfer strongly depends on the modified Schmidt number and the reaction rate parameter; it increases with increasing values of these parameters. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially shear-thinning phenomena. Shear thinning reduces the wall shear stress.     

Rotational motion and lateral migration of an elliptical magnetic particle in a microchannel under a uniform magnetic field

We have numerically investigated the motion of an elliptical magnetic particle in a microfluidic channel subjected to an external uniform magnetic field. By using the direct numerical simulation method and an arbitrary Lagrangian–Eulerian technique, the involved particle–fluid-magnetic field problem can be solved in a fully coupled manner. The numerical predictions of the particle trajectory and orientation with and without a uniform magnetic field are in qualitative agreement with the existing experimental results, and numerical results have revealed the impacts of key parameters such as inlet flow velocity, magnetic field direction, and particle shape on the rotational motion and lateral migration of the elliptical particle. Meanwhile, the shape-based particle separation in a low Reynolds number flow with the aid of an applied uniform magnetic field has also been numerically demonstrated.     

Simulating magnetic positive positioning of cryogenic propellants in a transient acceleration field

A computational simulation of magnetic positive positioning (MP²) is developed to model cryogenic propellant reorientation in reduced gravity. Previous efforts have successfully incorporated an electromagnetic field model into an axisymmetric, two-dimensional, incompressible fluid flow model yielding accurate predictions of fluid motion induced by a magnetic field. To simulate MP², a three-dimensional magnetic field and magnetic force model was developed as a feature of a commercially available fluid flow model which has been well validated. The computational tool was then improved upon to model magnetically induced flows in a transient acceleration field. Simulation predictions obtained with the enhanced model are compared to available reduced gravity experiment data. Evidence is presented and conclusions are drawn that support the continued use of the simulation as viable modeling and predictive tool in the continuing study of MP².     

Magnetohydrodynamic flow with slippage in an annular duct for microfluidic applications

In this paper, we investigate theoretically the 3D laminar flow of an electrolyte in an annular duct driven by a Lorentz force. The duct is formed by two concentric electrically conducting cylinders limited by insulating bottom and top walls. A uniform magnetic field acts along the axial direction, while a potential difference is applied between the cylinders so that a radial electric current traverses the fluid. The interaction of the current and the magnetic field produces a Lorentz force that drives an azimuthal flow. The steady flow is solved using a Galerkin method with Bessel–Fourier series in the radial direction and trigonometric series along the vertical direction, allowing different combinations of slip conditions at the walls. The orthogonality of both series with the general boundary conditions of the third kind is used to find an analytic approximation. Velocity patterns and flow rates are explored by varying the aspect ratio of the duct and the gap between the cylinders, as well as the slippage at the walls. Results can provide useful information for optimization and design of annular microfluidic devices.     

Particle flow control by induced dipolar interaction of superparamagnetic microbeads

Magnetic particles diluted in liquid agglomerate in rod-like particle arrays if an external homogeneous magnetic field is applied. This work introduces a method to specifically exploit particle–particle interaction to obtain flow control of magnetic particles without changing the motion state of the carrier liquid. Experiments show the possibility to uncouple the particle flux from the motion state of liquid. We show how this method may be applied to design a microfluidic geometry in which the particle flow in a specific direction is either enabled or suppressed by the relative orientation of the fluid velocity and the external field.     

Controlling capillary-driven surface flow on a paper-based microfluidic channel

This paper describes two methods for controlling capillary-driven liquid flow on microfluidic channels. Unlike flow driven by external forces, capillary-driven flow is dominated by interfacial phenomena and, therefore, is sensitive to the channel geometry and chemical composition (surface energy) along the channel. The first method to control fluid flow is based on altering surface energy along the channel through regulation of UV irradiation time, which enables adjusting the contact angle along the fluid path. The slowing down (delay) of the liquid flow depends on the stripe length and its position in the channel. Using this technique, we generated flow delays spanning from a second to over 3 min. In the second approach, we manipulated the flow velocity by introducing contractions and expansions in the channel. The methods used herein are inexpensive and can be incorporated to the microfluidic channel fabrication step. They are capable of controlling liquid flow with precise time delays without introducing the foreign matter in the fluidic device.     

Peristaltic transport of a third order fluid under the effect of a magnetic field

The peristaltic transport of a third order fluid in a planar channel is considered. The fluid is electrically conducting by a transverse magnetic field. The perturbation solution is obtained using small Deborah number. Expressions of stream function, longitudinal velocity and pressure gradient valid for long wavelength are developed. Numerical integration is performed to analyze the effect of Hartman number on the pressure rise and frictional force. It is noted that both Hartman and Deborah numbers suppress the flow.