Magnetically actuated artificial cilia: the effect of fluid inertia

Natural cilia are hairlike microtubule-based structures that are able to move fluid on the micrometer scale using asymmetric motion. In this article, we follow a biomimetic approach to design artificial cilia lining the inner surfaces of microfluidic channels with the goal of propelling fluid. The artificial cilia consist of polymer films filled with superparamagnetic nanoparticles, which can mimic the motion of natural cilia when subjected to a rotating magnetic field. To obtain the magnetic field and associated magnetization local to the cilia, we solve the Maxwell equations, from which the magnetic body moments and forces can be deduced. To obtain the ciliary motion, we solve the dynamic equations of motion, which are then fully coupled to the Navier-Stokes equations that describe the fluid flow around the cilia, thus taking full account of fluid inertial forces. The dimensionless parameters that govern the deformation behavior of the cilia and the associated fluid flow are arrived at using the principle of virtual work. The physical response of the cilia and the fluid flow for different combinations of elastic, fluid viscous, and inertia forces are identified.     

Artificial cilia for active micro-fluidic mixing

In lab-on-chip devices, on which complete (bio-)chemical analysis laboratories are miniaturized and integrated, it is essential to manipulate fluids in sub-millimetre channels and sub-microlitre chambers. A special challenge in these small micro-fluidic systems is to create good mixing flows, since it is almost impossible to generate turbulence. We propose an active micro-fluidic mixing concept inspired by nature, namely by micro-organisms that swim through a liquid by oscillating microscopic hairs, cilia, that cover their surface. We have fabricated artificial cilia consisting of electro-statically actuated polymer structures, and have integrated these in a micro-fluidic channel. Flow visualization experiments show that the cilia can generate substantial fluid velocities, up to 0.6 mm s(-1). In addition, very efficient mixing is obtained using specially designed geometrical cilia configurations in a micro-channel. Since the artificial cilia can be actively controlled using electrical signals, they have exciting applications in micro-fluidic devices.     

Experimental investigation of the flow induced by artificial cilia

The fluid transport produced by rectangular shaped, magnetically actuated artificial cilia of 70 μm length and 20 μm width was determined by means of phase-locked Micro Particle Image Velocimetry (μPIV) measurements in a closed microfluidic chamber. The phase-averaged flow produced by the artificial cilia reached up to 130 μm s(-1) with an actuation cycle frequency of 10 Hz. Analysis of the measured flow data indicate that the present system is capable of achieving volume flow rates of V[combining dot above](cilia) = 14 ± 4 μl min(-1) in a micro channel of 0.5 × 5 mm(2) cross-sectional area when no back pressure is built up. This corresponds to an effective pressure gradient of 6 ± 1 Pa m(-1), which equals a pressure difference of 0.6 ± 0.1 mPa over a distance of 100 μm between two rows of cilia. These results were derived analytically from the measured velocity profile by treating the cilia as a thin boundary layer. While the cilia produce phase-averaged velocities of the order of O(10(2)μm s(-1)), time-resolved measurements showed that the flow field reverses two times during one actuation cycle inducing instantaneous velocities of up to approximately 2 mm s(-1). This shows that the flow field is dominated by fluid oscillations and flow rates are expected to increase if the beating motion of the cilia is further improved.     

Designing synthetic, pumping cilia that switch the flow direction in microchannels

Using computational modeling, we simulate the 3D movement of actuated cilia in a fluid-filled microchannel. The cilia are modeled as deformable, elastic filaments, and the simulations capture the complex fluid-structure interactions among these filaments, the channel walls, and the surrounding solution. The cilia are tilted with respect to the surface and are actuated by a sinusoidal force that is applied at the free ends. We find that these cilia give rise to a unidirectional flow in the system and by simply altering the frequency of the applied force we can controllably switch the direction of the net flow. The findings indicate that beating, synthetic cilia could be harnessed to regulate the fluid streams in microfluidic devices.     

Field-flow fractionation of magnetic particles in a cyclic magnetic field

Although magnetic field-flow fractionation (MgFFF) is emerging as a promising technique for characterizing magnetic particles, it still suffers from limitations such as low separation efficiency due to irreversible adsorption of magnetic particles on separation channel. Here we report a novel approach based on the use of a cyclic magnetic field to overcome the particle entrapment in MgFFF. This cyclic field is generated by rotating a magnet on the top of the spiral separation channel so that magnetic and opposing gravitational forces alternately act on the magnetic particles suspended in the fluid flow. As a result, the particles migrate transversely between the channel walls and their adsorption at internal channel surface is prevented due to short residence time which is controlled by the rotation frequency. With recycling of the catch-release process, the particles follow saw-tooth-like downstream migration trajectories and exit the separation channel at velocities corresponding to their sedimentation coefficients. A retention model has been developed on the basis of the combined effects of magnetic, gravitational fields and hydrodynamic flow on particle migration. Two types of core-shell structured magnetic microspheres with diameters of 6.04- and 9.40-μm were synthesized and used as standard particles to test the proposed retention theory under varying conditions. The retention ratios of these two types of particles were measured as a function of magnet rotation frequency, the gap between the magnet and separation channel, carrier flow rate, and sample loading. The data obtained confirm that optimum separation of magnetic particles with improved separation efficiency can be achieved by tuning rotation frequency, magnetic field gradient, and carrier flow rate. In view of the widespread applications of magnetic microspheres in separation of biological molecules, virus, and cells, this new method might be extended to separate magnetically labeled proteins or organisms for multiplex analyte identification and purification.     

Passive and Active Mixing in Microfluidic Devices

In microfluidics the Reynolds number is small, preventing turbulence as a tool for mixing, while diffusion is that slow that time does not yield an alternative. Mixing in microfluidics therefore must rely on chaotic advection, as well-known from polymer technology practice where on macroscale the high viscosity makes the Reynolds numbers low and diffusion slow. The mapping method is used to analyze and optimize mixing also in microfluidic devices. We investigate passive mixers like the staggered herringbone micromixer (SHM), the barrier embedded micromixer (BEM) and a three-dimensional serpentine channel (3D-SC). Active mixing is obtained via incorporating particles that introduce a hyperbolic flow in e.g. two dimensional serpentine channels. Magnetic beads chains-up in a flow after switching on a magnetic field. Rotating the field creates a physical rotor moving the flow field. The Mason number represents the ratio of viscous forces to the magnetic field strength and its value determines the fate of the rotor: a single, an alternating single and double, or a multiple part chain-rotor results. The type of rotor determines the mixing quality with best results in the alternating case where crossing streamlines introduce chaotic advection. Finally, an active mixing device is proposed that mimics the cilia in nature. The transverse flow induced by their motion indeed enhances mixing at the microscale.     

Generation of concentration gradient by controlled flow distribution and diffusive mixing in a microfluidic chip

We have developed a simple method to generate a concentration gradient in a microfluidic device. This method is based on the combination of controlled fluid distribution at each intersection of a microfluidic network by liquid pressure and subsequent diffusion between laminas in the downstream microchannel. A fluid dynamic model taking into account the diffusion coefficient was established to simulate the on-chip flow distribution and diffusion. Concentration gradients along a distance of a few hundred micrometers were generated in a series of microchannels. The gradients could be varied by carefully regulating the liquid pressure applied to the sample injection vials. The observed concentration gradients of fluorescent dyes generated on the microfluidic channel are consistent with the theoretically predicted results. The microfluidic design described in this study may provide a new tool for applications based on concentration gradients, including many biological and chemical analyses such as cellular reaction monitoring and drug screening.     

Estimation of zeta potential by electrokinetic analysis of ionic fluid flows through a divergent microchannel

The streaming potential is generated by the electrokinetic flow effect within the electrical double layer of a charged solid surface. Surface charge properties are commonly quantified in terms of the zeta potential obtained by computation with the Helmholtz-Smoluchowski (H-S) equation following experimental measurement of streaming potential. In order to estimate a rigorous zeta potential for cone-shaped microchannel, the correct H-S equation is derived by applying the Debye-Hückel approximation and the fluid velocity of diverging flow on the specified position. The present computation provides a correction ratio relative to the H-S equation for straight cylindrical channel and enables us to interpret the effects of the channel geometry and the electrostatic interaction. The correction ratio decreases with increasing of diverging angle, which implies that smaller zeta potential is generated for larger diverging angle. The increase of Debye length also reduces the correction ratio due to the overlapping of the Debye length inside of the channel. It is evident that as the diverging angle of the channel goes to nearly zero, the correction ratio converges to the previous results for straight cylindrical channel.     

Bi-directional flow induced by an AC electroosmotic micropump with DC voltage bias

This paper discusses the principle of biased alternating current electroosmosis (ACEO) and its application to move the bulk fluid in a microchannel, as an alternative to mechanical pumping methods. Previous EO-driven flow research has looked at the effect of electrode asymmetry and transverse traveling wave forms on the performance of electroosmotic pumps. This paper presents an analysis that was conducted to assess the effect of combining an AC signal with a DC (direct current) bias when generating the electric field needed to impart electroosmosis (EO) within a microchannel. The results presented here are numerical and experimental. The numerical results were generated through simulations performed using COMSOL 3.5a. Currently available theoretical models for EO flows were embedded in the software and solved numerically to evaluate the effects of channel geometry, frequency of excitation, electrode array geometry, and AC signal with a DC bias on the flow imparted on an electrically conducting fluid. Simulations of the ACEO flow driven by a constant magnitude of AC voltage over symmetric electrodes did not indicate relevant net flows. However, superimposing a DC signal over the AC signal on the same symmetric electrode array leads to a noticeable net forward flow. Moreover, changing the polarity of electrical signal creates a bi-directional flow on symmetrical electrode array. Experimental flow measurements were performed on several electrode array configurations. The mismatch between the numerical and experimental results revealed the limitations of the currently available models for the biased EO. However, they confirm that using a symmetric electrode array excited by an AC signal with a DC bias leads to a significant improvement in flow rates in comparison to the flow rates obtained in an asymmetric electrode array configuration excited just with an AC signal.     

Impedance‐based viscoelastic flow cytometry

Elastic nature of the viscoelastic fluids induces lateral migration of particles into a single streamline and can be used by microfluidic based flow cytometry devices. In this study, we investigated focusing efficiency of polyethylene oxide based viscoelastic solutions at varying ionic concentration to demonstrate their use in impedimetric particle characterization systems. Rheological properties of the viscoelastic fluid and particle focusing performance are not affected by ionic concentration. We investigated the viscoelastic focusing dynamics using polystyrene (PS) beads and human red blood cells (RBCs) suspended in the viscoelastic fluid. Elasto‐inertial focusing of PS beads was achieved with the combination of inertial and viscoelastic effects. RBCs were aligned along the channel centerline in parachute shape which yielded consistent impedimetric signals. We compared our impedance‐based microfluidic flow cytometry results for RBCs and PS beads by analyzing particle transit time and peak amplitude at varying viscoelastic focusing conditions obtained at different flow rates. We showed that single orientation, single train focusing of nonspherical RBCs can be achieved with polyethylene oxide based viscoelastic solution that has been shown to be a good candidate as a carrier fluid for impedance cytometry.     

The profile control and displacement mechanism of continuous and discontinuous phase flooding agent

In order to further explore the profile control and displacement mechanism of continuous and discontinuous phase flooding agent, the concentration distribution mathematical model of microsphere dispersion system in different branch channels is established, and its particle phase separation is simulated by using microfluidic technology. On this basis, in order to research the migration and plugging characteristics of microspheres, the visualization experiments on micro oil displacement mechanism of polymer solution and microspheres are carried out. And the experiment on the injection, migration, and plugging performance of microspheres in the multi-point core is performed. Results indicate that microspheres are in the axis of the channel due to the effect of fluid shear stress, and preferentially enter the large channel with low resistance and high flow velocity, which results in no particle or few particles in the small aperture and low flow velocity channel. The microspheres have better migration and retention capacity in the core and their migration shows the characteristic of “fluctuating pressure change”. Compared with polymer solution, the alleviation of “entry profile inversion” and the better migration and plugging performance of microsphere dispersion system can realize deep fluid diversion and expand sweep volume.     

A study on dual solutions for water-based hybrid nanofluids flowing through convergent channel with dissipative heat transport

Over the years, the fluid flows in conjunction with thermal transport between non-parallel surfaces having converging nature is of great significance due to their broad spectrum of applications, which include fluid flows through nozzles in petroleum engineering, blood flow in arteries, lubrication systems, automobile radiators, thermal pumps, and water purification processes. Additionally, hybrid nanofluid is a prolific topic because of its thermal properties and potentials which provide a better performance even compared with common nanofluid in optimizing heat transfer. Therefore, this article presents a numerical simulation to investigate the heat transport characteristics of hybrid nanofluids in Jeffery-Hamel flow through a convergent channel. The considered hybrid nanofluids are composed of Copper (Cu) and Graphene-oxide (Go) as suspended nanoparticles and water as base fluid. This analysis further includes the impacts of viscous dissipation and magnetic field. A mathematical model for fluid flow and heat transfer are constructed with the help of cylindrical polar coordinates. The governing equations are converted into a system of ordinary differential equations (ODEs) by Lie symmetry group transformation. A MATLAB code is exercise to get the numerical solutions for flow and thermal distributions. An interesting phenomenon is that dual solutions are obtained in the computation. Thus, a comprehensive discussion is included on the dual solutions for various involved variables. The current findings may be employed in petroleum science, r biomedical scientists, polymer industry, etc.     

Magnetic Micromotors for Multiple Motile Sperm Cells Capture,Transport, and Enzymatic Release

An integrated system combining a magnetically-driven micromotor and a synthetized protein-based hyaluronic acid (HA) microflake is presented for the in situ selection and transport of multiple motile sperm cells (ca. 50). The system appeals for targeted sperm delivery in the reproductive system to assist fertilization or to deliver drugs. The binding mechanism between the HA microflake and sperm relies on the interactions between HA and the corresponding sperm HA receptors. Once sperm are captured within the HA microflake, the assembly is trapped and transported by a magnetically-driven helical microcarrier. The trapping of the sperm-microflake occurs by a local vortex induced by the microcarrier during rotation-translation under a rotating magnetic field. After transport, the microflake is enzymatically hydrolyzed by local proteases, allowing sperm to escape and finally reach the target location. This cargo-delivery system represents a new concept to transport not only multiple motile sperm but also other actively moving biological cargoes.     

Modeling electroosmotic and pressure-driven flows in porous microfluidic devices: zeta potential and porosity changes near the channel walls

This work presents analytical solutions for both pressure-driven and electroosmotic flows in microchannels incorporating porous media. Solutions are based on a volume-averaged flow model using a scaling of the Navier-Stokes equations for fluid flow. The general model allows analysis of fluid flow in channels with porous regions bordering open regions and includes viscous forces, permitting consideration of porosity and zeta potential variations near channel walls. To obtain analytical solutions problems are constrained to the linearized Poisson-Boltzmann equation and a variation of Brinkman's equation [Appl. Sci. Res., Sect. A 1, 27 (1947); 1, 81 (1947)]. Cases include one continuous porous medium, two adjacent regions of different porosities, or one open channel adjacent to a porous region, and the porous material may have a different zeta potential than that of the channel walls. Solutions are described for two geometries, including flow between two parallel plates or in a cylinder. The model illustrates the relative importance of porosity and zeta potential in different regions of each channel.     

Nanodrop of an Ising magnetic fluid on a solid surface

The density functional theory of inhomogeneous simple fluids is extended to an Ising magnetic fluid in contact with a solid surface, which is subjected to an external uniform or nonuniform magnetic field. The system is described by two coupled integral equations regarding the magnetic moment and fluid density distributions. The dependence of the contact angle that a nanodrop makes with the solid surface on the parameters involved in the magnetic interactions between the molecules of fluid and between the molecules of fluid and an external magnetic field is calculated. For the uniform magnetic field, the contact angle increases with increasing magnetic field, approaching an asymptotic value that depends on the strength of the fluid-fluid magnetic interactions. In the nonuniform field generated by a permanent magnet, the contact angle first increases with increasing magnetic field B(M) and then decreases, with the decrease being almost linear for large values of B(M). The obtained results are in qualitative agreement with the experimental data on the contact angle of magnetic drops on a solid surface available in the literature.     

A simple mechanism for reliable particle sorting in a microdevice with combined electroosmotic and pressure-driven flow

Selective transport and sorting of particles in microfluidic devices by electroosmosis is complicated due to superposition of uncontrolled hydrodynamic pressure contributions on the electroosmotic force. In this paper, we present a microfluidic concept for the reliable and simple separation and sorting of particles in a microchip by electroosmosis combined with pressure-driven flow. The presented device allows fluid quantities to be switched and particles to be sorted within a channel manifold using only a single power supply with fixed voltage and an electric switch. Consequently, chip operation and fluid switching procedure are greatly simplified compared to a situation, in which several independent power sources are used for flow balancing, as is the common procedure. With the triple-T channel design presented, backpressure flow disturbing the electrokinetic fluid and particle separation process is eliminated by introducing controlled opposed hydrodynamic flow of buffer from side channels. This pressure-driven flow is generated on-chip by setting up differences in the reservoir pressures in a defined manner. A detailed flow analysis based on the equivalence of fluid flow and electric current is performed and the conditions for reliable chip function are worked out.     

Microfluidic Wheatstone bridge for rapid sample analysis

We developed a microfluidic analogue of the classic Wheatstone bridge circuit for automated, real-time sampling of solutions in a flow-through device format. We demonstrate precise control of flow rate and flow direction in the "bridge" microchannel using an on-chip membrane valve, which functions as an integrated "variable resistor". We implement an automated feedback control mechanism in order to dynamically adjust valve opening, thereby manipulating the pressure drop across the bridge and precisely controlling fluid flow in the bridge channel. At a critical valve opening, the flow in the bridge channel can be completely stopped by balancing the flow resistances in the Wheatstone bridge device, which facilitates rapid, on-demand fluid sampling in the bridge channel. In this article, we present the underlying mechanism for device operation and report key design parameters that determine device performance. Overall, the microfluidic Wheatstone bridge represents a new and versatile method for on-chip flow control and sample manipulation.     

A pneumatic micromixer facilitating fluid mixing at a wide range flow rate for the preparation of quantum dots

A novel fluid micromixer based on pneumatic perturbation and passive structures was developed. This micromixer facilitates integration and is applicable to fluid mixing over a wide range of flow rates. The microfluidic mixing device consists of an S-shaped structure with two mixing chambers and two barriers, and two pneumatic chambers designed over the S-shaped channel. The performance of the micromixer for fluids with wide variation of flow rates was significantly improved owing to the integration of the pneumatic mixing components with the passive mixing structures. The mixing mechanism of the passive mixing structures was explored by numerical simulation, and the influencing factors on the mixing efficiency were investigated. The results showed that when using a gas pressure of 0.26 MPa and a 100 m-thick polydimethylsiloxane (PDMS) pneumatic diaphragm, the mixing of fluids with flow rates ranging from 1 to 650 L/min was achieved with a pumping frequency of 50 Hz. Fast synthesis of CdS quantum dots was realized using this device. Smaller particles were obtained, and the size distribution was greatly improved compared with those obtained using conventional methods.