Anomalous mixing behaviour in rotationally actuated microfluidic devices

We analyse the characteristics of two-fluid mixing in T-shaped microchannels on rotating platforms (Lab-on-a-Compact-Disk framework). Three regimes of mixing were identified based on the distinct flow behaviour in each of these regimes. A diffusion-based mixing regime was obtained for low rotation speeds. A Coriolis force based mixing regime was observed for intermediate rotation speeds, which introduced some nontrivial aspects in the mixing behaviour, which was explained through scaling analysis. At very high rotational speeds, rapid mixing close to the junction was achieved by exploiting flow instabilities (instability based mixing). A good agreement between the theoretical calculations and the experimental observations was obtained.     

Magnetohydrodynamic effects on a charged colloidal sphere with arbitrary double-layer thickness

An analytical study is presented for the magnetohydrodynamic (MHD) effects on a translating and rotating colloidal sphere in an arbitrary electrolyte solution prescribed with a general flow field and a uniform magnetic field at a steady state. The electric double layer surrounding the charged particle may have an arbitrary thickness relative to the particle radius. Through the use of a simple perturbation method, the Stokes equations modified with an electric force term, including the Lorentz force contribution, are dealt by using a generalized reciprocal theorem. Using the equilibrium double-layer potential distribution from solving the linearized Poisson-Boltzmann equation, we obtain closed-form formulas for the translational and angular velocities of the spherical particle induced by the MHD effects to the leading order. It is found that the MHD effects on the particle movement associated with the translation and rotation of the particle and the ambient fluid are monotonically increasing functions of κa, where κ is the Debye screening parameter and a is the particle radius. Any pure rotational Stokes flow of the electrolyte solution in the presence of the magnetic field exerts no MHD effect on the particle directly in the case of a very thick double layer (κa→0). The MHD effect caused by the pure straining flow of the electrolyte solution can drive the particle to rotate, but it makes no contribution to the translation of the particle.     

Thin layer flow cell with a rotating disk electrode

A channel-type electrochemical flow cell with a rotating disk electrode has been constructed and characterized. The work shows that the effect of rotation is to enhance the rate of mass transport. At rotation speeds higher than 900 rpm the response becomes independent of the flow rate and channel thickness. As a result, low flow rates can be used without sacrificing the sensitivity. Analytical advantages are demonstrated using liquid chromatography, stripping analysis, stopped rotation voltammetry and flow injection analysis.     

Batch-mode mixing on centrifugal microfluidic platforms

We present two novel fluidic concepts to drastically accelerate the process of mixing in batch-mode (stopped-flow) on centrifugal microfluidic platforms. The core of our simple and robust setup exhibits a microstructured disk with a round mixing chamber rotating on a macroscopic drive unit. In the first approach, magnetic beads which are prefilled into the mixing chamber are periodically deflected by a set of permanent magnets equidistantly aligned at spatially fixed positions in the lab-frame. Their radial positions alternatingly deviate by a slight positive and negative offset from the mean orbit of the chamber to periodically deflect the beads inbound and outbound during rotation. Advection is induced by the relative motion of the beads with respect to the liquid which results from the magnetic and centrifugal forces, as well as inertia. In a second approach--without magnetic beads--the disk is spun upon periodic changes in the sense of rotation. This way, inertia effects induce stirring of the liquids. As a result, both strategies accelerate mixing from about 7 minutes for mere diffusion to less than five seconds. Combining both effects, an ultimate mixing time of less than one second could be achieved.     

Electrokinetic lift force for a charged particle moving near a charged wall — a modified theory and experiment

We present the refined theory of the electrokinetic lift force for a charged particle moving at a charged wall at the distance much larger than the double layer thickness. The theory is based on the lubrication approximation for the solution of the Stokes equation for the flow around a long cylinder moving near a solid wall. The “thin double layer” approximation is used to solve the ionic balance and electro-osmotic flow equations. The electrokinetic lift force is then obtained by integration of the viscous stress tensor as well as the Maxwell stress tensor over the particle surface. The resulting lift force for the cylinder translating, rotating at the wall as well as for the stationary cylinder in the wall shear flow, is considered. Following this, we apply the Derjaguin approximation to transform the obtained results to the sphere–wall geometry and we compare our theoretical predictions with the measurements of the electrokinetic lift force performed in the “colloidal particle collider” apparatus for the latex particles suspended in the glycerol–water solutions. Our theoretical results for the electrokinetic lift force exceeds by several orders of magnitude one obtained from the previously developed theory and are in a good agreement with experimental findings.     

Étude d'un procédé de brassage électromagnétique en écoulement de Stokes

This note deals with a process allowing electromagnetic mixing of a conductor fluid in Stokes flow. The flow, which is generated by two inductor wires (arranged around a cylindrical vat), undergoes a rotation. In order to solve analytically this electromagnetic flow, we use a magnetostatic pattern and we replace the dynamics in the electromagnetic layer by a tangential velocity. We superimpose then a periodic rotation on the flow (triangular signal). The investigated parameters are an a dimensional number (τ), which compares the velocities of the rotation and the flow, the inversion's periodicity of the rotation (k) and the distance of the wires from the vat (d). In studying the stretching and scattering of a drop of the fluid, an optimal choice of these parameters is subsequently suggested. Finally, prospects are considered of the possibilities of stationary three-dimensional and mixing.     

Design and simulation of the micromixer with chaotic advection in twisted microchannels

Chaotic mixers with twisted microchannels were designed and simulated numerically in the present study. The phenomenon whereby a simple Eulerian velocity field may generate a chaotic response in the distribution of a Lagrangian marker is termed chaotic advection. Dynamic system theory indicates that chaotic particle motion can occur when a velocity field is either two-dimensional and time-dependent, or three-dimensional. In the present study, micromixers with three-dimensional structures of the twisted microchannel were designed in order to induce chaotic mixing. In addition to the basic T-mixer, three types of micromixers with inclined, oblique and wavelike microchannels were investigated. In the design of each twisted microchannel, the angle of the channels' bottoms alternates in each subsection. When the fluids enter the twisted microchannels, the flow sways around the varying structures within the microchannels. The designs of the twisted microchannels provide a third degree of freedom to the flow field in the microchannel. Therefore, chaotic regimes that lead to chaotic mixing may arise. The numerical results indicate that mixing occurs in the main channel and progressively larger mixing lengths are required as the Peclet number increased. The swaying of the flow in the twisted microchannel causes chaotic advection. Among the four micromixer designs, the micromixer with the inclined channel most improved mixing. Furthermore, using the inclined mixer with six subsections yielded optimum performance, decreasing the mixing length by up to 31% from that of the basic T-mixer.     

Simulation study of particle–fluid two-phase coupling flow field and its influencing factors of crystallization process

Obtaining the morphology of two-phase flow field accurately through experiments is very challenging, due to the complexity and the drainage area diversity of particle–fluid two-phase flow. Depending on the particle concentration, size, flow velocity, and so on, the two-phase flow tends to be in a more complex form, known as coupled flow status. Crystallisation process within a crystalliser is a typical engineering application of particle–fluid two-phase flow, and hence, the flow field within a potassium salt crystallizer is implemented to simulate the crystal suspension and to mix flow state during a continuous crystallisation process. Because the two-fluid model treats the particle phase and fluid phase as two distinct continuous media, this simulation model takes the effect of virtual mass force into considerations. The enhanced two-fluid model is then applied to investigate the influencing factors of the coupled flow field between the potassium salt particles and the fluid in the crystalliser under various operating conditions. The results indicated that the stirring speed, the concentration of the feed particles, and the particle size affected the distribution of coupled flow field at different levels and, thus, affected the crystallisation phenomena of a potassium salt. Among those factors, the stirring speed appears to have the most obvious effect on the flow field, as it affects the velocity of the two-phase flow. In the conditions listed in this paper, the minimum stirring speed is roughly 50 rpm to form a stable and circular flow field in the crystallizer, and the maximum particle size is controlled at around 12 mm and the feed particle concentration of roughly 32% to ensure cyclic crystallization. The research method used in this article provides a baseline for the study of the coupled flow field of particle–fluid two-phase flow and its influencing factors. This research also states theoretical guidance for the optimisation of operating conditions in the production and application of potassium salt crystallizer.     

Interaction between bending vibrations and molecular rotation: a model study

The classical mechanics of the interaction between bending vibration and molecular rotation is studied for a simple rigid bender model. A one-dimensional representation of rotational motion enables surfaces of section to be constructed. Quasiperiodic, resonant and chaotic motions are identified, and related to characteristic patterns of vibration-rotation energy flow.     

The hydrodynamics of the amperometric detector flow cell with a rotating disk electrode

Series of photographs of the sample flow pattern in the flow cell with a stationary as well as a rotating disk electrode (RDE) were taken with a motor-driven camera. With the stationary electrode, the flow pattern in the cell was mushroom-like. Rotating the electrode generated a secondary fluid motion in the flow cell which manifested itself as vertical circulation of the solution present in the flow cell. A qualitative hydrodynamic explanation of the observed flow patterns is given. Peak broadening effects induced by the RDE in the flow cell were observed only at very fast rotation speeds and high nozzle heights. The response surface of the amperometric detector flow cell with the RDE as a function of the rotation speed and the nozzle height was measured by applying the detector in combination with high-performance liquid chromatography, flow injection analysis and continuous flow analysis. Model curve-fitting calculations indicate that the flow pattern in the flow cell can be laminar or turbulent, depending on the exact cell geometry, rotation speed and nozzle height.     

Remote Actuation of a Light-Emitting Device Based on Magnetic Stirring and Wireless Electrochemistry

We propose a straightforward access to a rotating light-emitting device powered by wireless electrochemistry. A magnetic stirrer is used to rotate a light-emitting diode (LED) due to the intrinsic magnetic properties of the tips that contain iron. At the same time, the LED is submitted to an electric field and acts as a bipolar electrode. The electrochemical processes that are coupled on both extremities of the LED drive an electron flow across the device, resulting in light emission. The variation of the LED alignment in time enables an alternating light emission that is directly controlled by the rotation rate. The stirring also enables a continuous mixing of the electrolyte that improves the stability of the output signal. Finally, the LED brightness can readily reveal a change of chemical composition in the electrolyte solution.     

Numerical and experimental investigation of ‘water fan’ effect due to electrohydrodynamic force in a microchamber

Electrohydrodynamics is commonly used in microfluidics to control and manipulate the fluid. Though there are studies on the rotation flow in suspended films, the thin film liquid is easily broken and cannot last long hence not applicable in specific applications. Here, we established a three‐dimensional microchamber embedded with two pairs of microelectrodes to investigate the rotational phenomenon of bulk of liquid which we called ‘water fan’ effect based on the electrohydrodynamics force. When proper voltages were applied on these microelectrodes, the tornado‐like rotation would be generated. Both the numerical and experimental results showed that the controllable and continuous rotation could be achieved in the microchamber. In addition, the concentration effect resulting from the rotation flow was also observed. The proposed method offers great promises in providing theoretical and practical guideline in microfluidic devices for mixing, separating, and cooling applications.     

Chaotic mixing in microdroplets

We describe a general methodology for introducing thorough chaotic mixing in microdroplets. The mixing properties of fluid flows in microdroplets are governed by their symmetries, which give rise to invariant surfaces serving as barriers to transport. Complete three-dimensional mixing by chaotic advection requires destruction of all flow invariants. To illustrate this idea, we demonstrate that complete mixing can be obtained in a time-dependent flow produced by moving a microdroplet along a two-dimensional path. The theoretical predictions are confirmed by experiments that use the thermocapillary effect to manipulate microdroplets.     

Thermophoretic Motion of a Sphere Parallel to an Insulated Plane

An analytical study is presented for the thermophoresis of a sphere in a constant applied temperature gradient parallel to an adiabatic plane. The Knudsen number is assumed to be small so that the fluid flow can be described by a continuum model with a thermal creep and a hydrodynamic slip at the particle surface. A method of reflections is used to obtain the asymptotic formulas for the temperature and velocity fields in the quasisteady situation. The thermal insulated plane may be a solid wall (no-slip) and/or a free surface (perfect-slip). The boundary effect on the thermophoretic motion is found to be weaker than that on the axisymmetric thermophoresis of a sphere normal to a plane with constant temperature. In comparison with the motion driven by gravitational force, the interaction between the particle and the boundary is less significant under thermophoresis. Even so, the interaction between the plane and the particle can be very strong when the gap thickness approaches zero. For the thermophoretic motion of a particle parallel to a solid plane, the effect of the plane surface is to reduce the translational velocity of the particle. In the case of particle migration parallel to a free surface due to thermophoresis, the translating velocity of a particle can be either greater or smaller than that which would exist in the absence of the plane surface, depending on the relative thermal conductivity and the surface properties of the particle and its relative distance from the plane. Not only the translational velocity but also the rotational velocity of the thermophoretic sphere near the plane boundary is formulated analytically. The rotating direction of the particle is strongly dominated by its surface properties and the internal-to-external thermal conductivity. Besides the particle motion, the thickness of the thermophoretic boundary layer is evaluated by considering the thermophoretic mobility. Generally speaking, a free surface exerts less influence on the particle movement than a solid wall. Copyright 2000 Academic Press.     

Boundary effects on the electrophoretic motion of cylindrical particles: concentrically and eccentrically-positioned particles in a capillary

The bounded electrophoretic motion of a cylindrical particle in a circular cylindrical microchannel is explored for two cases: (1) the particle is located on the centerline of a channel (concentrically), with a symmetric wall boundary condition since gap width is constant throughout; and (2) the particle is at an eccentric location in the channel, with an asymmetric boundary condition set by the walls. The objective is to determine the effect of different boundary conditions, geometries, and physical properties on the velocity and orientation of the cylinder with respect to the boundary. A theoretical model for the motion of the cylinder is presented and the problem is solved numerically. The steady-state simulations show that the velocity of the cylinder is reduced at small gap widths for the concentric case, but the velocity is increased at small gap widths for the eccentric case. When the cylinder is angled with respect to the horizontal in the symmetric case or is near the boundary in the asymmetric case, vertical and rotational components of velocity are predicted. In such cases, transient simulations are appropriate for most accurately representing particle motion. Two such simulations are included herein and show both horizontal and vertical translation plus rotation of the particle as a function of time.     

Design parameters for rotating cylindrical filtration

Rotating cylindrical filtration displays significantly reduced plugging of filter pores and build-up of a cake layer, but the number and range of parameters that can be adjusted complicates the design of these devices. Twelve individual parameters were investigated experimentally by measuring the build-up of particles on the rotating cylindrical filter after a fixed time of operation. The build-up of particles on the filter depends on the rotational speed, the radial filtrate flow, the particle size and the gap width. Other parameters, such as suspension concentration and total flow rate are less important. Of the four mechanisms present in rotating filters to reduce pore plugging and cake build-up, axial shear, rotational shear, centrifugal sedimentation and vortical motion, the evidence suggests rotational shear is the dominant mechanism, although the other mechanisms still play minor roles. The ratio of the shear force acting parallel to the filter surface on a particle to the Stokes drag acting normal to the filter surface on the particle due to the difference between particle motion and filtrate flow can be used as a non-dimensional parameter that predicts the degree of particle build-up on the filter surface for a wide variety of filtration conditions.     

Analysis of rotation-driven electrokinetic flow in microscale gap regions of rotating disk systems

In the present study, a novel theoretical model is developed for the analysis of rotating thermal-fluid flow characteristics in the presence of electrokinetic effects in the microscale gap region between two parallel disks under specified electrostatic, rotational, and thermal boundary conditions. The major flow configuration considered is a rotor-stator disk system. Axisymmetric Navier-Stokes equations with consideration of electric body force stemming from streaming potential are employed in the momentum balance. Variations of the fluid viscosity and permittivity with the local fluid temperature are considered. Between two disks, the axial distribution of the electric potential is determined by the Poisson equation with the concentration distributions of positive and negative ions obtained from Nernst-Planck equations for convection-diffusion of the ions in the flow field. Effects of disk rotation and electrostatic and thermal conditions on the electrokinetic flow and thermal characteristics are investigated. The electrohydrodynamic mechanisms are addressed with an interpretation of the coupling nature of the electric and flow fields. Finally, solutions with electric potential determined by employing nonlinear or linearized Poisson-Boltzmann equation and/or invoking assumptions of constant properties are compared with the predictions of the present model for justification of various levels of approximation in solution of the electrothermal flow behaviors in rotating microfluidic systems.     

The annular space between rotating cylinders as a geometry for open-channel liquid chromatography

Summary The annular slit between two cylinders, one of which is rotating, looks attractive for carrying out open channel LC, with chromatographic flow in the axial direction. Under ideal conditions, the dynamics of chromatographic separation are as good as those prevailing in an open tubular column.As is the case for Myers and Gidding's open parallelplate LC, the sample capacity of the proposed geometry can be much higher than of open tubular chromatography.Rotation of one of the cyclinders offers two advantages, which may be helpful in achieving the ideal situation. First, the thickness of the slit between the cylinders tends to be more uniform at higher rotation speeds. Second, the increased mixing of the liquid in the direction perpendicular to chromatographic flow can be expected to diminish the detrimental effect of any remaining lack of uniformity in the thickness of the slit and the capacity factors.Preliminary results with such a system are reported.Dedicated to Professor J. F. K. Huber on the occasion of his 60th birthday.     

Boundary effects on electrophoresis of a colloidal cylinder with a nonuniform zeta potential distribution

The electrophoretic motion of a long dielectric circular cylinder with a general angular distribution of its surface potential under a transversely imposed electric field in the vicinity of a large plane wall parallel to its axis is analyzed. The thickness of the electric double layers adjacent to the solid surfaces is assumed to be much smaller than the particle radius and the gap width between the surfaces, but the applied electric field can be either perpendicular or parallel to the plane wall. The presence of the confining wall causes three basic effects on the particle velocity: (1) the local electric field on the particle surface is enhanced or reduced by the wall; (2) the wall increases viscous retardation of the moving particle; (3) an electroosmotic flow of the suspending fluid may exist due to the interaction between the charged wall and the tangentially imposed electric field. Through the use of cylindrical bipolar coordinates, the Laplace and Stokes equations are solved analytically for the two-dimensional electric potential and velocity fields, respectively, in the fluid phase, and explicit formulas for the quasisteady electrophoretic and angular velocities of the cylindrical particle are obtained. To apply these formulas, one has only to calculate the multipole moments of the zeta potential distribution at the particle surface. It is found that the existence of a plane wall near a nonuniformly charged particle can cause its translation or rotation which does not occur in an unbounded fluid with the same applied electric field.     

Numerical study of a novel induced-charge electrokinetic micro-mixer

A novel micro-mixer based on the induced-charge electrokinetic motion of an electrically conducting particle is proposed and numerically demonstrated in this paper. For most microfluidic applications, it is desired to mix different streams of solutions rapidly in a continuous flow mode. Therefore, in this work, we consider a mixing chamber containing an electrically conducting particle and the mixing chamber is located in the middle of a microchannel. Vortices are generated around the electrically conducting particle in an aqueous solution due to the interaction of the applied electric field and the induced surface charge on the particle. These vortices will enhance significantly the mixing of different solutions around the particle. The effectiveness of mixing the two streams entering the mixing chamber is numerically studied as functions of the applied electric field. Excellent mixing can be achieved in this system under two perpendicularly applied electric fields. The proposed micro-mixer is simple and easy to be fabricated for lab-on-a-chip applications.