Linear Asymptotic Analysis Research Articles

On hybrid electroosmotic kinetics for field-effect-reconfigurable nanoparticle trapping in a four-terminal spiral microelectrode array.

Induced-charge electroosmosis (ICEO) has attracted tremendous popularity for driving fluid motion from the microfluidic community since the last decade, while less attention has been paid to ICEO-based nanoparticle manipulation. We propose herein a unique concept of hybrid electroosmotic kinetics (HEK) in terms of bi-phase ICEO (BICEO) actuated in a four-terminal spiral electrode array, for effective electrokinetic enrichment of fluorescent polystyrene nanoparticles on ideally polarizable metal strips. First, by alternating the applied AC voltage waves between consecutive discrete terminals, the flow stagnation lines where the sample nanoparticles aggregate can be switched in time between two different distribution modes. Second, we innovatively introduce the idea of AC field-effect flow control on BICEO; by altering the combination of gating voltage sequence, not only the number of circulative particle trapping lines is doubled, but the collecting locations can be flexibly reconfigured as well. Third, hydrodynamic streaming of DC-biased BICEO is tested in our device design, wherein the global linear electroosmosis dominates BICEO contributed from both AC and DC components, resulting in a reduction of particle enrichment area, while with a sharp increase in sample transport speed inside the bulk phase. The flow field associated with HEK is predicted using a linear asymptotic analysis under Debye-Huckel limit, with the simulation results in qualitative agreement with in-lab observations of nanoparticle trapping by exploiting a series of improved ICEO techniques. This work provides an affordable and field-deployable platform for real-time nanoparticle trapping in the context of dilute electrolyte.

Induced-charge electrokinetics in rotating electric fields: A linear asymptotic analysis

Concerning the electroconvective analyte manipulation in microfluidics, we describe the basic physics of fluid flow driven by rotating induced-charge electro-osmosis (ROT-ICEO), which occurs on the planar surface of a single floating electrode in an external rotating electric field. First, based on a linear asymptotic analysis, the dynamic flow stagnation line in ROT-ICEO induced on the bipolar electrode from a rotary Debye screening charge revolves synchronously with the applied rotating fields. A net hydrodynamic torque is then generated that acts on any fluid or particle sample to produce either a synchronous or asynchronous co-field rotation depending on the frequency of the ac signal. Next, from the synergy between the hydrodynamic and electrochemical ion relaxations, an analytical solution of the sample rotation rate subject to ROT-ICEO slipping on an ideally polarizable surface is obtained for different frequency ranges and determined by the transient nature of the rotating electro-osmotic flow oscillating at twice the field frequency. To visualize the flow field in ROT-ICEO, experiments were performed with fluorescent tracer nanoparticles; they exhibited concentric rotational behavior at the polarized phase interface. Formed like the arms of a nebula disk, the four twisted tails of nanoparticles can be arbitrarily directed under voltage-phase rectification. These experimental results are in good agreement with our mathematical simulations using the Debye–Hückel approximation on ROT-ICEO.

On AC-Field-Induced Nonlinear Electroosmosis next to the Sharp Corner-Field-Singularity of Leaky Dielectric Blocks and Its Application in on-Chip Micro-Mixing.

Induced-charge electroosmosis has attracted lots of attention from the microfluidic community over the past decade. Most previous researches on this subject focused on induced-charge electroosmosis (ICEO) vortex streaming actuated on ideally polarizable surfaces immersed in electrolyte solutions. Starting from this point, we conduct herein a linear asymptotic analysis on nonlinear electroosmotic flow next to leaky dielectric blocks of arbitrary electrical conductivity and dielectric permittivity in harmonic AC electric fields, and theoretically demonstrate that observable ICEO fluid motion can be generated at high field frequencies in the vicinity of nearly insulating semiconductors, a very low electrical conductivity, of which can evidently increase the double-layer relaxation frequency (inversely proportional to the solid permittivity) to be much higher than the typical reciprocal RC time constant for induced double-layer charging on ideally polarizable surfaces. A computational model is developed to study the feasibility of this high-frequency vortex flow field of ICEO for sample mixing in microfluidics, in which the usage of AC voltage signal at high field frequencies may be beneficial to suppress electrochemical reactions to some extent. The influence of various parameters for developing an efficient mixer is investigated, and an integrated arrangement of semiconductor block array is suggested for achieving a reliable mixing performance at relatively high sample fluxes. Our physical demonstration with high-frequency ICEO next to leaky dielectric blocks using a simple channel structure offers valuable insights into the design of high-throughput micromixers for a variety of lab-on-a-chip applications.

Asymptotic and numerical solutions of three‐dimensional boundary‐layer flow past a moving wedge

We consider a laminar boundary‐layer flow of a viscous and incompressible fluid past a moving wedge in which the wedge is moving either in the direction of the mainstream flow or opposite to it. The mainstream flows outside the boundary layer are approximated by a power of the distance from the leading boundary layer. The variable pressure gradient is imposed on the boundary layer so that the system admits similarity solutions. The model is described using 3‐dimensional boundary‐layer equations that contains 2 physical parameters: pressure gradient (β) and shear‐to‐strain‐rate ratio parameter (α). Two methods are used: a linear asymptotic analysis in the neighborhood of the edge of the boundary layer and the Keller‐box numerical method for the full nonlinear system. The results show that the flow field is divided into near‐field region (mainly dominated by viscous forces) and far‐field region (mainstream flows); the velocity profiles form through an interaction between 2 regions. Also, all simulations show that the subsequent dynamics involving overshoot and undershoot of the solutions for varying parameter characterizing 3‐dimensional flows. The pressure gradient (favorable) has a tendency of decreasing the boundary‐layer thickness in which the velocity profiles are benign. The wall shear stresses increase unboundedly for increasing α when the wedge is moving in the x‐direction, while the case is different when it is moving in the y‐direction. Further, both analysis show that 3‐dimensional boundary‐layer solutions exist in the range −1<α<∞. These are some interesting results linked to an important class of boundary‐layer flows.

Simulation of non-axisymmetric floating zone crystal growth under microgravity

The possibility of growing crystals of non-circular cross-section by using the floating zone technique is considered, basing the analysis on the isothermal liquid bridge model, and restricting the study to a linear asymptotic analysis. An almost square initial seed is considered in more detail, although the analysis is general and can be applied to other initial shapes, not only of the seed but also of the supply rod, that can be of any cross-section. The influence of non-circular seed and/or feed cross-section shape, and of a possible axial acceleration typical of microgravity platforms (sounding rockets and space labs), on both the liquid interface shape and the solid grown shape, are analysed, including the stability limits by breaking of the molten bridge.

DIFFUSION LAG TIME FOR MULTIPLE AND PERIODIC LAMINATES

The permeability and lag time for a heterogeneous diffusion system, in which the diffusivity and partition coefficient for the diffusant are dependent on position, are formulated in terms of a linear asymptotic analysis. A repeated integration of the diffusion equation is used to obtain the time dependence of the total solute release into the receiver, Q(t). The asymptotic form of Q(t) is linear in time. The slope, and intercept of this linear asymptote with the time axis, respectively, give formulas for the steady-state permeability and lag time. These formulas are then applied to diffusion systems of multiple laminates, consisting of a series of different homogeneous slabs. Thus, for the first time, a concise treatment of diffusion in multiple laminates is obtained. The formulas are also applied to periodic laminates, consisting of a series of identical slabs, but with position-dependent diffusivity and partition coefficient. We found that the lag time can be well approximated by (nh))2/(6D eff), where ...