Computational electrochemistry: Lattice Boltzmann simulations of voltammetry at microelectrodes

This paper describes the development of a two-dimensional lattice Boltzmann method for the simulation of mass transport at a range of microelectrode geometries using potential step and linear sweep voltammetric techniques. The simulations of the current response for microband and micro hemicylinder geometries were compared with previously published analytical solutions. Excellent agreement between the numerical models and the analytical solutions was observed for a series of experimental parameters. To illustrate the flexibility of the lattice Boltzmann method the simulation of the current response for a range of electrode geometries, distorted from microband electrode geometry to micro hemicylinder electrode, is also described.     

Investigation of pumping mechanism for non‐Newtonian blood flow with AC electrothermal forces in a microchannel by hybrid boundary element method and immersed boundary‐lattice Boltzmann method

Efficient pumping of blood flow in a microfluidic device is essential for rapid detection of bacterial bloodstream infections (BSI) using alternating current (AC) electrokinetics. Compared with AC electro‐osmosis (ACEO) phenomenon, the advantage of AC electrothermal (ACET) mechanism is its capability of pumping biofluids with high electrical conductivities at a relatively high AC voltage frequency. In the current work, the microfluidic pumping of non‐Newtonian blood flow using ACET forces is investigated in detail by modeling its multi‐physics process with hybrid boundary element method (BEM) and immersed boundary‐lattice Boltzmann method (IB‐LBM). The Carreau–Yasuda model is used to simulate the realistic rheological behavior of blood flow. The ACET pumping efficiency of blood flow is studied in terms of different AC voltage magnitudes and frequencies, thermal boundary conditions of electrodes, electrode configurations, channel height, and the channel length per electrode pair. Besides, the effect of rheological behavior on the blood flow velocity is theoretically analyzed by comparing with the Newtonian fluid flow using scaling law analysis under the same physical conditions. The results indicate that the rheological behavior of blood flow and its frequency‐dependent dielectric property make the pumping phenomenon of blood flow different from that of the common Newtonian aqueous solutions. It is also demonstrated that using a thermally insulated electrode could enhance the pumping efficiency dramatically. Besides, the results conclude that increasing the AC voltage magnitude is a more economical pumping approach than adding the number of electrodes with the same energy consumption when the Joule heating effect is acceptable.     

Multicomponent diffusion in nanosystems

We present the detailed analysis of the diffusive transport of spatially inhomogeneous fluid mixtures and the interplay between structural and dynamical properties varying on the atomic scale. The present treatment is based on different areas of liquid state theory, namely, kinetic and density functional theory and their implementation as an effective numerical method via the lattice Boltzmann approach. By combining the first two methods, it is possible to obtain a closed set of kinetic equations for the singlet phase space distribution functions of each species. The interactions among particles are considered within a self-consistent approximation and the resulting effective molecular fields are analyzed. We focus on multispecies diffusion in systems with short-range hard-core repulsion between particles of unequal sizes and weak attractive long-range interactions. As a result, the attractive part of the potential does not contribute explicitly to viscosity but to diffusivity and the thermodynamic properties. Finally, we obtain a practical scheme to solve the kinetic equations by employing a discretization procedure derived from the lattice Boltzmann approach. Within this framework, we present numerical data concerning the mutual diffusion properties both in the case of a quiescent bulk fluid and shear flow inducing Taylor dispersion.     

Modeling the morphology and mechanical properties of sheared ternary mixtures

Through a combination of simulation techniques, we determine both the structural evolution and mechanical properties of blends formed from immiscible ternary mixtures. In this approach, we first use the lattice Boltzmann method to simulate the phase separation dynamics of A/B/C fluid mixtures for varying compositions within the spinodal region. We also investigate the effect of an imposed shear on the phase ordering of the mixture. We assume that the fluid is quenched sufficiently rapidly that the phase-separated structure is preserved in the resultant solid. Then, the output from our morphological studies serves as the input to the lattice spring model, which is used to simulate the elastic response of solids to an applied deformation. These simulations reveal how the local stress and strain fields and the global Young's modulus depend on the composition of the blend and the stiffness of the components. By comparing the results for the sheared and unsheared cases, we can isolate optimal processing conditions for enhancing the mechanical performance of the blends. Overall, the findings provide fundamental insight into the relationship between structure, processing, and properties for heterogeneous materials and can yield guidelines for formulating blends with the desired macroscopic mechanical behavior.     

An electrochemically driven poly(dimethylsiloxane) microfluidic actuator: oxygen sensing and programmable flows and pH gradients

We describe the fabrication and performance of an integrated microelectrochemical reactor-a design possessing utility for multiple applications that include electrochemical sensing, the generation and manipulation of in-channel microfluidic pH gradients, and fluid actuation and flow. The device architecture is based on a three-electrode electrochemical cell design that incorporates a Pt interdigitated array (IDA) working (WE), a Pt counter (CE), and Ag pseudo-reference (RE) electrodes within a microfluidic network in which the WE is fully immersed in a liquid electrolyte confined in the channels. The microchannels are made from a conventional poly(dimethylsiloxane)(PDMS) elastomer, which serves also as a thin gas-permeable membrane through which gaseous reactants in the external ambient environment are supplied to the working electrode by diffusion. Due to the high permeability of oxygen through PDMS, the microfluidic cell supports significantly (>order of magnitude) higher current densities in the oxygen reduction reaction (ORR) than those measured in conventional (quiescent) electrochemical cells for the same electrode areas. We demonstrate in this work that, when operated at constant potential under mass transport control, the device can be utilized as a membrane-covered oxygen sensor, the response of which can be tuned by varying the thickness of the PDMS membrane. Depending on the experimental conditions under which the electrochemical ORR is performed, the data establish that the device can be operated as both a programmable pH gradient generator and a microfluidic pump.     

Lattice Boltzmann model of microfluidics in the presence of external forces

We present here a lattice Boltzmann model in the presence of external force fields to describe electrokinetic microfluidic phenomena and consider pressure as the only external force to drive liquid flow. Our results from a 9-bit square lattice Boltzmann model are in good agreement with recent experimental data in a pressure-driven microchannel flow that could not be fully described by electrokinetic theory. The differences between the predicted and the experimental Reynolds numbers from pressure gradients are well within 5%. Results suggest that the lattice Boltzmann model described here is an effective computational tool for predicting the more complex microfluidic systems that might be problematic using conventional methods.     

Modeling the interactions between compliant microcapsules and pillars in microchannels

Using a computational model, we investigate the motion of microcapsules inside a microchannel that encompasses a narrow constriction. The microcapsules are composed of a compliant, elastic shell and an encapsulated fluid; these fluid-filled shells model synthetic polymeric microcapsules or biological cells (e.g., leukocytes). Driven by an imposed flow, the capsules are propelled along the microchannel and through the constricted region, which is formed by two pillars that lie in registry, extending from the top and bottom walls of the channels. The tops of these pillars (facing into the microchannel) are modified to exhibit either a neutral or an attractive interaction with the microcapsules. The pillars (and constriction) model topological features that can be introduced into microfluidic devices or the physical and chemical heterogeneities that are inherently present in biological vessels. To simulate the behavior of this complex system, we employ a hybrid method that integrates the lattice Boltzmann model (LBM) for fluid dynamics and the lattice spring model (LSM) for the micromechanics of elastic solids. Through this LBM/LSM technique, we probe how the capsule's stiffness and interaction with the pillars affect its passage through the chambers. The results yield guidelines for regulating the movement of microcarriers in microfluidic systems and provide insight into the flow properties of biological cells in capillaries.     

Protein diffusion across the interface in aqueous two-phase systems

We present a detailed study of the diffusive transport of proteins across a fluid phase boundary within aqueous two-phase systems. The aim of the work is to investigate whether local effects at the phase boundary cause a retardation of the diffusive transport between the phases. Possible modifications of interfacial mass transfer could be due to protein adsorption at the phase boundary or local electric fields from electric double layers. Experiments with a microfluidic system have been performed in which protein diffusion (bovine serum albumin and ovalbumin) within a bilaminated configuration of two phases containing polyethylene glycol and dextran is analyzed. A one-dimensional model incorporating phase-specific diffusion constants and the difference in chemical potential between the phases has been formulated. A comparison of experimental and simulation data shows a good overall agreement and suggests that a potential local influence of the phase boundary on protein transport is insignificant for the systems under investigation.     

Characterization of microfluidic gas reactors using remote-detection MRI and parahydrogen-induced polarization

A substantial boost in sensitivity (almost 10(5) -fold) achieved by combining remote-detection MRI and parahydrogen-induced polarization enabled microfluidic reactor imaging. Quantitative estimates of nuclear spin hyperpolarization, reaction product distribution, mass transport, and adsorption in the microfluidic reactors could thus be determined in?situ. The reactors also serve as microfluidic nuclear spin polarizers.     

Single- and two-phase flow in microfluidic porous media analogs based on Voronoi tessellation

The objective of this study was to create a microfluidic model of complex porous media for studying single and multiphase flows. Most experimental porous media models consist of periodic geometries that lend themselves to comparison with well-developed theoretical predictions. However, many real porous media such as geological formations and biological tissues contain a degree of randomness and complexity at certain length scales that is not adequately represented in periodic geometries. To design an experimental tool to study these complex geometries, we created microfluidic models of random homogeneous and heterogeneous networks based on Voronoi tessellations. These networks consisted of approximately 600 grains separated by a highly connected network of channels with an overall porosity of 0.11-0.20. We found that introducing heterogeneities in the form of large cavities within the network changed the permeability in a way that cannot be predicted by the classical porosity-permeability relationship known as the Kozeny equation. The values of permeability found in experiments were in excellent agreement with those calculated from three-dimensional lattice Boltzmann simulations. In two-phase flow experiments of oil displacement with water we found that the wettability of channel walls determined the pattern of water invasion, while the network topology determined the residual oil saturation. The presence of cavities increased the microscopic sweeping efficiency in water-oil displacement. These results suggest that complex network topologies lead to fluid flow behavior that is difficult to predict based solely on porosity. The novelty of this approach is a unique geometry generation algorithm coupled with microfabrication techniques to produce pore scale models of stochastic homogeneous and heterogeneous porous media. The ability to perform and visualize multiphase flow experiments within these geometries will be useful in measuring the mechanism(s) of displacement within micro- and nanoscale pores.     

Ultrathin layer convolution

Ultrathin layers are defined as thin layers which are sufficiently thin that no concentration gradients are established within the layer on the time scale of a voltammetric measurement. Mathematically, ultrathin layers are characterized by ordinary differential equations in time. These equations are simpler to solve than the space and time dependent partial differential equations which describe all other electrode geometries. In this paper, a method is presented which capitalizes on the mathematical simplicity of the ultrathin layer to model any arbitrary, parameterizable electrode geometry. Laplace transforms are used to find an integral relationship between the current response of the modeled geometry and the ultrathin layer current. The integral relationship can be evaluated either analytically or numerically. Any voltammetric perturbation, under either Nernstian or mass transport-controlled conditions, can be modeled. The method is demonstrated for both planar and spherical electrodes. Cyclic voltammetric responses are modeled numerically and potential step responses are modeled analytically. It is also shown that for cyclic voltammetric perturbations, the current-voltage curves for the following systems have the same functional form. That is, the curves are identical within known multiplicative constants. The functionally equivalent responses are for (1) radial diffusion to a point electrode (the polarographic curve), (2) convective transport to a rotating disk, (3) the integral of the ultrathin layer response, and (4) the convolution or semi-integration of the response for linear diffusion to a planar electrode.     

On the surface conductance, flow rate, and current continuities of microfluidics with nonuniform surface potentials

The characteristics of electrokinetic flow in a microchannel depend on both the nature of surface potentials, that is, whether it is uniform or nonuniform, and the electrical potential distribution along the channel. In this paper, the nonlinear Poisson-Boltzmann equation is used to model the electrical double layer and the lattice Boltzmann model coupled with the constraint of current continuity is used to simulate the microfluidic flow field in a rectangular microchannel with a step variation of surface potentials. This current continuity, including surface conduction, convection, and bulk conduction currents, has often been neglected in the literature for electroosmotic flow with nonuniform (heterogeneous) microchannels. Results show that step variation of ion distribution caused by step variation surface potential will influence significantly the electrical potential distribution along the channel and volumetric flow rate. For the system considered, we showed that the volumetric flow rate could have been overestimated by as much as 70% without consideration of the current continuity constraint.     

Chitosan-mediated in situ biomolecule assembly in completely packaged microfluidic devices

We report facile in situ biomolecule assembly at readily addressable sites in microfluidic channels after complete fabrication and packaging of the microfluidic device. Aminopolysaccharide chitosan's pH responsive and chemically reactive properties allow electric signal-guided biomolecule assembly onto conductive inorganic surfaces from the aqueous environment, preserving the activity of the biomolecules. A transparent and nonpermanently packaged device allows consistently leak-free sealing, simple in situ and ex situ examination of the assembly procedures, fluidic input/outputs for transport of aqueous solutions, and electrical ports to guide the assembly onto the patterned gold electrode sites within the channel. Both in situ fluorescence and ex situ profilometer results confirm chitosan-mediated in situ biomolecule assembly, demonstrating a simple approach to direct the assembly of biological components into a completely fabricated device. We believe that this strategy holds significant potential as a simple and generic biomolecule assembly approach for future applications in complex biomolecular or biosensing analyses as well as in sophisticated microfluidic networks as anticipated for future lab-on-a-chip devices.     

Multiphoton lithography of nanocrystalline platinum and palladium for site-specific catalysis in 3D microenvironments

Integration of catalytic nanostructured platinum and palladium within 3D microscale structures or fluidic environments is important for systems ranging from micropumps to microfluidic chemical reactors and energy converters. We report a straightforward procedure to fabricate microscale patterns of nanocrystalline platinum and palladium using multiphoton lithography. These materials display excellent catalytic, electrical, and electrochemical properties, and we demonstrate high-resolution integration of catalysts within 3D defined microenvironments to generate directed autonomous particle and fluid transport.     

Phononic crystal structures for acoustically driven microfluidic manipulations

The development of microfluidic systems is often constrained both by difficulties associated with the chip interconnection to other instruments and by limitations imposed by the mechanisms that can enable fluid movement and processing. Surface acoustic wave (SAW) devices have shown promise in allowing samples to be manipulated, although designing complex fluid operations involves using multiple electrode transducers. We now demonstrate a simple interface between a piezoelectric SAW device and a disposable microfluidic chip, patterned with phononic structures to control the acoustic wave propagation. The surface wave is coupled from the piezoelectric substrate into the disposable chip where it interacts with the phononic lattice. By implementing both a phononic filter and an acoustic waveguide, we illustrate the potential of the technique by demonstrating microcentrifugation for particle and cell concentration in microlitre droplets. We show for the first time that the interaction of the fluid within this metamaterial phononic lattice is dependent upon the frequency of the acoustic wave, providing a route to programme complex fluidic functions into a microchip (in much the same way, by analogy, that a holographic element would change the phase of a light wave in optical tweezers). A practical realisation of this involves the centrifugation of blood on the chip.     

The Optimal Control of Geometry and Voltage Parameters on Electrokinetic Transport to Avoid Sample Leakage in Microfluidic Chips

Computer simulation is used to investigate sample transport phenomena of cross microfluidic chips. In this study, Kirchhoff circuit theory is employed to calculate the electric field strength and approximate electroosmotic flow. It is apparent from the results that both the simulation and the theoretical data show similar trends in the electroosmosis of cross microchips. The main target in this study is to summarize the optimal controlling parameter values for avoiding sample leakage in the transport process. The effects of the applied voltage ratio, the geometry ratio and the zeta potential were simulated using a computational fluid dynamics and multiphysics solver software package (CFD-ACE+). Under our designed conditions, two major conclusions were reached: (1) for high-voltage ratios, the sample leakage can be avoided as the geometry ratio is large enough at 0.5 or greater, and (2) for small geometries, maintaining a smaller voltage ratio, 0.3 or less, is essential for avoiding sample leakage. The key is to govern the sample velocity in the upstream faster than that in the downstream. Although real experimental conditions can be further fine tuned under microscopy monitoring, these conclusions are helpful to design the proper channel geometry and set up suitable voltage parameters to avoid sample leakages in one cross-channel chip.     

A microfluidic device for kinetic optimization of protein crystallization and in situ structure determination

The unprecedented economies of scale and unique mass transport properties of microfluidic devices made them viable nano-volume protein crystallization screening platforms. However, realizing the full potential of microfluidic crystallization requires complementary technologies for crystal optimization and harvesting. In this paper, we report a microfluidic device which provides a link between chip-based nanoliter volume crystallization screening and structure analysis through "kinetic optimization" of crystallization reactions and in situ structure determination. Kinetic optimization through systematic variation of reactor geometry and actuation of micromechanical valves is used to screen a large ensemble of kinetic trajectories that are not practical with conventional techniques. Using this device, we demonstrate control over crystal quality, reliable scale-up from nanoliter volume reactions, facile harvesting and cryoprotectant screening, and protein structure determination at atomic resolution from data collected in-chip.     

Computational Electrochemistry: A Model to Studying Ohmic Distortion of Voltammetry in Multiple Working Electrode,Microfluidic Devices,an Adaptive FEM Approach

Characteristics of mass transport and potential distribution applicable to microfluidic electrochemical flow cell devices has been modelled using the finite element method. A flexible, automatic grid generation algorithm has been combined with an a‐posteriori error indication technique presented by Nann and Heinze to allow irregular cell geometries to be modelled. The code has been applied to the problem of steady state generator – detector linear sweep voltammetry in a channel flow cell showing the effects of IR drop on the voltammetric response of each electrode.     

Model based design of a microfluidic mixer driven by induced charge electroosmosis

Mixing chemical or biological samples with reagents for chemical analysis is one of the most time consuming operations on microfluidic platforms. This is primarily due to the low rate of diffusive transport in liquid systems. Additionally, much research has focused on detection, rather than sample preparation. In response, we describe a mixer for microfluidic sample preparation based on the electrokinetic phenomenon of induced-charge-electroosmosis (ICEO). ICEO creates microvortices within a fluidic channel by application of alternating current (AC) electric fields. The microvortices are driven by electrostatic forces acting on the ionic charge induced by the field near polarizable materials. By enabling mixing to be turned on or off within a channel of fixed volume, these electronically controlled mixers prevent sample dilution-a common problem with other strategies. A three-dimensional model based on the finite volume method was developed to calculate the electric field, fluid flow, and mass transport in a multi-species liquid. After preliminary experiments, the model was used to rapidly prototype a wide range of designs. A new microfabrication process was developed for devices with vertical sidewalls having conductive metal coatings and embedded electrodes. Mixing experiments were carried out in the devices and the results were compared to the model.