Analytical solutions for viscoelectric effects in electrokinetic nanochannels.

Understanding electrokinetic transport in nanochannels and nanopores is essential for emerging biological and electrochemical applications. The viscoelectric effect is an important mechanism implicated in the increase of local viscosity due to the polarization of a solvent under a strong electric field. However, most analyses of the viscoelectric effect have been limited to numerical analyses. In this work, we present a set of analytical solutions applicable to the physical description of viscoelectric effects in nanochannel electrokinetic systems. To achieve such closed-form solutions, we employ the Debye-Hückel approximation of small diffuse charge layer potentials compared to the thermal potential. We analyze critical parameters, including electroosmotic flow profiles, electroosmotic mobility, flow rate, and channel conductance. We compare and benchmark our analytical solutions with published predictions from numerical models. Importantly, we leverage these analytical solutions to identify essential thermophysical and nondimensional parameters that govern the behavior of these systems. We identify scaling parameters and relations among surface charge density, ionic strength, and nanochannel height.

Isotachophoresis: Theory and Microfluidic Applications.

Isotachophoresis (ITP) is a versatile electrophoretic technique that can be used for sample preconcentration, separation, purification, and mixing, and to control and accelerate chemical reactions. Although the basic technique is nearly a century old and widely used, there is a persistent need for an easily approachable, succinct, and rigorous review of ITP theory and analysis. This is important because the interest and adoption of the technique has grown over the last two decades, especially with its implementation in microfluidics and integration with on-chip chemical and biochemical assays. We here provide a review of ITP theory starting from physicochemical first-principles, including conservation of species, conservation of current, approximation of charge neutrality, pH equilibrium of weak electrolytes, and so-called regulating functions that govern transport dynamics, with a strong emphasis on steady and unsteady transport. We combine these generally applicable (to all types of ITP) theoretical discussions with applications of ITP in the field of microfluidic systems, particularly on-chip biochemical analyses. Our discussion includes principles that govern the ITP focusing of weak and strong electrolytes; ITP dynamics in peak and plateau modes; a review of simulation tools, experimental tools, and detection methods; applications of ITP for on-chip separations and trace analyte manipulation; and design considerations and challenges for microfluidic ITP systems. We conclude with remarks on possible future research directions. The intent of this review is to help make ITP analysis and design principles more accessible to the scientific and engineering communities and to provide a rigorous basis for the increased adoption of ITP in microfluidics.

Electric field-driven microfluidics for rapid CRISPR-based diagnostics and its application to detection of SARS-CoV-2.

The rapid spread of COVID-19 across the world has revealed major gaps in our ability to respond to new virulent pathogens. Rapid, accurate, and easily configurable molecular diagnostic tests are imperative to prevent global spread of new diseases. CRISPR-based diagnostic approaches are proving to be useful as field-deployable solutions. In one basic form of this assay, the CRISPR-Cas12 enzyme complexes with a synthetic guide RNA (gRNA). This complex becomes activated only when it specifically binds to target DNA and cleaves it. The activated complex thereafter nonspecifically cleaves single-stranded DNA reporter probes labeled with a fluorophore-quencher pair. We discovered that electric field gradients can be used to control and accelerate this CRISPR assay by cofocusing Cas12-gRNA, reporters, and target within a microfluidic chip. We achieve an appropriate electric field gradient using a selective ionic focusing technique known as isotachophoresis (ITP) implemented on a microfluidic chip. Unlike previous CRISPR diagnostic assays, we also use ITP for automated purification of target RNA from raw nasopharyngeal swab samples. We here combine this ITP purification with loop-mediated isothermal amplification and the ITP-enhanced CRISPR assay to achieve detection of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) RNA (from raw sample to result) in about 35 min for both contrived and clinical nasopharyngeal swab samples. This electric field control enables an alternate modality for a suite of microfluidic CRISPR-based diagnostic assays.

Detection and Discrimination of Single Nucleotide Polymorphisms by Quantification of CRISPR-Cas Catalytic Efficiency.

The specificity of CRISPR-Cas12 assays is attractive for the detection of single nucleotide polymorphisms (SNPs) implicated in, e.g., cancer and SARS-CoV-2 variants. Such assays often employ endpoint measurements of SNP or wild type (WT) activated Cas12 trans-cleavage activity; however, the fundamental kinetic effects of SNP versus WT activation remain unknown. We here show that endpoint-based assays are limited by arbitrary experimental choices (like used reporter concentration and assay duration) and work best for known target concentrations. More importantly, we show that SNP (versus WT) activation results in measurable kinetic shifts in the Cas12 trans-cleavage substrate affinity (KM) and apparent catalytic efficiency (kcat*/KM). To address endpoint-based assay limitations, we then develop an assay based on the quantification of Michaelis-Menten parameters and apply this assay to a 20 base pair WT target of the SARS-CoV-2 E gene. We find that the kcat*/KM measured for WT is 130-fold greater than the lowest kcat*/KM among all 60 measured SNPs (compared to a 4.8-fold for endpoint fluorescence of the same SNP). KM also offers a strong ability to distinguish SNPs, varies 27-fold over all the cases, and, importantly, is insensitive to the target concentration. Last, we point out trends among kinetic rates and SNP base and location within the CRISPR-Cas12 targeted region.

Enzyme Kinetics and Detector Sensitivity Determine Limits of Detection of Amplification-Free CRISPR-Cas12 and CRISPR-Cas13 Diagnostics.

Interest in CRISPR-Cas12 and CRISPR-Cas13 detection continues to increase as these detection schemes enable the specific recognition of nucleic acids. The fundamental sensitivity limits of these schemes (and their applicability in amplification-free assays) are governed by kinetic rates. However, these kinetic rates remain poorly understood, and their reporting has been inconsistent. We quantify kinetic parameters for several enzymes (LbCas12a, AsCas12a, AapCas12b, LwaCas13a, and LbuCas13a) and their corresponding limits of detection (LoD). Collectively, we present quantification of enzyme kinetics for 14 guide RNAs (gRNAs) and nucleic acid targets for a total of 50 sets of kinetic rate parameters and 25 LoDs. We validate the self-consistency of our measurements by comparing trends and limiting behaviors with a Michaelis-Menten trans-cleavage reaction kinetics model. For our assay conditions, activated Cas12 and Cas13 enzymes exhibit trans-cleavage catalytic efficiencies between order 105 and 106 M-1 s-1. For assays that use fluorescent reporter molecules (ssDNA and ssRNA) for target detection, the kinetic rates at the current assay conditions result in an amplification-free LoD in the picomolar range. The results suggest that successful detection of target requires cleavage (by an activated CRISPR enzyme) of the order of at least 0.1% of the fluorescent reporter molecules. This fraction of reporters cleaved is required to differentiate the signal from the background, and we hypothesize that this required fraction is largely independent of the detection method (e.g., endpoint vs reaction velocity) and detector sensitivity. Our results demonstrate the fundamental nature by which kinetic rates and background signal limit LoDs and thus highlight areas of improvement for the emerging field of CRISPR diagnostics.

Millisecond timescale reactions observed via X-ray spectroscopy in a 3D microfabricated fused silica mixer. Corrigendum.

A figure in the article by Huyke et al. [(2021), J. Synchrotron Rad. 28, 1100-1113] is corrected.

CRISPR Enzyme Kinetics for Molecular Diagnostics.

CRISPR-diagnostic assays have gained significant interest in the last few years. This interest has grown rapidly during the current COVID-19 pandemic, where CRISPR-diagnostics have been frontline contenders for rapid testing solutions. This surge in CRISPR-diagnostic research prompts the following question: what exactly are the achievable limits of detection and associated assay times enabled by the kinetics of enzymes such as Cas12 and Cas13? To explore this question, we here present a model based on Michaelis-Menten enzyme kinetics theory applied to CRISPR enzymes. We use the model to develop analytical solutions for reaction kinetics and develop back-of-the-envelope criteria to validate and check for consistency in reported enzyme kinetic parameters. We applied our analyses to all studies known to us, which report Michaelis-Menten-type kinetic data for CRISPR-associated enzymes. These studies include all subtypes of Cas12 and Cas13 and orthologs. We found all but one study clearly violate at least two of our three rules and therefore present data that violate basic physical limits. We performed an experimental study of reaction kinetics of LbCas12a with both ssDNA and dsDNA activators and use these data to validate our model and its predicted scaling. The validated model is used to explore CRISPR reaction time scales and the degree of reaction completion for practically relevant target concentrations applicable to CRISPR-diagnostic assays. The results have broad implications for achievable limits of detection and assay times of emerging, amplification-free CRISPR-detection methods.

Species Abundance and Reaction Off-Rate Regulate Product Formation in Reactions Accelerated Using Isotachophoresis.

We present a model for second-order and pseudo-first-order reversible chemical reactions accelerated using peak-mode isotachophoresis (ITP). In such systems, ITP preconcentrates and co-locates the reactants between the leading and trailing electrolyte zones, and this significantly accelerates chemical reactions. Our model quantifies the effects of reaction rate constants and species abundance on product formation rate. We identify two key non-dimensional parameters, which are specific groupings of reaction rate constants, species concentrations, and influx rates. We then use a regular perturbation to study the effects of reverse reaction rate and relative species abundance (and relative rates of species accumulation) on production rate. We also use this perturbation method to derive an analytical expression for the quasi-steady-state production rate achievable by ITP. Our analytical models and numerical solutions are generally applicable to a wide range of systems, which use ITP to enhance reactions. The model is also an interesting case study of the complex coupling of electric field-driven species transport and reaction kinetics.

Millisecond timescale reactions observed via X-ray spectroscopy in a 3D microfabricated fused silica mixer.

Determination of electronic structures during chemical reactions remains challenging in studies which involve reactions in the millisecond timescale, toxic chemicals, and/or anaerobic conditions. In this study, a three-dimensionally (3D) microfabricated microfluidic mixer platform that is compatible with time-resolved X-ray absorption and emission spectroscopy (XAS and XES, respectively) is presented. This platform, to initiate reactions and study their progression, mixes a high flow rate (0.50-1.5 ml min-1) sheath stream with a low-flow-rate (5-90 µl min-1) sample stream within a monolithic fused silica chip. The chip geometry enables hydrodynamic focusing of the sample stream in 3D and sample widths as small as 5 µm. The chip is also connected to a polyimide capillary downstream to enable sample stream deceleration, expansion, and X-ray detection. In this capillary, sample widths of 50 µm are demonstrated. Further, convection-diffusion-reaction models of the mixer are presented. The models are experimentally validated using confocal epifluorescence microscopy and XAS/XES measurements of a ferricyanide and ascorbic acid reaction. The models additionally enable prediction of the residence time and residence time uncertainty of reactive species as well as mixing times. Residence times (from initiation of mixing to the point of X-ray detection) during sample stream expansion as small as 2.1 ± 0.3 ms are also demonstrated. Importantly, an exploration of the mixer operational space reveals a theoretical minimum mixing time of 0.91 ms. The proposed platform is applicable to the determination of the electronic structure of conventionally inaccessible reaction intermediates.

Thermodynamics of Ion Separation by Electrosorption.

We present a simple, top-down approach for the calculation of minimum energy consumption of electrosorptive ion separation using variational form of the (Gibbs) free energy. We focus and expand on the case of electrostatic capacitive deionization (CDI). The theoretical framework is independent of details of the double-layer charge distribution and is applicable to any thermodynamically consistent model, such as the Gouy-Chapman-Stern and modified Donnan models. We demonstrate that, under certain assumptions, the minimum required electric work energy is indeed equivalent to the free energy of separation. Using the theory, we define the thermodynamic efficiency of CDI. We show that the thermodynamic efficiency of current experimental CDI systems is currently very low, around 1% for most existing systems. We applied this knowledge and constructed and operated a CDI cell to show that judicious selection of the materials, geometry, and process parameters can lead to a 9% thermodynamic efficiency and 4.6 kT per removed ion energy cost. This relatively high thermodynamic efficiency is, to our knowledge, by far the highest thermodynamic efficiency ever demonstrated for traditional CDI. We hypothesize that efficiency can be further improved by further reduction of CDI cell series resistances and optimization of operational parameters.

A modular and reconfigurable open-channel gated device for the electrokinetic extraction of cell-free DNA assays.

The high-efficiency separation and extraction of short fragments of cell-free DNA (cfDNA) remain challenging due to their low abundance and short lengths. This study presents a method for separating short cfDNA fragments, with lengths ranging from about 100 to 200 base pairs, from liquid human plasma samples into separable and extractable bands as solid agarose gel slabs. To achieve this, a novel millimeter-scale fluidic device is used for sample handling, transient isotachophoresis, and extraction. The device features open-to-atmosphere liquid chambers that define and manually actuated (i.e., movable) agarose-made gate valve structures. The agarose gates then define discrete zones for buffers, sample injection, DNA pre-concentration via isotachophoresis, size-based gel separation, and DNA-band extraction. As a demonstration of its efficacy, the device is applied to the enrichment and purification of M. tuberculosis genomic DNA fragments spiked in human plasma samples. This purified cfDNA is analyzed using the quantitative polymerase chain reaction (qPCR) of the IS6110 repetitive sequence in the M. tuberculosis genome. The data from this study demonstrates that high sensitivity can be achieved in cfDNA detection, as shown by the comparison with a typical solid-phase extraction method and buffer spiked with cfDNA. Evidence is presented that suggests plasma peptides generated by treatment of the sample with proteinase K acts as endogenous spacer molecules, which improve the resolution and purification of DNA relative to the marker dye and other contaminants that decrease the signal level in qPCR.

Simultaneous optical and infrared thermal imaging of isotachophoresis.

Joule heating in isotachophoresis (ITP) can limit minimum assay times and efforts to scale up processed sample volumes. Despite its significance, the dynamics of Joule heating on spatiotemporal temperature fields in ITP systems have not been investigated. We here present novel measurements of spatiotemporal temperature and electromigration fields in ITP. To achieve this, we obtain simultaneous and registered optical and infrared thermal images of the ITP process. We conduct a series of experiments at constant current operation and vary the leading electrolyte concentration to study and highlight the importance of buffer-dependent ionic conductivity on the resulted temperature rise. The measurements demonstrate a substantial increase of temperature in the adjusted trailing electrolyte region, and the propagation of a thermal wave in the ITP channel with a velocity equal to that of the electromigration front. We present scaling of the experimental data that indicates the dependence of front velocity and temperature rise on current density and ionic conductivity. The current study has direct application to the design and optimization of scaled-up ITP systems and the validation of numerical models of Joule heating.

Process design tools and techno-economic analysis for capacitive deionization.

Capacitive deionization (CDI) devices use cyclical electrosorption on porous electrode surfaces to achieve water desalination. Process modeling and design of CDI systems requires accurate treatment of the coupling among input electrical forcing, input flow rates, and system responses including salt removal dynamics, water recovery, energy storage, and dissipation. Techno-economic analyses of CDI further require a method to calculate and compare between a produced commodity (e.g. desalted water) versus capital and operational costs of the system. We here demonstrate a new modeling and analysis tool for CDI developed as an installable Matlab program that allows direct numerical simulation of CDI dynamics and calculation of key performance and cost parameters. The program is provided for free and is used to run open-source Simulink models. The Simulink environment sends information to the program and allows for a drag and drop design space where users can connect CDI cells to relevant periphery blocks such as grid energy, battery, solar panel, waste disposal, and maintenance/labor cost streams. The program allows for simulation of arbitrary current forcing and arbitrary flow rate forcing of one or more CDI cells. We employ validated well-mixed reactor formulations together with a non-linear circuit model formulation that can accommodate a variety of electric double layer sub-models (e.g. for charge efficiency). The program includes a graphical user interface (GUI) to specify CDI plant parameters, specify operating conditions, run individual tests or parameter batch-mode simulations, and plot relevant results. The techno-economic models convert among dimensional streams of species (e.g. feed, desalted water, and brine), energy, and cost and enable a variety of economic estimates including levelized water costs.

On the competition between mixing rate and uniformity in a coaxial hydrodynamic focusing mixer.

Fast microfluidic mixers for use with line-of-sight integrating detection schemes pose unique challenges. Such detectors typically cannot discriminate signal from slow moving (e.g. near internal walls) and fast-moving portions of the fluid stream. This convolves reaction rate dynamics with fluid flow residence time dynamics. Further, the small cross sections of typical three-dimensional hydrodynamic focusing devices lead to lower detection signals. The current study focuses on achieving both small time scales of mixing and homogenous residence times. This is achieved by injecting sample through a center capillary and hydrodynamically focusing using a sheath flow within a tapered second capillary. The current design also features a third, larger coaxial capillary. The mixed stream flows into the large cross-section of this third capillary to decelerate and expand the stream by up to 14-fold to improve line-of-sight signal strength of reaction products. Hydrodynamic focusing, mixing, and expansion are studied using analytical and numerical models and also studied experimentally using a fluorescein-iodide quenching reaction. The experimentally validated models are used to explore trade-offs between mixing rate and uniformity. For the first time, this work presents detailed analysis of the Lagrangian time history of species transport during mixing inside coaxial capillaries to measure mixing nonuniformity. The mixing region enables order 100 µs mixing times and residence time widths of the same order (140 µs).

High water recovery and improved thermodynamic efficiency for capacitive deionization using variable flowrate operation.

Water recovery is a measure of the amount of treated water produced relative to the total amount of water processed through the system, and is an important performance metric for any desalination method. Conventional operating methods for desalination using capacitive deionization (CDI) have so far limited water recovery to be about 50%. To improve water recovery for CDI, we here introduce a new operating scheme based on a variable (in time) flow rate wherein a low flow rate during discharge is used to produce a brine volume which is significantly less than the volume of diluent produced. We demonstrate experimentally and study systematically this novel variable flowrate operating scheme in the framework of both constant current and constant voltage charge-discharge modes. We show that the variable flowrate operation can increase water recovery for CDI to very high values of ∼90% and can improve thermodynamic efficiency by about 2- to 3-fold compared to conventional constant flowrate operation. Importantly, this is achieved with minimal performance reductions in salt removal, energy consumption, and volume throughput. Our work highlights that water recovery can be readily improved for CDI at very minimal additional cost using simple flow control schemes.

Performance metrics for the objective assessment of capacitive deionization systems.

In the growing field of capacitive deionization (CDI), a number of performance metrics have emerged to describe the desalination process. Unfortunately, the separation conditions under which these metrics are measured are often not specified, resulting in optimal performance at minimal removal. Here we outline a system of performance metrics and reporting conditions that resolves this issue. Our proposed system is based on volumetric energy consumption (Wh/m3) and throughput productivity (L/h/m2) reported for a specific average concentration reduction, water recovery, and feed salinity. To facilitate and rationalize comparisons between devices, materials, and operation modes, we propose a nominal standard separation of removing 5 mM from a 20 mM NaCl feed solution at 50% water recovery. We propose this particular separation as a standard, but emphasize that the rationale presented here applies irrespective of separation details. Using our proposed separation, we compare the desalination performance of a flow-through electrode (fte-CDI) cell and a flow between membrane (fb-MCDI) device, showing how significantly different systems can be compared in terms of generally desirable desalination characteristics. In general, we find that performance analysis must be considered carefully so to not allow for ambiguous separation conditions or the maximization of one metric at the expense of another. Additionally, for context and clarity, we discuss a number of important underlying performance indicators and cell characteristics that are not performance measures in and of themselves but can be examined to better understand differences in performance.

Frequency analysis and resonant operation for efficient capacitive deionization.

Capacitive deionization (CDI) performance metrics can vary widely with operating methods. Conventional CDI operating methods such as constant current and constant voltage show advantages in either energy or salt removal performance, but not both. We here develop a theory around and experimentally demonstrate a new operation for CDI that uses sinusoidal forcing voltage (or sinusoidal current). We use a dynamic system modeling approach, and quantify the frequency response (amplitude and phase) of CDI effluent concentration. Using a wide range of operating conditions, we demonstrate that CDI can be modeled as a linear time invariant system. We validate this model with experiments, and show that a sinusoid voltage operation can simultaneously achieve high salt removal and strong energy performance, thus very likely making it superior to other conventional operating methods. Based on the underlying coupled phenomena of electrical charge (and ionic) transfer with bulk advection in CDI, we derive and validate experimentally the concept of using sinusoidal voltage forcing functions to achieve resonance-type operation for CDI. Despite the complexities of the system, we find a simple relation for the resonant time scale: the resonant time period (frequency) is proportional (inversely proportional) to the geometric mean of the flow residence time and the electrical (RC) charging time. Operation at resonance implies the optimal balance between absolute amount of salt removed (in moles) and dilution (depending on the feed volume processed), thus resulting in the maximum average concentration reduction for the desalinated water. We further develop our model to generalize the resonant time-scale operation, and provide responses for square and triangular voltage waveforms as two examples. To this end, we develop a general tool that uses Fourier analysis to construct CDI effluent dynamics for arbitrary input waveforms. Using this tool, we show that most of the salt removal (∼95%) for square and triangular voltage forcing waveforms is achieved by the fundamental Fourier (sinusoidal) mode. The frequency of higher Fourier modes precludes high flow efficiency for these modes, so these modes consume additional energy for minimal additional salt removed. This deficiency of higher frequency modes further highlights the advantage of DC-offset sinusoidal forcing for CDI operation.

Self similarities in desalination dynamics and performance using capacitive deionization.

Charge transfer and mass transport are two underlying mechanisms which are coupled in desalination dynamics using capacitive deionization (CDI). We developed simple reduced-order models based on a mixed reactor volume principle which capture the coupled dynamics of CDI operation using closed-form semi-analytical and analytical solutions. We use the models to identify and explore self-similarities in the dynamics among flow rate, current, and voltage for CDI cell operation including both charging and discharging cycles. The similarity approach identifies the specific combination of cell (e.g. capacitance, resistance) and operational parameters (e.g. flow rate, current) which determine a unique effluent dynamic response. We here demonstrate self-similarity using a conventional flow between CDI (fbCDI) architecture, and we hypothesize that our similarity approach has potential application to a wide range of designs. We performed an experimental study of these dynamics and used well-controlled experiments of CDI cell operation to validate and explore limits of the model. For experiments, we used a CDI cell with five electrode pairs and a standard flow between (electrodes) architecture. Guided by the model, we performed a series of experiments that demonstrate natural response of the CDI system. We also identify cell parameters and operation conditions which lead to self-similar dynamics under a constant current forcing function and perform a series of experiments by varying flowrate, currents, and voltage thresholds to demonstrate self-similarity. Based on this study, we hypothesize that the average differential electric double layer (EDL) efficiency (a measure of ion adsorption rate to EDL charging rate) is mainly dependent on user-defined voltage thresholds, whereas flow efficiency (measure of how well desalinated water is recovered from inside the cell) depends on cell volumes flowed during charging, which is determined by flowrate, current and voltage thresholds. Results of experiments strongly support this hypothesis. Results show that cycle efficiency and salt removal for a given flowrate and current are maximum when average EDL and flow efficiencies are approximately equal. We further explored a range of CC operations with varying flowrates, currents, and voltage thresholds using our similarity variables to highlight trade-offs among salt removal, energy, and throughput performance.