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1.
J Chromatogr A ; 1722: 464853, 2024 Mar 31.
Artigo em Inglês | MEDLINE | ID: mdl-38579611

RESUMO

This study presents a methodology for designing effective insulator-based electrokinetic (iEK) systems for separating tertiary microparticle samples, which can be extended to more complex samples. First, 144 distinct iEK microchannel designs were built considering different shapes and arrangements of the insulating posts. Second, a mathematical model was developed with COMSOL software to predict the retention time of each particle type in the microchannel, this allowed identifying the best channel designs for two distinct types of separations: charge-based and sized-based. Third, the experimental charge-based and size-based separations of the tertiary microparticle mixtures were performed employing the improved designs identified with COMSOL modeling. The experimental results demonstrated successful separation in terms of separation resolution and good agreement with COMSOL predictions. The findings from this study show that the proposed method for device design, which combines mathematical modeling with varying post shape and post arrangement is an effective approach for identifying iEK systems capable of separating complex microparticle samples.

3.
Analyst ; 149(8): 2469-2479, 2024 Apr 15.
Artigo em Inglês | MEDLINE | ID: mdl-38516870

RESUMO

There is a growing interest in the advancement of microscale electrokinetic (EK) systems for biomedical and clinical applications, as these systems offer attractive characteristics such as portability, robustness, low sample requirements and short response time. The present work is focused on manipulating the characteristics of the insulating post arrangement in insulator-based EK (iEK) systems for separating a binary mixture of spherical microparticles with same diameter (5.1 µm), same shape, made from the same substrate material and only differing in their zeta potential by ∼14 mV. This study presents a combination of mathematical modeling and experimental separations performed by applying a low-frequency alternating current (AC) voltage in iEK systems with 12 distinct post arrangements. These iEK devices were used to systematically study the effect of three spatial characteristics of the insulating post array on particle separations: the horizontal separation and the vertical separation between posts, and introducing an offset to the posts arrangement. Through normalization of the spatial separation between the insulating posts with respect to particle diameter, guidelines to improve separation resolution for different particle mixtures possessing similar characteristics were successfully identified. The results indicated that by carefully designing the spatial arrangement of the post array, separation resolution values in the range of 1.4-2.8 can be obtained, illustrating the importance and effect of the arrangement of insulating posts on improving particle separations. This study demonstrates that iEK devices, with effectively designed spatial arrangement of the insulating post arrays, have the capabilities to perform discriminatory separations of microparticles of similar characteristics.

4.
Biosensors (Basel) ; 14(3)2024 Feb 22.
Artigo em Inglês | MEDLINE | ID: mdl-38534226

RESUMO

Analyte migration order is a major aspect in all migration-based analytical separations methods. Presented here is the manipulation of the migration order of microparticles in an insulator-based electrokinetic separation. Three distinct particle mixtures were studied: a binary mixture of particles with similar electrical charge and different sizes, and two tertiary mixtures of particles of distinct sizes. Each one of the particle mixtures was separated twice, the first separation was performed under low voltage (linear electrokinetic regime) and the second separation was performed under high voltage (nonlinear electrokinetic regime). Linear electrophoresis, which discriminates particles by charge, is the dominant electrokinetic effect in the linear regime; while nonlinear electrophoresis, which discriminates particles by size and shape, is the dominant electrokinetic effect in the nonlinear regime. The separation results obtained with the three particle mixtures illustrated that particle elution order can be changed by switching from the linear electrokinetic regime to the nonlinear electrokinetic regime. Also, in all cases, better separation performances in terms of separation resolution (Rs) were obtained by employing the nonlinear electrokinetic regime allowing nonlinear electrophoresis to be the discriminatory electrokinetic mechanism. These findings could be applied to analyze complex samples containing bioparticles of interest within the micron size range. This is the first report where particle elution order is altered in an iEK system.


Assuntos
Eletricidade , Poliestirenos , Tamanho da Partícula , Eletroforese/métodos
5.
Micromachines (Basel) ; 15(3)2024 Mar 08.
Artigo em Inglês | MEDLINE | ID: mdl-38542616

RESUMO

Bacteriophage therapy presents a promising avenue for combating antibiotic-resistant bacterial infections. Yet, challenges exist, particularly, the lack of a straightforward purification pipeline suitable for widespread application to many phage types, as some phages are known to undergo significant titer loss when purified via current techniques. Electrokinetic methods offer a potential solution to this hurdle, with nonlinear electrophoresis emerging as a particularly appealing approach due to its ability to discern both the size and shape of the target phage particles. Presented herein is the electrokinetic characterization of the mobility of nonlinear electrophoresis for two phages (SPN3US and ϕKZ) and three types of polystyrene nanoparticles. The latter served as controls and were selected based on their sizes and surface charge magnitude. Particle tracking velocimetry experiments were conducted to characterize the mobility of all five particles included in this study. The results indicated that the selected nanoparticles effectively replicate the migration behavior of the two phages under electric fields. Further, it was found that there is a significant difference in the nonlinear electrophoretic response of phages and that of host cells, as first characterized in a previous report, illustrating that electrokinetic-based separations are feasible. The findings from this work are the first characterization of the behavior of phages under nonlinear electrophoresis effects and illustrate the potential for the development of electrokinetic-based phage purification techniques that could aid the advancement of bacteriophage therapy.

6.
J Chromatogr A ; 1717: 464685, 2024 Feb 22.
Artigo em Inglês | MEDLINE | ID: mdl-38310700

RESUMO

This study contributes to the renewed interest in the study of nonlinear electrophoresis of colloidal particles. In this work the influence of cell shape on electrophoretic migration under the nonlinear regimes of moderate and strong field regimes was assessed. Four types of bacterial and yeast cells (one spherical, three non-spherical) were studied and their electrophoretic mobilities for the moderate and strong electric field magnitude regimes were estimated experimentally. The parameter of sphericity was employed to assess the effect cell shape on the nonlinear electrophoresis migration velocity and corresponding mobility under the two electric field magnitude regimes studied. As particle migration under nonlinear electrophoresis depends on particle size and shape, the results in terms of mobilities of nonlinear electrophoresis were presented as function of cell hydrodynamic diameter and sphericity. The results indicated that the magnitude of the mobilities of nonlinear electrophoresis for cells increase with increasing cell size and increase with increasing deviations from spherical shape, which is indicated by lower sphericity values. The results presented here are the very first assessment of the two types of mobilities of nonlinear electrophoresis of cells as a function of size and shape.


Assuntos
Eletricidade , Hidrodinâmica , Forma Celular , Eletroforese/métodos , Tamanho da Partícula
7.
Artigo em Inglês | MEDLINE | ID: mdl-38360552

RESUMO

Nonlinear electrokinetic phenomena offer label-free, portable, and robust approaches for particle and cell assessment, including selective enrichment, separation, sorting, and characterization. The field of electrokinetics has evolved substantially since the first separation reports by Arne Tiselius in the 1930s. The last century witnessed major advances in the understanding of the weak-field theory, which supported developments in the use of linear electrophoresis and its adoption as a routine analytical technique. More recently, an improved understanding of the strong-field theory enabled the development of nonlinear electrokinetic techniques such as electrorotation, dielectrophoresis, and nonlinear electrophoresis. This review discusses the operating principles and recent applications of these three nonlinear electrokinetic phenomena for the analysis and manipulation of particles and cells and provides an overview of some of the latest developments in the field of nonlinear electrokinetics. Expected final online publication date for the Annual Review of Analytical Chemistry, Volume 17 is May 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

8.
Micromachines (Basel) ; 14(12)2023 Dec 14.
Artigo em Inglês | MEDLINE | ID: mdl-38138408

RESUMO

There is a rising need for rapid and reliable analytical methods for separating microorganisms in clinical and biomedical applications. Microscale-insulator-based electrokinetic (iEK) systems have proven to be robust platforms for assessing a wide variety of microorganisms. Traditionally, iEK systems are usually stimulated with direct-current (DC) potentials. This work presents a comparison between using DC potentials and using DC-biased alternating-current (AC) potentials in iEK systems for the separation of microorganisms. The present study, which includes mathematical modeling and experimentation, compares the separation of bacterial and yeast cells in two distinct modes by using DC and DC-biased AC potentials. The quality of both separations, assessed in terms of separation resolution (Rs), showed a complete separation (Rs = 1.51) with the application of a DC-biased low-frequency AC signal but an incomplete separation (Rs = 0.55) with the application of an RMS-equivalent DC signal. Good reproducibility between experimental repetitions (<10%) was obtained, and good agreement (~18% deviation) was observed between modeling and experimental retention times. The present study demonstrates the potential of extending the limits of iEK systems by employing DC-biased AC potentials to perform discriminatory separations of microorganisms that are difficult to separate with the application of DC potentials.

9.
Electrophoresis ; 44(17-18): 1279-1341, 2023 09.
Artigo em Inglês | MEDLINE | ID: mdl-37537327

RESUMO

This review is in support of the development of selective, precise, fast, and validated capillary electrophoresis (CE) methods. It follows up a similar article from 1998, Wätzig H, Degenhardt M, Kunkel A. "Strategies for capillary electrophoresis: method development and validation for pharmaceutical and biological applications," pointing out which fundamentals are still valid and at the same time showing the enormous achievements in the last 25 years. The structures of both reviews are widely similar, in order to facilitate their simultaneous use. Focusing on pharmaceutical and biological applications, the successful use of CE is now demonstrated by more than 600 carefully selected references. Many of those are recent reviews; therefore, a significant overview about the field is provided. There are extra sections about sample pretreatment related to CE and microchip CE, and a completely revised section about method development for protein analytes and biomolecules in general. The general strategies for method development are summed up with regard to selectivity, efficiency, precision, analysis time, limit of detection, sample pretreatment requirements, and validation.


Assuntos
Eletroforese Capilar , Eletroforese em Microchip , Eletroforese Capilar/métodos , Proteínas , Preparações Farmacêuticas
10.
Anal Chem ; 95(26): 9914-9923, 2023 Jul 04.
Artigo em Inglês | MEDLINE | ID: mdl-37342914

RESUMO

There is an immediate need for the development of rapid and reliable methods for microparticle and cell assessments, and electrokinetic (EK) phenomena can be exploited to meet that need in a low cost and label-free fashion. The present study combines modeling and experimentation to separate a binary mixture of microparticles of the same size (5.1 µm), shape (spherical), and substrate material (polystyrene), but with a difference in particle zeta potentials of only ∼14 mV, by applying direct current (DC)-biased low-frequency alternating current (AC) voltages in an insulator-based-EK (iEK) system. Four distinct separations were carried out to systematically study the effect of fine-tuning each of the three main characteristics of the applied voltage: frequency, amplitude, and DC bias. The results indicate that fine-tuning each parameter improved the separation from an initial separation resolution Rs = 0.5 to a final resolution Rs = 3.1 of the fully fine-tuned separation. The separation method exhibited fair reproducibility in retention time with variations ranging from 6 to 26% between experimental repetitions. The present study demonstrates the potential to extend the limits of iEK systems coupled with carefully fine-tuned DC-biased low-frequency AC voltages to perform discriminatory micron-sized particle separations.

11.
Anal Chem ; 95(16): 6740-6747, 2023 Apr 25.
Artigo em Inglês | MEDLINE | ID: mdl-37040369

RESUMO

Contemporary findings in the field of insulator-based electrokinetics have demonstrated that in systems under the influence of direct current (DC) fields, dielectrophoresis (DEP) is not the main electrokinetic mechanism responsible for particle manipulation but rather the sum of electroosmosis, linear and nonlinear electrophoresis. Recent microfluidic studies have brought forth a methodology capable of experimentally estimating the nonlinear electrophoretic mobility of colloidal particles. This methodology, however, is limited to particles that fit two conditions: (i) the particle charge has the same sign as the channel wall charge and (ii) the magnitude of the particle ζ-potential is lower than that of the channel wall. The present work aims to expand upon this methodology by including particles whose ζ-potential has a magnitude larger than that of the wall, referred to as "type 2" particles, as well as to report findings on particles that appear to still be under the influence of the linear electrophoretic regime even at extremely high electric fields (∼6000 V/cm), referred to as "type 3" particles. Our findings suggest that both particle size and charge are key parameters in the determination of nonlinear electrophoretic properties. Type 2 microparticles were all found to be small (diameter ∼ 1 µm) and highly charged, with ζ-potentials above -60 mV; in contrast, type 3 microparticles were all large with ζ-potentials between -40 and -50 mV. However, it was also hypothesized that other nonconsidered parameters could be influencing the results, especially at higher electric fields (>3000 V/cm). The present work also aims to identify the current limitations in the experimental determination of µEP,NL and propose a framework for future work to address the current gaps in the evolving topic of nonlinear electrophoresis of colloidal particles.

12.
Anal Chem ; 95(16): 6595-6602, 2023 Apr 25.
Artigo em Inglês | MEDLINE | ID: mdl-37042833

RESUMO

This study focuses on the dependence of nonlinear electrophoretic migration of particles on the particle size and particle electrical charge. This is the first report of the experimental assessment of the mobilities of the nonlinear electrophoretic velocity of colloidal polystyrene microparticles under two distinct electric field dependences. A total of nine distinct types of polystyrene microparticles of varying size and varying electrical charge were divided into two groups to study separately the effects of particle size and the effects of particle charge. The mobilities of the nonlinear electrophoretic velocity of each particle type were determined in both the cubic and 3/2 regimes (µEP,NL(3) and µEP,NL(3/2)). The results unveiled that both mobilities had similar relationships with particle size and charge. The magnitude of both µEP,NL(3) and µEP,NL(3/2) increased with increasing particle size and decreased with increasing magnitude of particle charge. However, the observed trends were not perfect as discussed in the Results and Discussion section but still provide valuable information. These findings will aid in the design of future size-based and charge-based separations of particles and microorganisms.

13.
Electrophoresis ; 44(11-12): 884-909, 2023 Jun.
Artigo em Inglês | MEDLINE | ID: mdl-37002779

RESUMO

The selective positioning and arrangement of distinct types of multiscale particles can be used in numerous applications in microfluidics, including integrated circuits, sensors and biochips. Electrokinetic (EK) techniques offer an extensive range of options for label-free manipulation and patterning of colloidal particles by exploiting the intrinsic electrical properties of the target of interest. EK-based techniques have been widely implemented in many recent studies, and various methodologies and microfluidic device designs have been developed to achieve patterning two- and three-dimensional (3D) patterned structures. This review provides an overview of the progress in electropatterning research during the last 5 years in the microfluidics arena. This article discusses the advances in the electropatterning of colloids, droplets, synthetic particles, cells, and gels. Each subsection analyzes the manipulation of the particles of interest via EK techniques such as electrophoresis and dielectrophoresis. The conclusions summarize recent advances and provide an outlook on the future of electropatterning in various fields of application, especially those with 3D arrangements as their end goal.


Assuntos
Coloides , Microfluídica , Eletroforese/métodos
14.
Anal Chem ; 95(2): 1409-1418, 2023 01 17.
Artigo em Inglês | MEDLINE | ID: mdl-36599093

RESUMO

Presented here is the first continuous separation of microparticles and cells of similar characteristics employing linear and nonlinear electrokinetic phenomena in an insulator-based electrokinetic (iEK) system. By utilizing devices with insulating features, which distort the electric field distribution, it is possible to combine linear and nonlinear EK phenomena, resulting in highly effective separation schemes that leverage the new advancements in nonlinear electrophoresis. This work combines mathematical modeling and experimentation to separate four distinct binary mixtures of particles and cells. A computational model with COMSOL Multiphysics was used to predict the retention times (tR,p) of the particles and cells in iEK devices. Then, the experimental separations were carried out using the conditions identified with the model, where the experimental retention time (tR,e) of the particles and cells was measured. A total of four distinct separations of binary mixtures were performed by increasing the level of difficulty. For the first separation, two types of polystyrene microparticles, selected to mimic Escherichia coli and Saccharomyces cerevisiae cells, were separated. By leveraging the knowledge gathered from the first separation, a mixture of cells of distinct domains and significant size differences, E. coli and S. cerevisiae, was successfully separated. The third separation also featured cells of different domains but closer in size: Bacillus cereus versus S. cerevisiae. The last separation included cells in the same domain and genus, B. cereus versus Bacillus subtilis. Separation results were evaluated in terms of number of plates (N) and separation resolution (Rs), where Rs values for all separations were above 1.5, illustrating complete separations. Experimental results were in agreement with modeling results in terms of retention times, with deviations in the 6-27% range, while the variation between repetitions was between 2 and 18%, demonstrating good reproducibility. This report is the first prediction of the retention time of cells in iEK systems.


Assuntos
Escherichia coli , Saccharomyces cerevisiae , Reprodutibilidade dos Testes , Modelos Teóricos , Eletricidade , Eletroforese/métodos
15.
Electrophoresis ; 44(1-2): 217-245, 2023 01.
Artigo em Inglês | MEDLINE | ID: mdl-35977346

RESUMO

The use of microfluidic devices is highly attractive in the field of biomedical and clinical assessments, as their portability and fast response time have become crucial in providing opportune therapeutic treatments to patients. The applications of microfluidics in clinical diagnosis and point-of-care devices are continuously growing. The present review article discusses three main fields where miniaturized devices are successfully employed in clinical applications. The quantification of ions, sugars, and small metabolites is examined considering the analysis of bodily fluids samples and the quantification of this type of analytes employing real-time wearable devices. The discussion covers the level of maturity that the devices have reached as well as cost-effectiveness. The analysis of proteins with clinical relevance is presented and organized by the function of the proteins. The last section covers devices that can perform single-cell metabolomic and proteomic assessments. Each section discusses several strategically selected recent reports on microfluidic devices successfully employed for clinical assessments, to provide the reader with a wide overview of the plethora of novel systems and microdevices developed in the last 5 years. In each section, the novel aspects and main contributions of each reviewed report are highlighted. Finally, the conclusions and future outlook section present a summary and speculate on the future direction of the field of miniaturized devices for clinical applications.


Assuntos
Técnicas Analíticas Microfluídicas , Dispositivos Eletrônicos Vestíveis , Humanos , Microfluídica , Proteômica , Sistemas Automatizados de Assistência Junto ao Leito , Dispositivos Lab-On-A-Chip
16.
Anal Chem ; 94(17): 6451-6456, 2022 05 03.
Artigo em Inglês | MEDLINE | ID: mdl-35441512

RESUMO

Well-established techniques, e.g., chromatography and capillary electrophoresis, are available for separating nanosized particles, such as proteins. However, similar techniques for separating micron-sized particles are still needed. Insulator-based electrokinetic (iEK) systems can achieve efficient microparticle separations by combining linear and nonlinear EK phenomena. Of particular interest are charge-based separations, which could be employed for separating similar microorganisms, such as bacterial cells of the same size, same genus, or same strain. Several groups have reported charge-based separations of microparticles where a zeta potential difference of at least 40 mV between the microparticles was required. The present work pushes the limit of the discriminatory capabilities of iEK systems by reporting the charged-based separation of two microparticles of the same size (5.1 µm), same shape, same substrate material, and with a small difference in particle zeta potentials of only 3.6 mV, which is less than 10% of the difference in previous studies. By building an accurate COMSOL Multiphysics model, which correctly accounts for dielectrophoresis and electrophoresis of the second kind, it was possible to identify the conditions to achieve this challenging separation. Furthermore, the COMSOL model allowed predicting particle retention times (tR,p) which were compared with experimental values (tR,e). The separations results had excellent reproducibility in terms of tR,e with variations of only 9% and 11% between repetitions. These findings demonstrate that, by following a robust protocol that involves modeling and experimental work, it is possible to discriminate between highly similar particles, with much smaller differences in electrical charge than previously reported.


Assuntos
Eletricidade , Poliestirenos , Eletroforese/métodos , Poliestirenos/química , Reprodutibilidade dos Testes
17.
Anal Bioanal Chem ; 414(2): 885-905, 2022 Jan.
Artigo em Inglês | MEDLINE | ID: mdl-34664103

RESUMO

This review article presents an overview of the evolution of the field of insulator-based dielectrophoresis (iDEP); in particular, it focuses on insulator-based electrokinetic (iEK) systems stimulated with direct current and low-frequency(< 1 kHz) AC electric fields. The article covers the surge of iDEP as a research field where many different device designs were developed, from microchannels with arrays of insulating posts to devices with curved walls and nano- and micropipettes. All of these systems allowed for the manipulation and separation of a wide array of particles, ranging from macromolecules to microorganisms, including clinical and biomedical applications. Recent experimental reports, supported by important theoretical studies in the field of physics and colloids, brought attention to the effects of electrophoresis of the second kind in these systems. These recent findings suggest that DEP is not the main force behind particle trapping, as it was believed for the last two decades. This new research suggests that particle trapping, under DC and low-frequency AC potentials, mainly results from a balance between electroosmotic and electrophoretic effects (linear and nonlinear); although DEP is present in these systems, it is not a dominant force. Considering these recent studies, it is proposed to rename this field from DC-iDEP to DC-iEK (and low-frequency AC-iDEP to low-frequency AC-iEK). Whereas much research is still needed, this is an exciting time in the field of microscale EK systems, as these new findings seem to explain the challenges with modeling particle migration and trapping in iEK devices, and provide perhaps a better understanding of the mechanisms behind particle trapping.

18.
Electrophoresis ; 43(1-2): 263-287, 2022 01.
Artigo em Inglês | MEDLINE | ID: mdl-34796523

RESUMO

Miniaturized electrokinetic methods have proven to be robust platforms for the analysis and assessment of intact microorganisms, offering short response times and higher integration than their bench-scale counterparts. The present review article discusses three types of electrokinetic-based methodologies: electromigration or motion-based techniques, electrode-based electrokinetics, and insulator-based electrokinetics. The fundamentals of each type of methodology are discussed and relevant examples from recent reports are examined, to provide the reader with an overview of the state-of-the-art on the latest advancements on the analysis of intact cells and viruses with microscale electrokinetic techniques. The concluding remarks discuss the potential applications and future directions.


Assuntos
Vírus , Eletrodos
19.
Lab Chip ; 21(23): 4596-4607, 2021 11 25.
Artigo em Inglês | MEDLINE | ID: mdl-34739022

RESUMO

Insulator-based microfluidic devices are attractive for handling biological samples due to their simple fabrication, low-cost, and efficiency in particle manipulation. However, their widespread application is limited by the high operation voltages required to achieve particle trapping. We present a theoretical, numerical, and experimental study that demonstrates these voltages can be significantly reduced (to sub-100 V) in direct-current insulator-based electrokinetic (DC-iEK) devices for micron-sized particles. To achieve this, we introduce the concept of the amplification factor-the fold-increase in electric field magnitude due to the presence of an insulator constriction-and use it to compare the performance of different microchannel designs and to direct our design optimization process. To illustrate the effect of using constrictions with smooth and sharp features on the amplification factor, geometries with circular posts and semi-triangular posts were used. These were theoretically approximated in two different systems of coordinates (bipolar and elliptic), allowing us to provide, for the first time, explicit electric field amplification scaling laws. Finite element simulations were performed to approximate the 3D insulator geometries and provide a parametric study of the effect of changing different geometrical features. These simulations were used to predict particle trapping voltages for four different single-layer microfluidic devices using two particle suspensions (2 and 6.8 µm in size). The general agreement between our models demonstrates the feasibility of using the amplification factor, in combination with nonlinear electrokinetic theory, to meet the prerequisites for the development of portable DC-iEK microfluidic systems.


Assuntos
Técnicas Analíticas Microfluídicas , Eletricidade , Eletroforese , Dispositivos Lab-On-A-Chip , Microfluídica , Tamanho da Partícula
20.
Micromachines (Basel) ; 12(6)2021 May 28.
Artigo em Inglês | MEDLINE | ID: mdl-34071691

RESUMO

The manner of sample injection is critical in microscale electrokinetic (EK) separations, as the resolution of a separation greatly depends on sample quality and how the sample is introduced into the system. There is a significant wealth of knowledge on the development of EK injection methodologies that range from simple and straightforward approaches to sophisticated schemes. The present study focused on the development of optimized EK sample injection schemes for direct current insulator-based EK (DC-iEK) systems. These are microchannels that contain arrays of insulating structures; the presence of these structures creates a nonuniform electric field distribution when a potential is applied, resulting in enhanced nonlinear EK effects. Recently, it was reported that the nonlinear EK effect of electrophoresis of the second kind plays a major role in particle migration in DC-iEK systems. This study presents a methodology for designing EK sample injection schemes that consider the nonlinear EK effects exerted on the particles being injected. Mathematical modeling with COMSOL Multiphysics was employed to identify proper voltages to be used during the EK injection process. Then, a T-microchannel with insulating posts was employed to experimentally perform EK injection and separate a sample containing two types of similar polystyrene particles. The quality of the EK injections was assessed by comparing the resolution (Rs) and number of plates (N) of the experimental particle separations. The findings of this study establish the importance of considering nonlinear EK effects when planning for successful EK injection schemes.

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