Tradeoff between mixing and transport for electroosmotic flow in heterogeneous microchannels with nonuniform surface potentials

Electroosmotic flow (EOF) is a phenomenon associated with the movement of an aqueous solution induced by the application of an electric field in microchannels. The characteristics of EOF depend on the nature of the surface potential, i.e., whether it is uniform or nonuniform. In this paper, a lattice Boltzmann model (LBM) combined with the Poisson-Boltzmann equation is used to simulate flow field in a rectangular microchannel with nonuniform (step change) surface potentials. The simulation results indicate that local circulations can occur near a heterogeneous region with nonuniform surface potentials, in agreement with those by other authors. Largest circulations, which imply a highest mixing efficiency due to convection and short-range diffusion, were found when the average surface potential is zero, regardless of whether the distribution of the heterogeneous patches is symmetric or asymmetric. In this work, we have illustrated that there is a trade-off between the mixing and liquid transport in EOF microfluidics. One should not simply focus on mixing and neglect liquid transport, as performed in the literature. Excellent mixing could lead to a poor transport of electroosmotic flow in microchannels.     

Detecting deviations from pure EOF during CE separations

CE separations are known for their high separation efficiencies. In systems with EOF, the high efficiencies benefit from the flat, plug profile that is characteristic of EOF. When a velocity gradient is present, such as in separations which have nonuniform buffer ionic strength, surface adsorption or differences in the height of the ends of the capillary, a parabolic flow component is introduced. This deviation from purely EOF yields increased peak dispersion and a subsequent decrease in separation performance. This work details a rapid method for detecting deviations from ideal plug flow during the course of a separation using the radially averaged flow profile of a photobleached fluorophore added to the BGE. By comparing the ratio of two different data analysis procedures, deviations from ideal plug flow can be detected. This method allows rapid measurement of flow character and does not interfere with the concurrent separation. We demonstrate easy detection of the onset of hydrodynamic flow induced by both gravity siphoning and an ionic strength buffer discontinuity. A brief analysis of the radially averaged peak shapes is also presented.     

Separation of basic proteins by capillary zone electrophoresis with coatings of a copolymer of vinylpyrrolidone and vinylimidazole

Capillary zone electrophoretic (CZE) separation of basic proteins has been achieved with capillary columns modified with copolymers of vinylpyrrolidone (VP) and vinylimidazole (VI). The copolymerization reaction is performed inside the capillary column and involves chemical bonding of the polymer to silica. The electroosmotic flow (EOF) is greatly decreased by this surface modification. The presence of positive charges on the coating surface, due to the cationic property of vinylimidazole at pH below 7, reduces the adsorption of basic proteins onto the silanol groups of the capillary surface. Acidic proteins are irreversibly adsorbed, but rapid separation and good performance reproducibility are obtained with basic proteins. In the case of capillaries modified with VP, the acidic and basic proteins are eluted within 10 min. In this work, we studied the effects of pH and buffer concentration on the magnitude of the EOF, as well as the effect of copolymer composition on the separation efficiency.     

Microfluidic device for capillary electrochromatography-mass spectrometry

A novel microfabricated device that integrates a monolithic polymeric separation channel, an injector, and an interface for electrospray ionization-mass spectrometry detection (ESI-MS) was devised. Microfluidic propulsion was accomplished using electrically driven fluid flows. The methacrylate-based monolithic separation medium was prepared by photopolymerization and had a positively derivatized surface to ensure electroosmotic flow (EOF) generation for separation of analytes in a capillary electrochromatography (CEC) format. The injector operation was optimized to perform under conditions of nonuniform EOF within the microfluidic channels. The ESI interface allowed hours of stable operation at the flow rates generated by the monolithic column. The dimensions of one processing line were sufficiently small to enable the integration of 4-8 channel multiplexed structures on a single substrate. Standard protein digests were utilized to evaluate the performance of this microfluidic chip. Low- or sub-fmol amounts were injected and detected with this arrangement.     

Adsorption of buffer ion pairs can alter long‐term electroosmotic flow stability

Dynamic capillary coatings have become widespread due to their efficacy in modifying the EOF in capillary electrophoretic separations and ability to limit unwanted analyte‐surface interactions. However, our understanding of exactly what types of interactions are taking place at the surface of a capillary when these dynamic additives are present is limited. In this work, we have chosen a simple, small molecule additive, tetramethylammonium to examine its influence on the EOF under typical separation conditions. What we have revealed is that this simple compound does not interact with the capillary surface in a very simple manner. Our initial hypothesis of a direct ionic interaction with the silanol surface has evolved with evidence of complex ion pairing between the silanols, the tetramethylammonium, and the buffer ions. This ion pairing can result in drastic changes in the EOF over time, and that the EOF can only be restored to initial levels with harsh rinses containing sodium hydroxide.     

Conditions for similitude and the effect of finite Debye length in electroosmotic flows

Under certain conditions, the velocity field is similar to the electric field for electroosmotic flow (EOF) inside a channel. There was a disagreement between investigators on the necessity of the infinitesimal-Reynolds-number condition for the similarity when the Helmholtz-Smoluchowski relation is applied throughout the boundaries. What is puzzling is a recent numerical result that showed, contrary to the conventional belief, an evident Reynolds number dependence of the EOF. We show here that the notion that the infinitesimal-Reynolds-number condition is required originates from the misunderstanding that the EOF is the Stokes flow. We point out that the EOF becomes the potential flow when the Helmholtz-Smoluchowski relation is applied at the boundaries. We carry out a numerical simulation to investigate the effect of finiteness of the Debye length and the vorticity layer inherently existing at the channel wall. We show that the Reynolds number dependence of the previous numerical simulation resulted from the finiteness of the Debye length and subsequent convective transport of vorticity toward the bulk flow. We discuss in detail how the convection of vorticity occurs and what factors are involved in the transport process, after carrying out the simulation for different Reynolds numbers, Debye lengths, corner radii, and geometries.     

Shear-induced structure in polymer-clay nanocomposite solutions

The equilibrium structure and shear response of model polymer-clay nanocomposite gels are measured using X-ray scattering, light scattering, optical microscopy, and rheometry. The suspensions form physical gels via the "bridging" of neighboring colloidal clay platelets by the polymer, with reversible adsorption of polymer segments onto the clay surface providing a short-range attractive force. As the flow disrupts this transient network, coupling between composition and stress leads to the formation of a macroscopic domain pattern, while the clay platelets orient with their surface normal parallel to the direction of vorticity. We discuss the shear-induced structure, steady-shear rheology, and oscillatory-shear response of these dynamic networks, and we offer a physical explanation for the mesoscale shear response. In contrast to flow-induced "banding" transitions, no stress plateau is observed in the region where macroscopic phase separation occurs. The observed platelet orientation is different from that reported for polymer-melt clay nanocomposites, which we attribute to effects associated with macroscopic phase separation under shear flow.     

A new and selective capillary column coated with cationic diazacrown ether for separation of organic and inorganic anions by capillary electrophoresis

A new coated capillary has been introduced for capillary electrophoretic separation of anions by using a positively charged diazacrown ether with a 12-membered ring. A positive charge spread over the inner capillary surface led to a substantial anodic electroosmotic flow (EOF) over the range of migrating buffer of pH 2-11. Under the optimum conditions of 25 mM phosphate buffer at pH 7, the diazacrown-coated capillary showed a successful simultaneous separation of 7 inorganic anions and 13 aromatic anions (including positional isomers) in less than 15 min. The migration times of the sample anions and EOF marker for consecutive runs on a single column were highly reproducible, giving a relative standard deviation of 1%. Theoretical treatment of the migration behavior clearly demonstrated that ion association between the diazacrown and analyte anions is strongly dependent on the nature of the functional groups of anions (e.g., sulfonate groups > carboxyl groups) and the number of negative charges (e.g., trivalent anions > divalent anions > monovalent anions) on the analyte.     

Capillary electrochromatography with monolithic stationary phases. 4. Preparation of neutral stearyl-acrylate monoliths and their evaluation in capillary electrochromatography of neutral and charged small species as well as peptides and proteins

A neutral, nonpolar monolithic capillary column having a relatively strong electroosmotic flow (EOF) yet free of electrostatic interactions with charged solutes was developed for the reversed-phase capillary electrochromatography (RP-CEC) of neutral and charged species including peptides and proteins. The neutral nonpolar monolith is based on the in situ polymerization of pentaerythritol diacrylate monostearate (PEDAS) in a ternary porogenic solvent composed of cyclohexanol, ethylene glycol, and water. PEDAS plays the role of both the cross-linker and the ligand provider, generating a macroporous nonpolar monolith having C17 chains as the chromatographic ligands. Despite the fact that the neutral PEDAS monolith is devoid of fixed charges, the monolithic capillary columns exhibited a relatively strong EOF due to the ability of PEDAS to adsorb sufficient amounts of electrolyte ions from the mobile phase. The adsorbed ions imparted the neutral PEDAS monolith the zeta potential necessary to support the EOF required for mass transport across the monolithic column. The absence of fixed charges on the surface of the neutral PEDAS monolith and in turn the adsorption sites for electrostatic attraction of charged solutes allowed the rapid and efficient separations of proteins and peptides at pH 7.0, with an average plate number of 255,000 and 121,000 plates/m, respectively. To the best of our knowledge, this constitutes the first report on the separation of proteins at neutral pH by RP-CEC using a neutral monolithic column.     

Layer‐by‐Layer Assembly of Polyelectrolyte and Nanoparticles,Monitored by Capillary Electrophoresis

Layer‐by‐layer (LBL) assembly is a versatile nanofabrication technique, and investigation of its kinetics is essential for understanding the assembly mechanism and optimizing the assembly procedure. In this work, the LBL assembly of polyelectrolyte and nanoparticles were monitored in situ by capillary electrophoresis (CE) for the first time. The assembly of poly(diallyldimethylammonium chloride) (PDDA), and gold nanoparticles (AuNPs) on capillary walls causes surface‐charge neutralization and resaturation, and thus yields synchronous changes in the electroosmotic flow (EOF). The EOF data show that formation of multilayers follows first‐order adsorption kinetics. On the basis of the fit results, influencing factors, including number of layers, concentration of materials, flow rate, and size of AuNPs, were investigated. The stability and robustness of the assembled coatings were also characterized by CE. It was found that degradation of PDDA layers follows first‐order chemical kinetics, while desorption of AuNPs takes place in a disorderly manner. The substrate strongly affects assembly of the underlying layer, while this effect is rapidly screened with increasing number of layers. Furthermore, we demonstrate that the EOF measuring step does not disturb LBL assembly, and the proposed method is reliable and rugged. This work not only studies in detail the LBL adsorption/desorption process of polyelectrolyte and nanoparticles, but also offers an alternative tool for monitoring multilayer buildup. It may also reveal the potential of CE in fields other than analytical separation.     

Fluid dynamics in capillary and chip electrochromatography

This review is concerned with the phenomenological fluid dynamics in capillary and chip electrochromatography (EC) using high-surface-area random porous media as stationary phases. Specifically, the pore space morphology of packed beds and monoliths is analyzed with respect to the nonuniformity of local and macroscopic EOF, as well as the achievable separation efficiency. It is first pointed out that the pore-level velocity profile of EOF through packed beds and monoliths is generally nonuniform. This contrasts with the plug-like EOF profile in a single homogeneous channel and is caused by a nonuniform distribution of the local electrical field strength in porous media due to the continuously converging and diverging pores. Wall effects of geometrical and electrokinetic nature form another origin for EOF nonuniformities in packed beds which are caused by packing hard particles against a hard wall with different zeta potential. The influence of the resulting, systematic porosity fluctuations close to the confining wall over a distance of a few particle diameters becomes aggravated at low column-to-particle diameter ratio. Due to the hierarchical structure of the pore space in packed beds and silica-based monoliths which are characterized by discrete intraparticle (intraskeleton) mesoporous and interparticle (interskeleton) macroporous spatial domains, charge-selective transport prevails within the porous particles and the monolith skeleton under most general conditions. It forms the basis for electrical field-induced concentration polarization (CP). Simultaneously, a finite and -- depending on morphology -- often significant perfusive EOF is realized in these hierarchically structured materials. The data collected in this review show that the existence of CP and its relative intensity compared to perfusive EOF form fundamental ingredients which tune the fluid dynamics in EC employing monoliths and packed beds as stationary phases. This addresses the (electro)hydrodynamics, associated hydrodynamic dispersion, as well as the migration and retention of charged analytes.     

Non-uniform surface charge distributions in CE: theoretical and experimental approach based on Taylor dispersion

The control of the EOF direction and magnitude remains one of the more challenging issues for the optimization of separations in CE. In this work, we investigated the possibility to use non-uniform surface charge distribution for the modulation of the EOF in CE. Non-uniform zeta potentials were obtained by modifying a section of the capillary surface using adsorption of polyelectrolytes. Three different methods were studied: (i) partial polycation coating on a fused silica capillary, (ii) partial polycation (or polyanion) coating on polyelectrolyte multilayers, and (iii) partial polycation coating on a capillary previously modified with poly(ethylene oxide). The magnitude and the direction of the EOF as a function of the coated capillary length were first studied. The stability of the EOF and the separation performances were also considered taking two dialanine diastereoisomers as model compounds. In partially coated capillaries, the average solvent flow is the sum of two contributions: a non-dispersive electroosmotic contribution related to the capillary surface charge, and a dispersive hydrodynamic contribution that depends on the difference of surface charge between the coated and the non-coated capillary zones. To get a better insight into the influence of the hydrodynamic contribution to the total peak dispersion, the peak variances corresponding to the Taylor dispersion, the injection plug, and the axial diffusion were calculated. This work demonstrates that peak dispersion in a capillary partially coated by the inlet end is different from that obtained when the coating is performed by the outlet end. Experimentally, the combination of a partially coated capillary with a large volume sample stacking preconcentration step can be used for injecting up to 95% of the capillary volume. This approach leads to a preconcentration factor of 60 compared with CZE with classical injection.     

Electroosmotic flow in a poly(dimethylsiloxane) channel does not depend on percent curing agent

Poly(dimethylsiloxane) (PDMS) microfluidic devices were prepared from different ratios of "curing agent" (which contains silicon hydride groups) to "base" (which contains vinyl-terminated noncross-linked PDMS), to determine the effect of this ratio on electroosmotic flow (EOF). In fabricating devices for this purpose, a novel method for permanently enclosing PDMS channels was developed. As a supplement to the microfluidic method, the inner walls of capillaries were coated with PDMS formed from varying ratios of curing agent to base. EOF was found to be constant for PDMS formed with each ratio, which implies that the negative surface charges do not arise from chemical species present only in the base or the curing agent.     

Capillary electrochromatography with bare silicas of different pore sizes as stationary phases

Bare silica can be used with reversed phase eluents for the chromatographic separation of basic analytes. It provides high surface charge density within a certain pH range, thus generating a high electroosmotic flow (EOF) when applied in electrochromatography. The influence of pore size on EOF velocity and mass transport is demonstrated. High EOF and fast mass transfer were encountered with 100 nm and 200 nm material and related to a pore perfusion mechanism. On a silica with 200 nm average pore size at pH 7, an EOF velocity of 2 mm/s was obtained at 600 V/cm. Silicas with pore diameters between 6 nm and 200 nm, corresponding to surface areas between 500 m/g and 10 m/g (data calculated from inverse size exclusion chromatography experiments), were used for CEC and HPLC separation of strongly basic solutes. On separation of tricyclic antidepressants by CEC, “normal” and “abnormal” efficiencies were achieved and were found to vary with the charge density within the separation column.     

Advantages and limitations of a new cationic coating inducing a slow electroosmotic flow for CE-MS peptide analysis: a comparative study with commercial coatings

Capillary coatings are crucial for high-quality separation performance in capillary electrophoresis analysis of proteins or peptides as they prevent analyte adsorption at the capillary wall. These coating materials have to fulfill many requirements such as a good separation performance and ensuring a good repeatability. The number of commercially available coating materials is still limited, especially with regard to the charge density on the coating material and the induced electroosmotic flow (EOF) velocity. In this work, we compare the separation performance of the novel self-made cationic capillary coating OHNOON and two commercially available coating materials, the acrylamide based, neutral LN® and the cationic hexadimethrine bromide (Polybrene), using the same coating procedure for all three coating materials. The coatings are investigated regarding the separation efficiency, analyte resolution, coating stability, and migration time stability in tryptic peptide analysis. Good separation performance was confirmed for all three coating materials: all coatings provided high plate numbers of up to 400,000–500,000 and a repeatability of the EOF and the analyte migration times in the range of 1 % relative standard deviation or below. Our results reveal a moderate EOF velocity for the novel OHNOON coating in comparison to the Polybrene coating. We present a detailed discussion of the impact of this reduced EOF velocity and the separation performance. The results presented here will help to define the necessary properties of coating materials to achieve the best compromise between speed of analysis and resolution for the respective application. We show that our novel OHNOON coating is especially valuable for the analysis of low mobility analytes and for samples with a broad range of analyte mobilities.     

Microchip electrophoretic protein separation using electroosmotic flow induced by dynamic sodium dodecyl sulfate-coating of uncoated plastic chips

Separation of sodium dodecyl sulfate (SDS)-protein complexes is difficult on plastic microchips due to protein adsorption onto the wall. In this paper, we elucidated the reasons for the difficulties in separating SDS-protein complexes on plastic microchips, and we then demonstrated an effective method for separating proteins using polymethyl methacrylate (PMMA) microchips. Separation difficulties were found to be dependent on adsorption of SDS onto the hydrophobic surface of the channel, by which cathodic electroosmotic flow (EOF; reversed flow) was generated. Our developed method effectively utilized the reversed flow from this cathodic EOF as a driving force for sample proteins using permanently uncoated but dynamic SDS-coated PMMA microchips. High-speed (6 s) separation of proteins and peptides up to 116 kDa was successfully achieved using this system.     

Micellar electrokinetic capillary chromatography using polymeric hollow fibers

Summary In this paper, polymeric hollow fibers prepared from pH-stable polypropylene were used as columns for micellar electrokinetic capillary chromatography (MECC). The electroosmotic flow (EOF) for polypropylene hollow fibers was evaluated in the pH range of 5.0–12.0. With untreated polypropylene hollow fibers a stabilized but enhanced EOF was achieved when SDS was used in the buffer, decreasing the separation window for uncharged substances in MECC to impractical levels. Uncharged acrylamide and charged 2-acryloylamido-2-methylpropane sulfonic acid surface modifications were used to lower the strength of the EOF, increase the separation window and prevent local overheating that could melt the column wall.     

Effect of surface conduction–induced electromigration on current monitoring method for electroosmotic flow measurement

Current monitoring method for measurement of EOF in microchannels involves measurement of time-varying current while an electrolyte displaces another electrolyte having different conductivity due to EOF. The basic premise of the current monitoring method is that an axial gradient in conductivity of a binary electrolyte in a microchannel advects only due to EOF. In the current work, using theory and experiments, we show that this assumption is not valid for low concentration electrolytes and narrow microchannels wherein surface conduction is comparable with bulk conduction. We show that in presence of surface conduction, a gradient in conductivity of binary electrolyte not only advects with EOF but also undergoes electromigration. This electromigration phenomenon is nonlinear and is characterized by propagation of shock and rarefaction waves in ion concentrations. Consequently, in presence of surface conduction, the current–time relationships for forward and reverse displacement in the current monitoring method are asymmetric and the displacement time is also direction dependent. To quantify the effect of surface conduction, we present analytical expressions for current–time relationship in the regime when surface conduction is comparable to bulk conduction. We validate these relations with experimental data by performing a series of current monitoring experiments in a glass microfluidic chip at low electrolyte concentrations. The experimentally validated analytical expressions for current–time relationships presented in this work can be used to correctly estimate EOF using the current monitoring method when surface conduction is not negligible.     

Continuous and precise particle separation by electroosmotic flow control in microfluidic devices

A new scheme has been described for continuous particle separation using EOF in microfluidic devices. We have previously reported a method for particle separation, called "pinched flow fractionation (PFF)", in which size-dependent and continuous particle separation can be achieved by introducing pressure-driven flows with and without particles into a pinched microchannel. In this study, EOF was employed to transport fluid flows inside a microchannel. By controlling the applied voltage to electrodes inserted in each inlet/outlet port, the flow rates from both inlets, and flow rates distributed to each outlet could be accurately tuned, thus enabling more effective separation compared to the pressure-driven scheme. In the experiment, the particle behaviors were compared between EOF and pressure-driven flow schemes. In addition, micrometer- and submicrometer-sized particles were accurately separated and individually collected using a microchannel with multiple outlet branch channels, demonstrating the high efficiency of the presented scheme.