Transient electrophoresis of a conducting spherical particle embedded in an electrolyte-saturated Brinkman medium

In this study, the time-dependent electrophoretic motion of a conducting spherical particle embedded in an arbitrary electrolyte solution saturated porous medium is investigated. The porous medium is uniformly charged and the embedded hard particle is charged with constant -potential or constant surface charge density. The unsteady modified Brinkman equation with an electric force term, which governs the fluid velocity field, is used to model the porous medium and is solved by Laplace's transform technique. An analytical expression for the electrophoretic velocity of the spherical particle is obtained in Laplace transform domain as a function of the relevant parameters, and its inversion is obtained through numerical techniques. Also, in this study, the steady-state electrophoretic velocity is obtained analytically as linear functions of -potential (or surface density charge) and the fixed charge density. The steady-state electrophoretic velocity is displayed graphically for various relevant parameters and compered with the available data in the literature. Also, the numerical values of the transient electrophoretic velocity are plotted versus the nondimensional elapsed time and discussed for different values of the Debye length parameter, density ratio, permeability of the porous medium, and for high and nonconducting particles.     

Transient electrophoresis of a charged porous particle

The starting electrophoretic motion of a porous, uniformly charged, spherical particle, which models a solvent-permeable and ion-penetrable polyelectrolyte coil or floc of nanoparticles, in an arbitrary electrolyte solution due to the sudden application of an electric field is studied for the first time. The unsteady Stokes/Brinkman equations with the electric force term governing the fluid velocity fields are solved by means of the Laplace transform. An analytical formula for the electrophoretic mobility of the porous sphere is obtained as a function of the dimensionless parameters , , , and , where a is the radius of the particle, κ is the Debye screening parameter, λ is the reciprocal of the square root of the fluid permeability in the particle, ρ_p and ρ are the mass densities of the particle and fluid, respectively, ν is the kinematic viscosity of the fluid, and t is the time. The electrophoretic mobility normalized by its steady-state value increases monotonically with increases in and , but decreases monotonically with an increase in , keeping the other parameters unchanged. In general, a porous particle with a high fluid permeability trails behind an identical porous particle with a lower permeability and a corresponding hard particle in the growth of the normalized electrophoretic mobility The normalized electrophoretic acceleration of the porous sphere decreases monotonically with an increase in the time and increases with an increase in from zero at .     

Effect of magnetic field on electroosmotic flow of viscoelastic fluids in a microchannel

Electroosmotic flow is an efficient transportation technology driven by applying an external electric field across the microchannel, which has a great potential for future application. This work is presented to study the unsteady electroosmotic flow of viscoelastic fluids combined with a constant pressure gradient and a vertical magnetic field through a parallel plate microchannel. For the reason that the upper and bottom walls of the parallel plate microchannel in microfluidic devices can be made of different materials, this leads to different hydrophobic properties, asymmetric zeta wall potentials, and different slip boundary conditions. The Navier slip model with different slip coefficients at walls is considered. The generalized Maxwell fluid with fractional derivative is adopted for the constitutive equation of the fluid. The analytical and numerical solutions of velocity are derived by employing the integral transform method and finite difference method, respectively. Excellent agreement is found between the numerical solutions and analytical solutions. Finally, the effects of fractional parameter , relaxation time , slip coefficients and , the ratio of wall zeta potentials , Hartmann number , and electrical field strength parameter on velocity profiles are interpreted graphically in detail.     

The lift force on a charged sphere that translates and rotates in an electrolyte

The distortion of the charge cloud around a uniformly charged, dielectric, rigid sphere that translates and rotates in an unbounded binary, symmetric electrolyte at zero Reynolds number is examined. The zeta potential of the particle ζ is assumed small relative to the thermal voltage scale. It is assumed that the equilibrium structure of the cloud is slightly distorted, which requires that the Péclet numbers characterizing distortion due to particle translation, , and rotation, , are small compared to unity. Here, a is radius of the particle; D is the ionic diffusion coefficient; and , where U and Ω are the rectilinear and angular velocities of the particle, respectively. Perturbation expansions for small and are employed to calculate the nonequilibrium structure of the cloud, whence the force and torque on the particle are determined. In particular, we predict that the sphere experiences a force orthogonal to its directions of translation and rotation. This “lift” force arises from the nonlinear distortion of the cloud under the combined actions of particle translation and rotation. The lift force is given by . Here, ε is the permittivity of the electrolyte; is the Debye length; and is a negative function that decreases in magnitude with increasing . The lift force implies that an unconstrained particle would follow a curved path; an electrokinetic analog of the inertial Magnus effect. Finally, the implication of the lift force on cross‐streamline migration of an electrophoretic particle in shear flow is discussed.     

Simulations of a weakly conducting droplet under the influence of an alternating electric field

We investigate the electrohydrodynamics of an initially spherical droplet under the influence of an external alternating electric field by conducting axisymmetric numerical simulations using a charge-conservative volume-of-fluid based finite volume flow solver. The mean amplitude of shape oscillations of a droplet subjected to an alternating electric field for leaky dielectric fluids is similar to the steady-state deformation under an equivalent root mean squared direct electric field for all possible electrical conductivity ratio and permittivity ratio of the droplet to the surrounding fluid. In contrast, our simulations for weakly conducting media show that this equivalence between alternating and direct electric fields does not hold for . Moreover, for a range of parameters, the deformation obtained using the alternating and direct electric fields is qualitatively different, that is, for low and high , the droplet becomes prolate under alternating electric field but deforms to an oblate shape in the case of the equivalent direct electric field. A parametric study is conducted by varying the time period of the applied alternating electric field, the permittivity and the electrical conductivity ratios. It is observed that while increasing has a negligible effect on the deformation dynamics of the droplet for , it enhances the deformation of the droplet when for both alternating and direct electric fields. We believe that our results may be of immense consequence in explaining the morphological evolution of droplets in a plethora of scenarios ranging from nature to biology.     

Measurement of the amplitude and phase of the electrophoretic and electroosmotic mobility based on fast single-particle tracking

The electrophoretic mobility of micron-scale particles is of crucial importance in applications related to pharmacy, electronic ink displays, printing, and food technology as well as in fundamental studies in these fields. Particle mobility measurements are often limited in accuracy because they are based on ensemble averages and because a correction for electroosmosis needs to be made based on a model. Single-particle approaches are better suited for examining polydisperse samples, but existing implementations either require multiple measurements to take the effect of electroosmosis into account or are limited in accuracy by short measurement times. In this work, accurate characterization of monodisperse and polydisperse samples is achieved by measuring the electrophoretic mobility on a particle-to-particle basis while suppressing electroosmosis. Electroosmosis can be suppressed by measuring in the middle of a microchannel while applying an AC voltage with a sufficiently high frequency. An accurate measurement of the electrophoretic mobility is obtained by analyzing the oscillating particle motion for per particle with a high-speed camera measuring at , synchronized to the applied electric field. Attention is paid to take into account the effect of the rolling shutter and the non-uniform sampling in order to obtain the accurate amplitude and phase of the electrophoretic mobility. The accuracy of method is experimentally verified and compared with a commercial apparatus for polystyrene microspheres in water. The method is further demonstrated on a range of particle materials and particle sizes and for a mixture of positively and negatively charged particles.     

Measurement of the real part of the Clausius–Mossotti factor of dielectrophoresis for Brownian particles

A method is proposed for measuring the real part of the Clausius–Mossotti factor () of dielectrophoresis for Brownian particles based on a solution of the Smoluchowski equation using a designed polydimethysilloxane microchannel with planar hyperbolic electrodes on its glass substrate. An approximate two-dimensional spring-like dielectrophoretic force is generated in the device, and the data necessarily measured is the time evolution of the in-plane particle displacement undergoing confined Brownian motion. Validity of the measurement was checked against the zeta potentials in the literature based on the classical theory of surface conductance using polystyrene particles of size of one micron. As the dielectrophoretic force depends on , which is usually unknown for bio-particles and some engineered particles, and is seldom measured; this study is important from the academic point of view and could be helpful for the manipulation and characterization of sub-micron particles using dielectrophoresis. Extension of the method to the measurement of permanent dipole moment and total polarizability of particle was developed theoretically and discussed by incorporating an optical tweezer into the present device.     

Electrophoresis of a highly charged fluid droplet in dilute electrolyte solutions: Analytical Hückel-type solution

An analytical formula is presented here for the electrophoresis of a dielectric or perfectly conducting fluid droplet with arbitrary surface potentials suspended in a very dilute electrolyte solution. In other words, when the Debye length (κ⁻¹) is very large, or κa$\ll$1, where κ is the electrolyte strength and a stands for the droplet radius. This formula can be regarded as an extension of the famous Hückel solution valid for weakly charged rigid particles to arbitrarily charged fluid droplets. The formula reduces successfully to the ones obtained by Booth for a dielectric droplet, and Ohshima for a perfectly conducting droplet, both under Debye–Hückel approximation valid for weakly charged droplets. Moreover, the formula is valid for a gas bubble and a rigid solid particle as well. Classic results obtained by Hückel for a rigid particle are reproduced as well. We found that for a dielectric droplet, the more viscous the droplet is, the faster it moves regardless of its surface potential, contrary to the intuition based on the purely hydrodynamic consideration. For a perfectly conducting liquid droplet, on the other hand, the situation is reversed: The less viscous the droplet is, the faster it moves. The presence or absence of the spinning electric driving force tangent to the droplet surface is found to be responsible for it. As a result, an axisymmetric exterior vortex flow surrounding the droplet is always present for a dielectric liquid droplet, and never there for a conducting liquid droplet.     

Nonaqueous capillary electrophoresis and quantum chemical calculations applied to investigation of acid–base and electromigration properties of azahelicenes

Nonaqueous capillary electrophoresis (NACE) using methanol (MeOH) as a solvent of the BGEs and quantum mechanical density functional theory (DFT) have been applied to determine the thermodynamic acidity (ionization) constants (pK_a) of mono- and diaza[5]helicenes, mono- and diaza[6]helicenes, and their dibenzo derivatives in MeOH and water. First, the mixed acidity constants, , of ionogenic pyridinium groups of azahelicenes and their derivatives in MeOH were obtained by nonlinear regression analysis of pH dependence of their effective electrophoretic mobilities. The effective mobilities were measured by NACE in a large series of methanolic BGEs within a wide conventional pH range (pH_MeOH 1.6–12.0) and at ambient temperature (21–26°C) in a home-made CE device. Prior to mixed acidity constant calculation, the effective mobilities were corrected to reference temperature (25°C) and constant ionic strength (25 mM). Then, the mixed acidity constants were recalculated to the thermodynamic acidity constants pK_a,MeOH by the Debye–Hückel theory of nonideality of electrolyte solutions. Finally, from the methanolic thermodynamic pK_a,MeOH values, the aqueous thermodynamic constants were estimated using the empirical relations between methanolic and aqueous acidity constants derived for structurally related pyridine derivatives. Depending on the number and position of the nitrogen atoms in their molecules, the analyzed azahelicenes were found to be weak to moderate bases with methanolic pK_a,MeOH in the range 2.01–8.75 and with aqueous in the range 1.67–8.28. The thermodynamic pK_a,MeOH obtained by the DFT calculations were in a good agreement with those determined experimentally by NACE.     

Numerical study supplemented with simplified model on electrophoresis of a hydrophobic colloid incorporating finite ion size effects and ion-solvent interactions

We consider a modified electrokinetic model to study the electrophoresis of a hydrophobic particle by considering the finite sized ions. The mathematical model adopted in this study incorporates the ion steric repulsion, ion-solvent interactions as well as Maxwell stress on the electrolyte. The dielectric permittivity and viscosity of the electrolyte is considered to vary with the local ionic volume fraction. Based on this modified model for the electrokinetics we have analyzed the electrophoresis in a single as well as mixture of electrolytes of monovalent and non-$z:z$ electrolytes. The dependence of viscosity on local ionic volume fraction modifies the hydrodynamic drag as well as diffusivity of ions, which are ignored in existing studies on electrophoresis. A simplified model for electrophoresis of a hydrophobic particle incorporating the ion steric repulsion and ion-solvent interactions is developed based on the first-order perturbation on applied electric field. This simplified model is established to be efficient for a Debye layer thinner than the particle size and a smaller range of slip length. This model can be implemented for any number of ionic species as well as non-$z:z$ electrolytes. It is established that the ion steric interactions and dielectric decrement creates a counterion saturation in the Debye layer leading to an enhanced mobility compared to the standard model. However, experimental data for non-dilute cases often under predicts the theoretically determined mobility. The present modified model fills this lacuna and demonstrate that the consideration of finite ion size modifies the medium viscosity and hence, ionic mobility, which in combination lowers the mobility value.     

Dielectrophoresis microbial characterization and isolation of Staphylococcus aureus based on optimum crossover frequency

Characterization of antibiotic-resistant bacteria is a significant concern that persists for the rapid classification and analysis of the bacteria. A technology that utilizes the manipulation of antibiotic-resistant bacteria is key to solving the significant threat of these pathogenic bacteria by rapid characterization profile. Dielectrophoresis (DEP) can differentiate between antibiotic-resistant and susceptible bacteria based on their physical structure and polarization properties. In this work, the DEP response of two Gram-positive bacteria, namely, Methicillin-resistant Staphylococcus aureus (MRSA) and Methicillin-susceptible S. aureus (MSSA), was investigated and simulated. The DEP characterization was experimentally observed on the bacteria influenced by oxacillin and vancomycin antibiotics. MSSA control without antibiotics has crossover frequencies ($f_{x0}$) from 6 to 8 MHz, whereas MRSA control is from 2 to 3 MHz. The $f_{x0}$ changed when bacteria were exposed to the antibiotic. As for MSSA, the $f_{x0}$ decreased to 3.35 MHz compared to $f_{x0}$ MSSA control without antibiotics, MRSA, $f_{x0}$ increased to 7 MHz when compared to MRSA control. The changes in the DEP response of MSSA and MRSA with and without antibiotics were theoretically proven using MyDEP and COMSOL simulation and experimentally based on the modification to the bacteria cell walls. Thus, the DEP response can be employed as a label-free detectable method to sense and differentiate between resistant and susceptible strains with different antibiotic profiles. The developed method can be implemented on a single platform to analyze and identify bacteria for rapid, scalable, and accurate characterization.     

Effects of electrode size and surface morphology on electrode polarization in physiological buffers

Electrode polarization (EP) is inevitable in high conductivity buffers at low AC frequencies due to the accumulation of free charges at the electrode/electrolyte interface. Electrode miniaturization increases EP effect on impedance measurements. In this paper, six gold planar (GP) electrodes having different diameters () were used to investigate the size effect on EP with parallel plate electrode geometry. GP electrode surface was electrochemically deposited with gold nanostructures (GNs) to minimize the EP effect. Equivalent circuit model was used to attain electrode/electrolyte interfacial impedance. Constant phase element model was used to analyze the relation between the size and morphology of electrodes on EP. The surface morphology of gold nanostructured electrodes was examined using SEM, and the influence of different applied potential on the growth of GNs was elucidated with Nernst equilibrium condition. Surface roughness and wettability characteristics were examined performing surface roughness and contact angle measurements, respectively. The improvement of GNs deposited electrode performance was investigated by analytically generated Jurkat cell suspension spectra. The results show that the error in estimating the subcellular properties can be drastically reduced by using GNs deposited electrodes.     

Rapid prototyping of polydimethylsiloxane (PDMS) microchips using electrohydrodynamic jet printing: Application to electrokinetic assays

Polydimethylsiloxane (PDMS) based microfluidic devices have found increasing utility for electrophoretic and electrokinetic assays because of their ease of fabrication using replica molding. However, the fabrication of high-resolution molds for replica molding still requires the resource-intensive and time-consuming photolithography process, which precludes quick design iterations and device optimization. We here demonstrate a low-cost, rapid microfabrication process, based on electrohydrodynamic jet printing (EJP), for fabricating non-sacrificial master molds for replica molding of PDMS microfluidic devices. The method is based on the precise deposition of an electrically stretched polymeric solution of polycaprolactone in acetic acid on a silicon wafer placed on a computer-controlled motion stage. This process offers the high-resolution (order 10 $\mu$m) capability of photolithography and rapid prototyping capability of inkjet printing to print high-resolution templates for elastomeric microfluidic devices within a few minutes. Through proper selection of the operating parameters such as solution flow rate, applied electric field, and stage speed, we demonstrate microfabrication of intricate master molds and corresponding PDMS microfluidic devices for electrokinetic applications. We demonstrate the utility of the fabricated PDMS microchips for nonlinear electrokinetic processes such as electrokinetic instability and controlled sample splitting in ITP. The ability to rapid prototype customized reusable master molds with order 10 $\mu$m resolution within a few minutes can help in designing and optimizing microfluidic devices for various electrokinetic applications.     

Stiffness measurement of nanosized liposomes using solid‐state nanopore sensor with automated recapturing platform

This paper describes a method to gauge the stiffness of nanosized liposomes – a nanoscale vesicle – using a custom‐made recapture platform coupled to a solid‐state nanopore sensor. The recapture platform electrically profiles a given liposome vesicle multiple times through automated reversal of the voltage polarity immediately following a translocation instance to re‐translocate the same analyte through the nanopore – provides better statistical insight at the molecular level by analyzing the same particle multiple times compared to conventional nanopore platforms. The capture frequency depends on the applied voltage with lower voltages (i.e., 100 mV) permitting higher recapture instances than at higher voltages (>200 mV) since the probability of particles exiting the nanopore capture radius increases with voltage. The shape deformation was inferred by comparing the normalized relative current blockade ( at the two voltage polarities to that of a rigid particle, i.e., polystyrene beads. We found that liposomes deform to adopt a prolate shape at higher voltages. This platform can be further applied to investigate the stiffness of other types of soft matters, e.g., virus, exosomes, endosomes, and accelerate the potential studies in pharmaceutics for increasing the drug packing and unpacking mechanism by controlling the stiffness of the drug vesicles.     

Quantitative model for predicting the electroosmotic flow in dual-pole nanochannels

Developing and assessing nanofluidic systems is time-consuming and costly owing to the method's novelty; hence, modeling is essential to determine the optimal areas for implementation and to grasp its workings. In this work, we examined the influence of dual-pole surface and nanopore configuration on ion transfer simultaneously. To achieve this, the two trumpet and cigarette configuration were coated with a dual-pole soft surface so that the negative charge could be positioned in the nanopore's small aperture. Subsequently, the Poisson–Nernst–Planck and Navier–Stokes equations were simultaneously solved under steady-state circumstances using varied values physicochemical properties for the soft surface and electrolyte. The pore's selectivity was $S_{\mathrm{Trumpet}}>S_{\mathrm{Cigarette}}$, and the rectification factor, on the other hand, was , when the overall concentration was very low. When the ion partitioning effect is taken into account, we clearly show that the rectifying variables for the cigarette configuration and the trumpet configuration can reach values of 45 and 49.2, when the charge density and mass concentration were 100 mol/m³ and 1 mM, respectively. By using dual-pole surfaces, the controllability of nanopores’ rectifying behavior may be modified to produce superior separation performance.     

Short-chain polyphosphates: Extraction effects on migration and size estimation of Saccharomyces cerevisiae extracts with polyacrylamide gel electrophoresis

Polyacrylamide gel electrophoresis is commonly used to characterize the chain length of polyphosphates (polyP), more generally called condensed phosphates. After separation, nonradioactive, optical polyP staining is limited to chain lengths greater than 15 ${\mathrm{PO}}_3^{-}$monomers with toluidine blue or 4′,6-diamidino-2-phenylindole. PolyP chain lengths longer than 62${\mathrm{PO}}_3^{-}$monomers were correlated to the shortest DNA ladders. In this study, synthetic linear polyPs (Sigma-Aldrich “Type 45”, estimated mean length of 45 ${\mathrm{PO}}_3^{-}$ monomers), trimetaphosphate (trimetaP: 3 ${\mathrm{PO}}_3^{-}$ ring), tripolyphosphate (tripolyP), pyrophosphate (PP_i), and inorganic orthophosphate (o-P_i) were visualized after separation by an in situ hydrolytic degradation process to o-P_i that was subsequently stained with methyl green. Statistically insignificant migration reduction of synthetic short-chain polyP after perchloric acid or phenol–chloroform extraction was confirmed with the Friedman test. ³¹P diffusion–ordered NMR spectroscopy confirmed that extraction also reduced PP_i diffusivity by <10%. Linear regression between the R_f peak migration value and the logarithm of synthetic polyP molecular weights enabled estimation of extracted polyP chain lengths from 2 to 45 ${\mathrm{PO}}_3^{-}$monomers. Linear polyP extracts from Saccharomyces cerevisiae grown in aerobic conditions were generally shorter than extracts cultured in anaerobic conditions. Extractions from both aerobic and anaerobic S. cerevisiae included tripolyP and o-P_i, but no PP_i.     

Analysis of the Binding of Cytokines to Highly Charged Polymer Networks

A model describing the binding of biological signaling proteins to highly charged polymer networks is presented. The networks are formed by polyelectrolyte chains for which the distance between two charges at the chain is smaller than the Bjerrum length. Counterion condensation on such highly charged chains immobilizes a part of the counterions. The Donnan-equilibrium between the polymer network and the aqueous solution with salt concentration $c_s^b$ is used to calculate the salt concentration of the co- and counterions $c_s^g$ entering the network. Two factors are decisive: i) The electrostatic interaction between the network and the protein is given by the Donnan-potential of the network and the net charge of the protein. In addition to this leading term, a second term describes the change in the Born-energy of the proteins when entering the network. ii) The interaction of the protein with the highly charged chains within the network is governed by counterion release: Patches of positive charge at the protein become multivalent counterions of the polyelectrolyte chains thus releasing a concomitant number of condensed counterions. The model compares favorably to experimental data obtained on a set of biohybrid polymer networks composed of crosslinked glycosaminoglycan chains that interact with a mixture of key signaling proteins.     

High-throughput dielectrophoretic separator based on printed circuit boards

The separation of particles with respect to their intrinsic properties is an ongoing task in various fields such as biotechnology and recycling of electronic waste. Especially for small particles in the lower micrometer or nanometer range, separation techniques are a field of current research since many existing approaches lack either throughput or selectivity. Dielectrophoresis (DEP) is a technique that can address multiple particle properties, making it a potential candidate to solve challenging separation tasks. Currently, DEP is mostly used in microfluidic separators and thus limited in throughput. Additionally, DEP setups often require expensive components, such as electrode arrays fabricated in the clean room. Here, we present and characterize a separator based on two inexpensive custom-designed printed circuit boards (80 × 120 mm board size). The boards consist of interdigitated electrode arrays with $250\mu$m electrode width and spacing. We demonstrate the separation capabilities using polystyrene particles ranging from 500 nm to $6\mu$m in monodisperse experiments. Further, we demonstrate selective trapping at flow rates up to 240 ml/h in the presented device for a binary mixture. Our experiments demonstrate an affordable way to increase throughput in electrode-based DEP separators.     

Electrophoresis simulations using Chebyshev pseudo-spectral method on a moving mesh

We present the implementation and demonstration of the Chebyshev pseudo-spectral method coupled with an adaptive mesh method for performing fast and highly accurate electrophoresis simulations. The Chebyshev pseudo-spectral method offers higher numerical accuracy than all other finite difference methods and is applicable for simulating all electrophoresis techniques in channels with open or closed boundaries. To improve the computational efficiency, we use a novel moving mesh scheme that clusters the grid points in the regions with poor numerical resolution. We demonstrate the application of the Chebyshev pseudo-spectral method on a moving mesh for simulating nonlinear electrophoretic processes through examples of isotachophoresis (ITP), isoelectric focusing (IEF), and electromigration-dispersion in capillary zone electrophoresis (CZE) at current densities as high as 1000 A/m. We also show the efficacy of our moving mesh method over existing methods that cluster the grid points in the regions with large concentration gradients. We have integrated the adaptive Chebyshev pseudo-spectral method in the open-source SPYCE simulator and verified its implementation with other electrophoresis simulators.