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.     

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.     

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.     

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.     

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.     

A dielectrophoresis-based platform of cancerous cell capture using aptamer-functionalized gold nanoparticles in a microfluidic channel

In this paper, a microfluidic chip for the manipulation and capture of cancer cells was introduced, in which the combination of dielectrophoresis (DEP) and a binding method based on chemical interactions by using cell-specific aptamers was performed to enhance the capture strength and specificity. The device has been simply constructed from a straight-channel PDMS placed on a glass substrate that has patterned electrode structures and a self-assembled monolayer of gold nanoparticles (AuNPs). The target cells were transported to the manipulation area by flow and attracted down to the region between the electrodes under the influence of positive DEP force. This approach facilitated subsequent selective capture by the modified aptamers on the AuNPs. The distribution of the electric field in the channel has also been simulated to clarify the DEP operation. As a result, the device has been shown to effectively capture target lung cancer cells with a concentration as low as $2\times {10}^4$cells/mL. The capture specificity in a sample of mixed cells is up to 80.4%. This technique has the potential to be applied to detection methods for many types of cancer.     

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.     

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.     

Continuous organelle separation in an insulator-based dielectrophoretic device

Heterogeneity in organelle size has been associated with devastating human maladies such as neurodegenerative diseases or cancer. Therefore, assessing the size-based subpopulation of organelles is imperative to understand the biomolecular foundations of these diseases. Here, we demonstrated a ratchet migration mechanism using insulator-based dielectrophoresis in conjunction with a continuous flow component that allows the size-based separation of submicrometer particles. The ratchet mechanism was realized in a microfluidic device exhibiting an array of insulating posts, tailoring electrokinetic and dielectrophoretic transport. A numerical model was developed to elucidate the particle migration and the size-based separation in various conditions. Experimentally, the size-based separation of a mixture of polystyrene beads (0.28 and 0.87 $\mu$m) was accomplished demonstrating good agreement with the numerical model. Furthermore, the size-based separation of mitochondria was investigated using a mitochondria mixture isolated from HepG2 cells and HepG2 cells carrying the gene Mfn-1 knocked out, indicating distinct size-related migration behavior. With the presented continuous flow separation device, larger amounts of fractionated organelles can be collected in the future allowing access to the biomolecular signature of mitochondria subpopulations differing in size.     

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.     

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 .     

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.     

Modeling of a linear ion trap with driving rectangular waveforms

We consider the operation of a digital linear ion trap with resonant radial ejection. A sequence of rectangular voltage pulses with a dipole resonance signal is applied to the trap electrodes. The periodic waveform is piecewise constant, has zero mean, and is determined by an asymmetry parameter $d$: one value is taken on interval $\left(0,\mathit{dT}\right)$ and another on $\left(\mathit{dT},T\right)$, where $T$ is the RF period. Ion mass scanning is performed by varying the asymmetry parameter $d$ and amplitude of the negative pulse part with time. The ion oscillation frequencies and acceptance of the linear trap are calculated. The dependence of the ion mass to charge ratio $m/z$ on the parameter $d$ is $m/z~d^2$. The maximum value is about $m/z=30$ kDa for typical parameters of the linear trap: frequency 0.5 MHz, rod radius 4 mm, and negative pulse amplitude 1 kV. The dipolar excitation frequency is 0.125 MHz at which the LIT acceptance is maximal.     

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.     

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.     

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.     

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.     

A periodic array of nano‐scale parallel slats for high‐efficiency electroosmotic pumping

It is known that the eletroosmotic (EO) flow rate through a nano‐scale channel is extremely small. A channel made of a periodic array of slats is proposed to effectively promote the EO pumping, and thus greatly improve the EO flow rate. The geometrically simple array is complicated enough that four length scales are involved: the vertical period 2L, lateral period 2aL, width of the slat 2cL as well as the Debye length . The EO pumping rate is determined by the normalized lengths: a, c, or the perforation fraction of slats and the dimensionless electrokinetic width . In a nano‐scale channel, K is of order unity or less. EO pumping in both longitudinal and transverse directions (denoted as longitudinal EO pumping (LEOP) and transverse EO pumping (TEOP), respectively) is investigated by solving the Debye–Hückel approximation and viscous electro‐kinetic equation. The main findings include that (i) the EO pumping rates of LEOP for small K are remarkably improved (by one order of magnitude) when we have longer slats () and a large perforation fraction of slats (η > 0.7); (ii) the EO pumping rates of TEOP for small K can also be much improved but less significantly with longer slats and a large perforation fraction of slats. Nevertheless, it must be noted that in practice K cannot be made arbitrarily small as the criterion of for the reference potential at the channel center put lower bounds on K; in other words, there are geometrical limits for the use of the Poisson–Boltzmann equation.