A Brownian dynamics-finite element method for simulating DNA electrophoresis in nonhomogeneous electric fields

The objective of this work is to develop a numerical method to simulate DNA electrophoresis in complicated geometries. The proposed numerical scheme is composed of three parts: (1) a bead-spring Brownian dynamics (BD) simulation, (2) an iterative solver-enhanced finite element method (FEM) for the electric field, and (3) the connection algorithm between FEM and BD. A target-induced searching algorithm is developed to quickly address the electric field in the complex geometry which is discretized into unstructured finite element meshes. We also develop a method to use the hard-sphere interaction algorithm proposed by Heyes and Melrose [J. Non-Newtonian Fluid Mech. 46, 1 (1993)] in FEM. To verify the accuracy of our numerical schemes, our method is applied to the problem of lambda-DNA deformation around an isolated cylindrical obstacle for which the analytical solution of the electric field is available and experimental data exist. We compare our schemes with an analytical approach and there is a good agreement between the two. We expect that the present numerical method will be useful for the design of future microfluidic devices to stretch and/or separate DNA.     

Brownian dynamics simulations of a flexible polymer chain which includes continuous resistance and multibody hydrodynamic interactions

Using methods adapted from the simulation of suspension dynamics, we have developed a Brownian dynamics algorithm with multibody hydrodynamic interactions for simulating the dynamics of polymer molecules. The polymer molecule is modeled as a chain composed of a series of inextensible, rigid rods with constraints at each joint to ensure continuity of the chain. The linear and rotational velocities of each segment of the polymer chain are described by the slender-body theory of Batchelor [J. Fluid Mech. 44, 419 (1970)]. To include hydrodynamic interactions between the segments of the chain, the line distribution of forces on each segment is approximated by making a Legendre polynomial expansion of the disturbance velocity on the segment, where the first two terms of the expansion are retained in the calculation. Thus, the resulting linear force distribution is specified by a center of mass force, couple, and stresslet on each segment. This method for calculating the hydrodynamic interactions has been successfully used to simulate the dynamics of noncolloidal suspensions of rigid fibers [O. G. Harlen, R. R. Sundararajakumar, and D. L. Koch, J. Fluid Mech. 388, 355 (1999); J. E. Butler and E. S. G. Shaqfeh, J. Fluid Mech. 468, 204 (2002)]. The longest relaxation time and center of mass diffusivity are among the quantities calculated with the simulation technique. Comparisons are made for different levels of approximation of the hydrodynamic interactions, including multibody interactions, two-body interactions, and the "freely draining" case with no interactions. For the short polymer chains studied in this paper, the results indicate a difference in the apparent scaling of diffusivity with polymer length for the multibody versus two-body level of approximation for the hydrodynamic interactions.     

Mechanical stability of two immiscible liquid drops resting on a solid substrate

The mechanical stability of two immiscible liquid drops of water and mercury resting on a polypropylene solid substrate was attained. It is found that the mechanical stability and the complete encapsulation of mercury drop, by a Millipore water drop, depends severely on the volume of the droplets. The merging of four phases along a single contact line as claimed by Mahadevan et al. [L. Mahadevan, M. Adda-Bedia, and Y. Pomeau, J. Fluid Mech. 451, 411 (2002)] is experimentally shown to be invalid.     

Dielectric study on the flow alignment in 4-n-pentyl-4'-cyanobiphenyl

Dielectric permittivity and loss are measured under steady shear flow as functions of temperature, shear rate, electric field frequency, and electric field strength in the nematic (N) and the isotropic (I) phases of 4-n-pentyl-4'-cyanobiphenyl. In the N phase, the dielectric permittivity in the quiescent state is largely modified if the steady shear flow is applied. These behaviors are discussed based on the Leslie-Ericksen theory [Q. J. Mech. Appl. Math. 19, 357 (1966); Arch. Ration. Mech. Anal. 4, 231 (1960)], showing that the dielectric properties under the shear flow are consistently interpreted in terms of the flow alignment of the director, a unit vector specifying the orientation of the liquid crystals. It is also suggested that the behaviors of dielectric permittivities are similar to those of the viscosities.     

Brownian dynamics algorithm for bead-rod semiflexible chain with anisotropic friction

A model of semiflexible bead-rod chain with anisotropic friction can mimic closely the hydrodynamics of a slender filament. We present an efficient algorithm for Brownian dynamics simulations of this model with configuration dependent anisotropic bead friction coefficients. The algorithm is an extension of that given previously for the case of configuration independent isotropic friction coefficients by Grassia and Hinch [J. Fluid Mech. 308, 255 (1996)]. We confirm that the algorithm yields predicted values for various equilibrium properties. We also present a stochastic algorithm for evaluation of the stress tensor, and we show that in the limit of stiff chains the algorithm recovers the results of Kirkwood and Plock [J. Chem. Phys. 24, 665 (1956)] for rigid rods with hydrodynamic interactions.     

The Primary Electroviscous Effect: Thin Double Layers (akappa>1) and a Stern Layer

The primary electroviscous effect due to the charge clouds surrounding spherical charged particles suspended in an electrolyte was studied by Hinch and Sherwood (J. Fluid Mech. 132, 337 (1983)) in the limit of double layers thin compared to the particle radius a. Here we introduce the effect of a dynamic Stern layer into that analysis, in order to explain the numerical results of Rubio-Hernández et al. (J. Colloid Interface Sci. 206, 334 (1998)) in terms of the ratio of the tangential ionic fluxes within the charge cloud to those within the Stern layer. The predictions of the asymptotic analysis are compared with those of numerical computations. The thickness of the charge cloud is characterized by the Debye length kappa(-1). If akappa>10 the predictions of the asymptotic analysis exhibit the same qualitative behavior as the numerical results, but akappa>1000 is required to achieve quantitative agreement to within 2.5%. Copyright 2000 Academic Press.     

Do orientation effects contribute to the molecular weight dependence of the free solution mobility of DNA?

The free solution mobility of DNA increases with increasing molecular weight and then levels off and becomes constant at molecular weights above approximately 400 bp (Stellwagen, N. C., Gelfi, C., Righetti, P. G., Biopolymers 1997,42, 687-703). To investigate whether the increase in mobility could be attributed to an increased orientation of the larger DNA molecules in the electric field, the free solution mobility of DNA was measured by capillary electrophoresis as a function of electric field strength. Mixtures containing 20-, 118- and 422-bp DNA molecules, and 20-, 422- and 2116-bp DNAs, were studied. If the larger DNA molecules in each mixture were oriented by the electric field, their mobilities should increase with electric field strength faster than the mobility of the 20-bp oligomer, which is too small to be oriented by the electric fields used in this study. Instead, the ratios of the mobilities of the 118-, 422- and 2116-bp fragments to the mobility of the 20-bp oligomer were independent of electric field strength. Hence, orientation effects are not important for DNA molecules up to 2 kbp in size, in electric fields up to 500 V/cm in amplitude. An explanation is suggested.     

Experimental studies on affinity chromatography in an electric field.

A multicompartment electrolyzer, which has been used for preparative electrophoresis [Z. Liu, Z. Huang, J.-Y. Cong, et al., Sep. Sci. Technol. 31 (1996) 427], is applied for carrying out affinity chromatography in an alternating electric field. The effect of electric field strength on the adsorption and desorption characteristics is experimentally examined with human serum albumin and Blue Sepharose Fast Flow as a model system. It is shown that the existence of an electric field leads to a significant change in the adsorption capacity of the blue dye, which may be used for establishing a preferential adsorption to achieve a high resolution. The adsorption speed increases slightly with respect to the increase of electric field strength, while adsorption capacity in the presence of an electric field is independent of the electric field strength. Different elution behavior is observed as function of adsorption condition and a high recovery of the adsorbed protein is obtained when the adsorption is carried out in the presence of an electric field.     

A 2D electrohydrodynamic model for electrorotation of fluid drops

A theoretical analysis of spontaneous electrorotation of deformable fluid drops in a DC electric field is presented with a 2D electrohydrodynamic model. The fluids in the system are assumed to be leaky dielectric and Newtonian. If the rotating flow is dominant over the cellular convection type of electrohydrodynamic flow, closed-form solutions for drops of small deformations can be obtained. Because the governing equations are in general nonlinear even when drop deformations are ignored, the general solution for even undeformed drop takes a form of infinite series and can only be evaluated by numerical means. Both closed-form solutions for special cases and numerical solutions for more general cases are obtained here to describe steady-state field variables and first-order drop deformations. In a DC electric field of strength beyond the threshold value, spontaneous electrorotation of a drop is shown to occur when charge relaxation in the surrounding fluid is faster than the fluid inside the drop. With increasing the strength of the applied electric field from the threshold for onset of electrorotation, the axis of drop contraction deviates from from that of the applied electric field in the direction of the rotating flow with an angle increasing with the field strength.     

Translational motion of a spherical particle near a planar liquid-fluid interface

The translational electrophoretic motion of a colloidal spherical particle parallel to a planar liquid-fluid interface is analyzed by using the reciprocal theorem developed by Yariv and Brenner [E. Yariv, H. Brenner, J. Fluid Mech. 484 (2003) 85]. Based on the thin electric double layers assumption, analytical solutions of the forces acting on the particle are obtained, and the influence of the liquid-fluid interface on the electrophoretic velocity of the particle is studied. It is found that the speed of the particle's electrokinetic motion will increase as the separation distance between the particle and the interface decreases. This enhancement of electrophoretic mobility becomes more significant when the viscosity of the fluid phase becomes larger.     

Novel microfabricated device for electrokinetically induced pressure flow and electrospray ionization mass spectrometry

A novel microchip device for electrospray ionization has been fabricated and interfaced to a time-of-flight mass spectrometer. Fluid is electrokinetically transported through the chip to a fine fused-silica capillary inserted directly into a channel at the edge of the device. Electrospray is established at the tip of the capillary, which assures a stable, efficient spray. The electric potential necessary for electrospray generation and the voltage drop for electroosmotic pumping are supplied through an electrically permeable glass membrane contacting the fluidic channel holding the capillary. The membrane is fabricated on the microchip using standard photolithographic and wet chemical etching techniques. Performance relative to other microchip electrospray sources has been evaluated and the device tested for potential use as a platform for on-line electrophoretic detection. Sensitivity was found to be approximately three orders of magnitude better than spraying from the flat edge of the chip. The effect of the capillary on electroosmotic flow was examined both experimentally and theoretically.     

Modeling of ion processes in atmospheric pressure matrix-assisted laser desorption/ionisation

Atmospheric pressure matrix-assisted laser desorption/ionization (AP-MALDI) has proven a convenient and rapid method for ion production in the mass spectrometric analysis of biomolecules. This technique, like other atmospheric pressure ionization methods, suffers from ion loss during ion transmission from the atmosphere into the vacuum of the mass spectrometer. In this work, a simple model describing ion formation and ion motion towards the inlet capillary of the mass spectrometer is described. Both the gas flow and electric field near the MALDI plate were numerically calculated using the boundary element method (BEM). The ions were moving along with the gas flow and drifting in the electric field in accordance with their ion mobility properties. The ion signal dependence on an electric field strength obtained in the proposed model correlates well with experimental results.     

Deviation from Ohm's law in electric field assisted capillary liquid chromatography

Earlier studies of electric field assisted LC (EF-LC) have shown that the effect on charged analytes of the application of an electric field over a capillary LC column is relatively small. Charged analytes can only be affected by the electric field while present in the mobile phase, which makes the effective time for influence of the electric field t(0) independent of retention time. Because the charged analytes only can be affected for a short time the electric field strength ought to be high in order to increase the impact of the electric field on the separation. We have, however, found that only a relatively low electric field strength can be used in EF-LC when pressure is used as main driving force. The useful field strength was limited by a dramatic increase in the current. This increase in current was found to origin from an increased concentration of buffer ions that have an electrophoretic mobility towards the pumped flow.     

Deformation and motion of a charged conducting drop in a dielectric liquid under a nonuniform electric field

As a tool for transporting a drop inside another fluid, a charged conducting drop driven by Coulombic force is considered. Specifically, deformation and motion of a charged conducting drop under nonuniform electric fields are studied using the perturbation method. For simplicity in analysis, the applied electric field is assumed to be expressed as the sum of a uniform field and a linear field and the flow is assumed to be in the Stokes flow range. The deformed drop shape due to electrical stress is computed to the first order of the electrical Weber number (W). Then the electric force and the hydrodynamic drag are computed to derive the formula of the translation velocity, which is valid up to O(W). Several important results have also been obtained for the effect of drop deformation on the electric and hydrodynamic forces exerted on the drop.     

Changes in mobile phase ion distribution when combining pressurized flow and electric field

The distribution of ions in a capillary with both pressurized flow and an electric field has been studied. We have earlier reported that the overall concentration of ions increase in a capillary with high electric field and a pressurized flow. Now we describe how the ions are distributed in the capillary both along the capillary length and in the radial direction as a result of the parabolic flow profile. We have combined current measurements with finite element techniques in order to get better understanding of the system. We have found that the concentration of the ions that because of the electric mobility moves towards the flow primarily increases at the beginning of the electric field and close to the capillary wall. In view of the results we have proposed an alterative explanation of earlier published results concerning voltage-induced variation in capacity factors.     

Capillary zone electrophoresis of sub-microm-sized particles in electrolyte solutions of various ionic strengths: size-dependent electrophoretic migration and separation efficiency

To gain insight into the mechanisms of size-dependent separation of microparticles in capillary zone electrophoresis (CZE), sulfated polystyrene latex microspheres of 139, 189, 268, and 381 nm radius were subjected to CZE in Tris-borate buffers of various ionic strengths ranging from 0.0003 to 0.005, at electric field strengths of 100-500 V cm(-1). Size-dependent electrophoretic migration of polystyrene particles in CZE was shown to be an explicit function of kappaR, where kappa(-1) and rare the thickness of electric double layer (which can be derived from the ionic strength of the buffer) and particle radius, respectively. Particle mobility depends on kappaR in a manner consistent with that expected from the Overbeek-Booth electrokinetic theory, though a charged hairy layer on the surface of polystyrene latex particles complicates the quantitative prediction and optimization of size-dependent separation of such particles in CZE. However, the Overbeek-Booth theory remains a useful general guide for size-dependent separation of microparticles in CZE. In accordance with it, it could be shown that, for a given pair of polystyrene particles of different sizes, there exists an ionic strength which provides the optimal separation selectivity. Peak spreading was promoted by both an increasing electric field strength and a decreasing ionic strength. When the capillary is efficiently thermostated, the electrophoretic heterogeneity of polystyrene microspheres appears to be the major contributor to peak spreading. Yet, at both elevated electric field strengths (500 V/cm) and the highest ionic strength used (0.005), thermal effects in a capillary appear to contribute significantly to peak spreading or can even dominate it.     

Melt electrospinning in a parallel electric field

Electrospinning is an efficient and direct method of fabricating nanofibers. Fibers are frequently unstable in the electrospinning process, and the uneven distribution of the electric field is an important factor leading to instability. Experimental and finite element simulation studies are conducted on the process of melt electrospinning in a parallel electric field. Two parallel metal disks are used to successfully generate a uniform electric field. Electric field intensity on the edges of the metal disk is always stronger than the field at the center of the disk or at the spinneret bottom. The diameters, distances, and relative areas of these disks significantly affect the distribution of the electric field. Thus, the parallel electric field effectively reduces jet buckling in melt electrospinning. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 946–952     

Combination of electrophoresis,chromatography, and magnetism in a single separation technique: Part 1: a first theoretical evaluation

Magnetic nanoparticles incorporated into the layer of a (polymeric) sorbent, covering the inner surface of a fused silica capillary, can produce—upon applying an electric field across the capillary length—an electromagnetic field that would affect to some extent the separation of charged analytes. A first theoretical assessment of such phenomenon is given here with a view of developing a novel hybrid separation technique based on the principles of electrophoresis, chromatography, and magnetism. Specifically, the effect of built-in magnetic nanoparticles, varying in absolute number, on the strength of axial electric field in an open-tubular column for capillary electrochromatography (CEC) column for CEC—being expressed through the associated changes in near-wall dielectric constant—was analyzed using linearized Poisson–Boltzmann equation.