Dielectrophoretic force microscopy of aqueous interfaces

A novel scanning probe microscopy technique has allowed dielectrophoretic force imaging with nanoscale spatial resolution. Dielectrophoresis (DEP) traditionally describes the mobility of polarizable particles in inhomogeneous alternating current (ac) electric fields. Integrating DEP with atomic force microscopy allows for noncontact imaging with the image contrast related to the local electric polarizability. By tuning the ac frequency, dielectric spectroscopy can be performed at solid/liquid interfaces with high spatial resolution. In studies of cells, the frequency-dependent dielectrophoretic force is sensitive to biologically relevant electrical properties, including local membrane capacitance and ion mobility. Consequently, dielectrophoretic force microscopy is well suited for in vitro noncontact scanning probe microscopy of biological systems.     

Electrostatic double layer force between a sphere and a planar substrate in the presence of previously deposited spherical particles

A finite element model of the electrostatic double layer interaction between an approaching colloidal particle and a small region of a charged planar surface containing four previously deposited particles is presented. The electrostatic interaction force experienced by the approaching particle is obtained by solving the Poisson-Boltzmann equation with appropriate boundary conditions representing this complex geometry. The interaction forces obtained from the detailed three-dimensional finite element simulations suggest that for the many-body scenario addressed here, the electrostatic double layer repulsion experienced by the approaching particle is less than the corresponding sphere-plate interaction due to the presence of the previously deposited particles. The reduction in force is quite significant when the screening length of the electric double layer becomes comparable to the particle radius (kappaa approximately 1). The results also suggest that the commonly used technique of pairwise addition of binary interactions can grossly overestimate the net electrostatic double layer interaction forces in such situations. The simulation methodology presented here can form a basis for investigating the influence of several previously deposited particles on the electrostatic repulsion experienced by a particle during deposition onto a substrate.     

Dielectrophoretic tweezers as a platform for molecular force spectroscopy in a highly parallel format

We demonstrated the application of a simple electrode geometry for dielectrophoresis (DEP) on colloidal probes as a form of molecular force spectroscopy in a highly parallel format. The electric field between parallel plates is perturbed with dielectric microstructures, generating uniform DEP forces on colloidal probes in the range of several hundred piconewtons across a macroscopic sample area. We determined the approximate crossover frequency between negative and positive DEP using electrodes without dielectric microstructures-a simplification over standard experimental methods involving quadrupoles or optical trapping. 2D and 3D simulations of the electric field distributions validated the experimental behavior of several of our DEP tweezers geometries and provided insight into potential improvements. We applied the DEP tweezers to the stretching of a short DNA oligomer and detected its extension using total-internal reflection fluorescence microscopy. The combination of a simple cell fabrication, a uniform distribution of high axial forces, and a facile optical detection of our DEP tweezers makes this form of molecular force spectroscopy ideal for highly parallel detection of stretching or unbinding kinetics of biomolecules.     

Dielectrophoretic immobilization of proteins: Quantification by atomic force microscopy

The combination of alternating electric fields with nanometer‐sized electrodes allows the permanent immobilization of proteins by dielectrophoretic force. Here, atomic force microscopy is introduced as a quantification method, and results are compared with fluorescence microscopy. Experimental parameters, for example the applied voltage and duration of field application, are varied systematically, and the influence on the amount of immobilized proteins is investigated. A linear correlation to the duration of field application was found by atomic force microscopy, and both microscopical methods yield a square dependence of the amount of immobilized proteins on the applied voltage. While fluorescence microscopy allows real‐time imaging, atomic force microscopy reveals immobilized proteins obscured in fluorescence images due to low S/N. Furthermore, the higher spatial resolution of the atomic force microscope enables the visualization of the protein distribution on single nanoelectrodes. The electric field distribution is calculated and compared to experimental results with very good agreement to atomic force microscopy measurements.     

The lateral electric force on an off-axis sphere in a circular cylinder

The electrophoretic velocity of a sphere within a liquid-filled circular cylinder in a direction parallel to the cylinder axis has been studied by Yariv and Brenner (Phys. Fluids 2002, 14, 3354–3357; SIAM J. Appl. Math. 2003, 64, 423–441). We use their analyses of the electric field in order to determine the electrical force on the sphere along the cylinder radius (i.e., perpendicular to its axis) when either the radius of the sphere is small compared to that of the cylinder, or when the radius of the sphere is only slightly smaller than that of the cylinder. In both cases the force acts towards the centreline of the cylinder, and hence this force tends to stabilize electrophoresis of the sphere along the cylinder axis.     

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.     

Structure of hard sphere packings near Bernal density

The structural features of packings of similar hard spheres in the vicinity of Bernal density corresponding to space occupancy ∼0.64 have been studied. This is maximum density for disordered packings, which give way to crystallization at higher densities. The structure was analyzed using Delaunay simplices. Aggregates of simplices approximating a regular tetrahedron (polytetrahedra) in form have been studied. They have a high local density and various morphologies, but are incompatible with translation symmetry. Percolation analysis of these clusters was carried out. The “critical” nature of structural transformations at Bernal density is related with the appearance of percolation through tetrahedra. The closest disordered packings really have no significant nucleating seeds of crystal structures, as shown by a sensitive seed detection procedure. Their appearance and fast growth are observed after passing through Bernal density. The total fraction of the crystal phase increases monotonically with the density; the fcc and hcp structures appear in different proportions in the packings.     

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.     

Thermophoretic motion of a solid spherical particle near a solid planar surface

The thermophoretic motion of a solid spherical aerosol particle directed normally to an infinite planar solid surface is analyzed. The solution is performed in a bispherical coordinate system with allowance for linear corrections in the Knudsen number. The finite thermal conductivity of a solid body is taken into account in the analysis.     

Dielectrophoretic forces on the nanoscale

We have developed a method of calculation of the dielectrophoretic force on a nanoparticle in a fluid environment where variations in the electric field and electric field gradients are on the same nanoscale as the particle. The Boundary Element Dielectrophoretic Force (BEDF) method involves constructing a solvent-accessible or molecular surface surrounding the particle, calculating the normal component of the electric field at the surface boundary elements, and then solving a system of linear equations for the induced surface polarization charge on each element. Different surface elements of the molecule may experience quite different polarizing electric fields, unlike the situation in the point dipole approximation. A single 100-A-radius ring test configuration is employed to facilitate comparison with the well-known point dipole approximation (PDA). We find remarkable agreement between the forces calculated by the BEDF and PDA methods for a 1 A polarizable sphere. However, for larger particles, the differences between the methods become qualitative as well as quantitative; the character of the force changes from attractive at the origin of the ring for a 50-A sphere, to repulsive for a 75-A sphere. Equally dramatic differences are found in a more complex electrical environment involving two sets of 10 rings.     

Effect of a charged boundary on electrophoresis: a sphere at an arbitrary position in a spherical cavity

The effect of the presence of a charged boundary on the electrophoretic behavior of a particle is investigated by considering a sphere at an arbitrary position in a spherical cavity under conditions of low surface potential and weak applied electric field. Previous analyses are modified by using a more realistic electrostatic force formula and several interesting results, which are not reported in the literature, are observed. We show that the qualitative behavior of a particle depends largely on its position, its size relative to that of a cavity, and the thickness of the electric double layer. In general, the presence of a cavity has the effect of increasing the conventional hydrodynamic drag on a particle through a nonslip condition on the former. Also, a decrease in the thickness of the double layer surrounding a sphere has the effect of increasing the electrostatic force acting on its surface so that its mobility increases. However, this may not be the case when an uncharged particle in placed in a positively charged cavity, where the electroosmotic flow plays a role; for example, the mobility can exhibit a local maximum and the direction of electrophoresis can change.     

Hydrodynamic screening near planar boundaries: effects on semiflexible polymer dynamics

The influence of hydrodynamic screening near a surface on the dynamics of a single semiflexible polymer is studied by means of Brownian dynamics simulations and hydrodynamic mean field theory. The polymer motion is characterized in terms of the mean squared displacements of the end-monomers, the end-to-end vector, and the scalar end-to-end distance. In order to control hydrodynamic screening effects, the polymer is confined to a plane at a fixed separation from the wall. When gradually decreasing this separation, a crossover from Zimm-type towards Rouse (free-draining) polymer dynamics is induced. However, this crossover is rather slow and the free-draining limit is not completely reached--substantial deviations from Rouse-like dynamics are registered in both simulations and theory--even at distances of the polymer from the wall on the order of the monomer size. Remarkably, the effect of surface-induced screening of hydrodynamic interactions sensitively depends on the type of dynamic observable considered. For vectorial quantities such as the end-to-end vector, hydrodynamic interactions are important and therefore surface screening effects are sizeable. For a scalar quantity such as the end-to-end distance, on the other hand, hydrodynamic interactions are less important, but a pronounced dependence of dynamic scaling exponents on the persistence length to contour length ratio becomes noticeable. Our findings are discussed against the background of single-molecule experiments on f-actin [L. Le Goff et al., Phys. Rev. Lett. 89, 258101 (2002)].     

An experimental study of the drag force on a sphere exposed to an argon thermal plasma flow

Experimental data are presented concerning the drag force on a stationary phere exposed to an argon plasma flow with temperatures about 10⁴ K and velocities about 10² m/s. A novel probe construction has been employed in the drag measurements in order to exclude the effect of the supporting wire on the sphere drag data. By using the new probe construction with a compensating wire, drag forces on an individual steel sphere in the plasma flow have been measured and compared with those obtained by using the probe construction ernployed by a few previous authors. Experimental results show that the measured drag forces are always less than their counterparts obtained from the standard sphere-drag curve under isothermal flow conditions with the same Reynolds numbers based on the oncoming plasma properties. The drag force on a sphere increases only slightly with the increasing surface temperature of the sphere before it melts. Appreciable diference was found between the experimental data and the predicted results of the available expressions for drag on a sphere exposed to a thermal plasma flow. Further research effort is required to build a more suitable drag correlation.     

Influence of Brownian motion on blood platelet flow behavior and adhesive dynamics near a planar wall

We used the platelet adhesive dynamics computational method to study the influence of Brownian motion of a platelet on its flow characteristics near a surface in the creeping flow regime. Two important characterizations were done in this regard: (1) quantification of the platelet's ability to contact the surface by virtue of the Brownian forces and torques acting on it, and (2) determination of the relative importance of Brownian motion in promoting surface encounters in the presence of shear flow. We determined the Peclet number for a platelet undergoing Brownian motion in shear flow, which could be expressed as a simple linear function of height of the platelet centroid, H from the surface Pe (platelet) = . (1.56H + 0.66) for H > 0.3 microm. Our results demonstrate that at timescales relevant to shear flow in blood Brownian motion plays an insignificant role in influencing platelet motion or creating further opportunities for platelet-surface contact. The platelet Peclet number at shear rates >100 s-1 is large enough (>200) to neglect platelet Brownian motion in computational modeling of flow in arteries and arterioles for most practical purposes even at very close distances from the surface. We also conducted adhesive dynamics simulations to determine the effects of platelet Brownian motion on GPIbalpha-vWF-A1 single-bond dissociation dynamics. Brownian motion was found to have little effect on bond lifetime and caused minimal bond stressing as bond rupture forces were calculated to be less than 0.005 pN. We conclude from our results that, for the case of platelet-shaped cells, Brownian motion is not expected to play an important role in influencing flow characteristics, platelet-surface contact frequency, and dissociative binding phenomena under flow at physiological shear rates (>50 s(-1)).     

Localized functions on a sphere

This article provides a fully consistent group theoretical procedure for finding atomic hybrids on a sphere and for relating them to the matrices representing the operators x, y, and z with respect to given basis functions. The tetrahedral, octahedral, and cubic hybrids based on the cube are derived. These functions are localized and directional. They can be used to describe valence aspects of atoms. © 1996 John Wiley & Sons, Inc.     

Effect of a charged boundary on electrophoresis in a Carreau fluid: a sphere at an arbitrary position in a spherical cavity

The influence of a charged boundary on the electrophoretic behavior of an entity in a non-Newtonian fluid is studied by considering a sphere at an arbitrary position in a spherical cavity filled with a Carreau fluid under the conditions of low surface potential and weak applied electric field. The dependence of the mobility of a sphere on its position in a cavity, the size of a cavity, the thickness of a double layer, and the nature of a fluid is investigated. In addition to the fact that the effect of shear-thinning is advantageous to the movement of a sphere, several other interesting results are also observed. For instance, if an uncharged sphere is in a positively charged cavity, where the electroosmotic flow and the induced charge on the sphere surface play a role, the effect of shear-thinning is important only if the thickness of the double layer is either sufficiently thin or sufficiently thick. However, this might not be the case if a positively charged sphere is in an uncharged cavity.     

Wetting of a drop on a sphere

In this work, the equilibrium morphology of a drop on a sphere is analyzed as a function of the contact angle and drop volume experimentally and with analytical effective interfacial energy calculations. Experimentally, a drop on a sphere geometry is realized in an oil bath by placing a water drop on a sphere coated with a dielectric, of which the radii of curvature are comparable with that of the drop. Electrowetting (EW) is used to change the contact angle of the water drop on the sphere. To validate the applicability of EW and the Lippman-Young equation on nonflat surfaces, we systematically investigate the response of the contact angle to the applied voltage (EW response) for various drop volumes and compared the results with the case of a planar surface. The effective interfacial energy of two competing morphologies, namely, the spherically symmetric "completely engulfing" and "partially engulfing" morphologies are calculated analytically. The analytical calculations are then compared to the experimental results to confirm which morphology is energetically more favored for a given contact angle and drop volume. Our findings indicate that the "partially engulfing" morphology is always the energetically more favorable morphology.     

Dielectrophoretic deformation of breast cancer cells for lab on a chip applications

This paper presents the development and experimental analysis of a curved microelectrode platform for the DEP deformation of breast cancer cells (MDA‐MB‐231). The platform is composed of arrays of curved DEP microelectrodes which are patterned onto a glass slide and samples containing MDA‐MB‐231 cells are pipetted onto the platform's surface. Finite element method is utilised to characterise the electric field gradient and DEP field. The performance of the system is assessed with MDA‐MB‐231 cells in a low conductivity 1% DMEM suspending medium. We applied sinusoidal wave AC potential at peak to peak voltages of 2, 5, and 10 V_pp at both 10 kHz and 50 MHz. We observed cell blebbing and cell shrinkage and analyzed the percentage of shrinkage of the cells. The experiments demonstrated higher percentage of cell shrinkage when cells are exposed to higher frequency and peak to peak voltage electric field.     

Dielectrophoretic manipulation of a single chlorella cell with dual-microdisk electrode

Dielectrophoretic manipulation of a single chlorella cell was performed using a dual-microdisk electrode, which consists of two Pt-Rh ultrafine wires (ca. 1-microm radius) sealed in a glass capillary. An attractive or repulsive force was induced on the chlorella depending on the frequency of the ac voltage applied between the two disk electrodes. To avoid the direct contact of a chlorella with the metal, a dual electrode with retracted disks was fabricated and used for forming a micropattern of chlorellas at a solid substrate. The effect of both the frequency and ion concentration of the solutions on the dielectrophoretic force exerted on a chlorella cell was investigated in detail based on the theories of dielectrophoresis.