Unidirectional rotation of micromotors on water powered by pH-controlled disassembly of chiral molecular crystals.

Biological and synthetic molecular motors, fueled by various physical and chemical means, can perform asymmetric linear and rotary motions that are inherently related to their asymmetric shapes. Here, we describe silver-organic micro-complexes of random shapes that exhibit macroscopic unidirectional rotation on water surface through the asymmetric release of cinchonine or cinchonidine chiral molecules from their crystallites asymmetrically adsorbed on the complex surfaces. Computational modeling indicates that the motor rotation is driven by a pH-controlled asymmetric jet-like Coulombic ejection of chiral molecules upon their protonation in water. The motor is capable of towing very large cargo, and its rotation can be accelerated by adding reducing agents to the water.

Electro-Orientation and Electro-Rotation of Metallodielectric Janus Particles.

The electro-rotation (EROT) and electro-orientation (EOR) behavior of metallodielectric spherical Janus particles (JP) are studied analytically and verified experimentally. This stands in contrast to previous either heuristic or numerically computed models of JP dipoles. First, we obtain frequency-dependent analytic expressions for the corresponding dipole terms for a JP composed of dielectric and metallic hemispheres by applying the "standard" (weak-field) electrokinetic model and using a Fourier-Legendre collocation method for solving two sets of linear equations. EROT and EOR spectra, describing the variation of the JP's angular velocity on the forcing frequency of a rotating and nonrotating spatially uniform electric field, respectively, are explicitly determined and compared against experiments (different JP sizes and solution conductivities). While a favorably good agreement between theory and experimental measurements was found for the frequency response (∼8% difference), there is still a factor of ∼2 difference in the amplitude of the angular velocity, which necessitates further future improvements to the model.

Travelling-Wave Electrophoresis, Electro-Hydrodynamics, Electro-Rotation, and Symmetry- Breaking of a Polarizable Dimer in Non-Uniform Fields.

A theoretical framework is presented for calculating the polarization, electro-rotation, travelling-wave dielectrophoresis, electro-hydrodynamics and induced-charge electroosmotic flow fields around a freely suspended conducting dimer (two touching spheres) exposed to non-uniform direct current (DC) or alternating current (AC) electric fields. The analysis is based on employing the classical (linearized) Poisson-Nernst-Planck (PNP) formulation under the standard linearized 'weak-field' assumption and using the tangent-sphere coordinate system. Explicit expressions are first derived for the axisymmetric AC electric potential governed by the Robin (mixed) boundary condition applied on the dimer surface depending on the resistance-capacitance circuit (RC) forcing frequency. Dimer electro-rotation due to two orthogonal (out-of-phase) uniform AC fields and the corresponding mobility problem of a polarizable dimer exposed to a travelling-wave electric excitation are also analyzed. We present an explicit solution for the non-linear induced-charge electroosmotic (ICEO) flow problem of a free polarized dimer in terms of the corresponding Stokes stream function determined by the Helmholtz-Smoluchowski velocity slip. Next, we demonstrate how the same framework can be used to obtain an exact solution for the electro-hydrodynamic (EHD) problem of a polarizable sphere lying next to a conducting planar electrode. Finally, we present a new solution for the induced-charge mobility of a Janus dimer composed of two fused spherical colloids, one perfectly conducting and one dielectrically coated. So far, most of the available electrokinetic theoretical studies involving polarizable nano/micro shapes dealt with convex configurations (e.g., spheres, spheroids, ellipsoids) and as such the newly obtained electrostatic AC solution for a dimer provides a useful extension for similar concave colloids and engineered particles.

Travelling-Wave Dipolophoresis: Levitation and Electrorotation of Janus Nanoparticles.

We present a theoretical study of the hydrodynamic and electrokinetic response of both metallic spherical polarized colloids as well as metallodielectic Janus particles, which are subjected to an arbitrary non-uniform ambient electric field (DC or AC forcing). The analysis is based on employing the linearized 'standard' model (Poisson-Nernst-Planck formulation) and on the assumptions of a 'weak' field and small Debye scale. In particular, we consider cases of linear and helical time-harmonic travelling-wave excitations and provide explicit expressions for the resulting dielectrophoretic and induced-charge electrophoretic forces and moments, exerted on freely suspended particles. The new analytic expressions thus derived for the linear and angular velocities of the initially uncharged polarizable particle are compared against some available solutions. We also analyze the levitation problem (including stability) of metallic and Janus particles placed in a cylindrical (insulating or conducting) pore near a powered electrode.

Electrorotation of leaky-dielectric and conducting microspheres in asymmetric electrolytes and angular velocity reversal.

We consider the central problem of polarizable and leaky-dielectric uncharged spherical particle freely suspended in an unbounded nonsymmetric binary electrolyte, which is forced by an ambient time-harmonic uniform electric field. Under the assumption of a "weak field," we employ the linearized standard electrokinetic model of binary electrolytes to account for such anion/cation asymmetry. A simplified generalized asymmetric dipole-term approximation, valid for a dielectric/conducting microsphere, is analytically derived for an arbitrary Debye scale and for any mismatch between ion diffusivities and valances. A two-peak unified dispersion spectrum covering all range of practical frequencies (KHz to MHz), is found for the case of a rotating electric field (ROT). The angular velocity of a free polarized particle is composed of dielectrophoretic contribution, resulting from the electrical torque (dipole term) as well as from the induced electroosmotic (ICEO) flow field. The two effects usually act in opposite directions. Under ROT excitation, we obtain a cofield rotation at high frequencies (MHz) and a counter-field behavior at low frequencies (KHz). The low-frequency dispersion is generally governed by electric double-layer charging and the high frequency by a Maxwell-Wagner relaxation process. ICEO generally dominates the low-frequency cofield response; however, it can be shown that depending on the electrolyte asymmetry, yet another dielectrophoretic related switching (reversal) point might exist. Furthermore, for large frequencies and depending on the complex permittivity ratio between the particle and electrolyte, we find a second switching point. Explicit expressions for the above two frequency reversal values are obtained in terms of the problem physical parameters and are compared against experimental results. Finally, we provide an analytical solution for the ROT ICEO velocity field of a microsphere as a function of electrolyte asymmetry and Debye length and compare it with numerical simulations.

AC Electrokinetics of Polarizable Tri-Axial Ellipsoidal Nano-Antennas and Quantum Dot Manipulation.

By realizing the advantages of using a tri-axial ellipsoidal nano-antenna (NA) surrounded by a solute for enhancing light emission of near-by dye molecules, we analyze the possibility of controlling and manipulating the location of quantum dots (similar to optical tweezers) placed near NA stagnation points, by means of prevalent AC electric forcing techniques. First, we consider the nonlinear electrokinetic problem of a freely suspended, uncharged, polarized ellipsoidal nanoparticle immersed in a symmetric unbounded electrolyte which is subjected to a uniform AC ambient electric field. Under the assumption of small Peclet and Reynolds numbers, thin Debye layer and 'weak-field', we solve the corresponding electrostatic and hydrodynamic problems. Explicit expressions for the induced velocity, pressure, and vorticity fields in the solute are then found in terms of the Lamé functions by solving the non-homogeneous Stokes equation forced by the Coulombic density term. The particular axisymmetric quadrupole-type flow for a conducting sphere is also found as a limiting case. It is finally demonstrated that stable or equilibrium (saddle-like) positions of a single molecule can indeed be achieved near stagnation points, depending on the directions of the electric forcing and the induced hydrodynamic (electroosmotic) and dielectrophoretic dynamical effects. The precise position of a fluorophore next to an ellipsoidal NA, can thus be simply controlled by adjusting the frequency of the ambient AC electric field.

Light-induced self-thermophoresis of Janus spheroidal nanoparticles.

A theoretical framework is provided for determining the self-thermophoretic velocity of a light irradiated spheroidal Janus nanoparticle consisting of symmetric dielectric and perfectly conducting semi-spheroids. The analysis is based on solving the linearized Joule heating problem due to uniform laser irradiance and on explicitly determining the temperature fields inside and outside the particle. We employ the thermoelectric (Peltier- Seebeck) methodology to find the surface self - induced temperature gradient and the related slip velocity which determines the autonomous phoretic (self - propulsion) mobility of the Janus particle. Simplified explicit expressions for the self - thermophoretic velocities of spheroidal (prolate and oblate) Janus particles in terms of their aspect ratios are found and few practical limiting cases (i.e., sphere, disk and needle) are also discussed.

Active colloids as mobile microelectrodes for unified label-free selective cargo transport.

Utilization of active colloids to transport both biological and inorganic cargo has been widely examined in the context of applications ranging from targeted drug delivery to sample analysis. In general, carriers are customized to load one specific target via a mechanism distinct from that driving the transport. Here we unify these tasks and extend loading capabilities to include on-demand selection of multiple nano/micro-sized targets without the need for pre-labelling or surface functionalization. An externally applied electric field is singularly used to drive the active cargo carrier and transform it into a mobile floating electrode that can attract (trap) or repel specific targets from its surface by dielectrophoresis, enabling dynamic control of target selection, loading and rate of transport via the electric field parameters. In the future, dynamic selectivity could be combined with directed motion to develop building blocks for bottom-up fabrication in applications such as additive manufacturing and soft robotics.

Propulsion of Active Colloids by Self-Induced Field Gradients.

Previously, metallodielectric Janus particles have been shown to travel with their dielectric hemisphere forward under low frequency applied electric fields as a result of asymmetric induced-charge electroosmotic flow. Here, it is demonstrated that at high frequencies, well beyond the charge relaxation time of the electric double layer induced around the particle, rather than the velocity decaying to zero, the Janus particles reverse direction, traveling with their metallic hemisphere forward. It is proposed that such motion is the result of a surface force, arising from localized nonuniform electric field gradients, induced by the dual symmetry-breaking of an asymmetric particle adjacent to a wall, which act on the induced dipole of the particle to drive net motion even in a uniform AC field. Although the field is external, since the driving gradient is induced on the particle level, it may be considered an active colloid. We have thus termed this propulsion mechanism "self-dielectrophoresis", to distinguish from traditional dielectrophoresis where the driving nonuniform field is externally fixed and the particle direction is restricted. It is demonstrated theoretically and experimentally that the critical frequency at which the particle reverses direction can be characterized by a nondimensional parameter which is a function of electrolyte concentration and particle size.

Exact Markov chain and approximate diffusion solution for haploid genetic drift with one-way mutation.

The classical Kimura solution of the diffusion equation is investigated for a haploid random mating (Wright-Fisher) model, with one-way mutations and initial-value specified by the founder population. The validity of the transient diffusion solution is checked by exact Markov chain computations, using a Jordan decomposition of the transition matrix. The conclusion is that the one-way diffusion model mostly works well, although the rate of convergence depends on the initial allele frequency and the mutation rate. The diffusion approximation is poor for mutation rates so low that the non-fixation boundary is regular. When this happens we perturb the diffusion solution around the non-fixation boundary and obtain a more accurate approximation that takes quasi-fixation of the mutant allele into account. The main application is to quantify how fast a specific genetic variant of the infinite alleles model is lost. We also discuss extensions of the quasi-fixation approach to other models with small mutation rates.

Spinning Janus doublets driven in uniform ac electric fields.

We provide an experimental proof of concept for a robust, continuously rotating microstructure-consisting of two metallodielectric (gold-polystyrene) Janus particles rigidly attached to each other-which is driven in uniform ac fields by asymmetric induced-charge electro-osmosis. The pairs (doublets) are stabilized on the substrate surface which is parallel to the plane of view and normal to the direction of the applied electric field. We find that the radius of orbit and angular velocity of the pair are predominantly dependent on the relative orientations of the interfaces between the metallic and dielectric hemispheres and that the electrohydrodynamic particle-particle interactions are small. Additionally, we verify that both the angular and linear velocities of the pair are proportional to the square of the applied field which is consistent with the theory for nonlinear electrokinetics. A simple kinematic rigid body model is used to predict the paths and doublet velocities (angular and linear) based on their relative orientations with good agreement.

Dipolophoresis of Janus nanoparticles in a microchannel.

A nonlinear dipolophoretic analysis is applied to analytically explain the counterintuitive experimental results of Gangwal et al. that an uncharged micro/nanosize dielectric Janus particle is attracted to the wall of a microchannel when exposed to an AC-uniform electric field in the direction parallel to the no-slip boundaries. We employ the so-called "weak" field assumption and consider a metallodielectric Janus colloid comprising two semispheres of distinct dielectric properties subject to an oscillating-uniform electric field with moderate frequency (below the Maxwell-Wagner limit). The Debye scale (ratio of electric double layer thickness to particle size) is considered unrestricted. Under the low Reynolds number hypothesis, Faxén's theorem and the Green's function (Stokeslet) method of singularities, including appropriate images with respect to the no-slip boundary, are applied under the remote-field approximation to determine the dynamics and trajectory of a small colloid moving near a wall. When assuming maximum dielectric contrasts between hemispheres and relatively low Debye scale (compared to particle radius), a rather simple relation for the equilibrium position of the colloid (i.e. tilt angle and distance from the wall) is obtained and found to be in qualitative good agreement with the experimental observations of Gangwal et al. and the predictions of Kilic and Bazant.

Induced-charge electrophoresis of uncharged dielectric spherical Janus particles.

We derive the equations governing the dipolophoretic motion of an electrically inhomogeneous Janus particle composed of two hemispheres with differing permittivities. The general formulation is valid for any electric forcing, including alternating current (AC) and makes no assumptions regarding the size of the electric double layer (EDL). The solution is thus valid even for nanoparticles where the particle radius can be of the same order as the EDL thickness. Semi-analytic and numerical solutions for the linear phoretic velocity and angular rotation of a single Janus particle suspended in an infinite medium are given in the limit of uniform direct current (DC) electric forcing. It is determined that particle mobility is a function of the permittivity in each hemisphere and the contrast between them as well as the EDL length. For a particle in which both hemispheres are characterized by a finite permittivity, we discover that maximum mobility and rotation is not obtained in the Helmholtz-Smoluchowski thin EDL limit but is rather a function of the permittivity and EDL properties.

Sound scattering by free surface piercing and fluid-loaded cylindrical shells.

A vertical flexible, thin, cylindrical shell is considered to be clamped to a rigid base in shallow water and piercing its surface. The shell is composed of an isotropic and homogeneous material and may be empty inside or filled with compressible fluid. Linear acoustics and structural dynamics are used to model sound scattering caused by an external incident sound wave. A solution is derived using a Fourier transform in the tangential and vertical directions. A collocation technique coupled with an orthogonalization procedure is used to account for the edge conditions of the shell. It is shown that zero sound scattering, indicating acoustic invisibility, is theoretically attainable and can be achieved when a continuous distribution of an oscillating pressure load is applied on the shell's wall. Similarly, zero sound transmission into the shell's inner fluid can also be considered. The possibility of using a pre-determined discrete distribution of the applied pressure load is also discussed. The derived equations are numerically solved to examine sound scattering by a thin aluminium shell in shallow water.

Nonlinear electrokinetic phenomena around nearly insulated sharp tips in microflows.

This contribution seeks to provide for the first time a combined comprehensive theoretical prediction and quantitative experimental (microparticle imaging velocimetry--micro-PIV) measurements of the nonlinear electrokinetic flow around sharp tips in order to substantiate former theoretical and qualitative experimental flow visualization results [S.K. Thamida, H.C Chang, Phys. Fluids 14 (2002) 12; P. Takhistov, K. Duginova, H.C. Chang, J. Colloid Interface Sci. 263 (2003) 133; G. Yossifon, I. Frankel, T. Miloh, Phys. Fluids 18 (2006) 117108]. The study focuses on two microchannel designs: an L-shaped channel and two isolated tips in a straight channel, important in engineering for mixing and particle-trapping purposes. The new experimental results were explained in terms of an induced-charge electrokinetic mechanism alone, without the concentration polarization mechanism as suggested by earlier studies. The vortex generation phenomenon around corners was explained in terms of the varying ratio between the equilibrium and the induced-charge zeta-potentials, showing fair qualitative agreement between numerical and experimental results. Hence, a transition from an irrotational to nonlinear-dominated flow with a vortex pattern occurs beyond a certain electric-field threshold. In particular, for the L-shaped channel case, it is demonstrated that beyond a second field threshold an upstream vortex appears in addition to the downstream one.