Session GF: Microfluidics: Electric Fields and Particles

Electro-hydrodynamic particle levitation on electrodes

When colloidal particles deposit electro-phoretically onto a planar electrode, they slowly aggregate, eventually forming planar 2D crystalline structures. The attractive particle-particle interaction is due to electrokinetic flows associated with the particle Debye layer as well as the induced Debye layer surrounding the electrode. A common feature in the experimental observations is the small thickness of the particle-electrode gap separation, which was indeed reflected in the numerical figures employed hitherto in the existing numerical analyses. Here, we exploit it using singular perturbation methods. Thus, the fluid domain is separated into an ``inner'' gap region, where the electric field and flow strain rate are intensive, and an ``outer'' domain, consisting of the remaining fluid domain, where they are moderate. The inner region is analyzed using standard lubrication approximation, and the outer region is investigated using tangent-spheres coordinates. This method provides an analytic approximation for the hydrodynamic force that keeps the particle levitating against the action of gravity, as well as far-field approximations for the velocity decay, which agree with existing numerical simulations.   

Near-contact electrokinetic interactions between ideally polarizable particles

When a zero-net-charge spherical particle is exposed to a uniformly applied electric field it polarizes, giving rise to an induced zeta potential distribution and a concomitant electro-osmotic flow field. Due to symmetry, the particle does not experience any electrophoretic motion. This symmetry is disturbed when an adjacent boundary (e.g. another particle or a channel wall) is introduced. This gives rise to boundary-driven particle motion, which is nonlinear in the applied field, approximately quadratic in it when it is weak. Using matched asymptotic expansions, we analyze electrokinetic interactions between a pair of ideally polarizable particles at small gap separations. When the field is applied perpendicular to their line of center, it tends to repel the particles away from each other. This repulsion is dominated by the pressure field within the gap, animated by the intense electric field there. The resulting pair interaction weakly diverges as an irrational power of the gap thickness. When the field is applied in parallel to the line of center, the electric field within the gap is exponentially small, and the pair interaction is bounded.   

DC electrokinetic transport of a cylindrical particle in a rectangular microchannel

Electrokinetic transport of a cylindrical microparticle in a straight microchannel under direct current (DC) electric fields is numerically and experimentally investigated. DC dielectrophoresis (DEP) is taken into account in the proposed mathematical model, which is composed of the Navier-Stokes equations for the flow field and the Laplace equation for the electric field solved in an arbitrary Lagrangian-Eulerian (ALE) framework. Cylindrical particles experience an oscillatory motion under low electric fields. As the electric field increases, the induced DEP force acting on the particle gradually diminishes the oscillatory motion. Once the electric field is larger than a certain threshold value, the particle only translates with its axis parallel to the applied electric field after a short oscillatory motion. The numerical predictions are in good agreement with the experimental results.   

Modeling Electrophoresis of Microtubules in Microchannels

We simulate the electrophoretic motion of individual microtubules in microchannels in order to obtain their anisotropic mobility and compare with recent experimental results (van den Heuvel et al., PNAS, 2007). We include for comparison simulation results for a circular cylinder with a similar ``effective'' radius, in order to examine how the surface roughness of microtubules affects the electrical double layer, the externally applied field, and hence the electrophoretic mobility. The simulation method is based on the smoothed profile method (SPM) -- an immersive-boundary-like method --and spectral element discretization. The new method allows for arbitrary differences in the electrical conductivities between the charged surfaces and the ionized solution.   

Electrophoresis of deformable elastic particles

Electrophoretic motion of a deformable dielectric elastic particle, having a fixed zeta potential,placed in an external electric field, has been numerically simulated. The potential field is solved in the fluid external to the particle, to compute the applicable Helmholtz-Smoluchowski slip boundary conditions on the particle surface. A constitutive equation is constructed for an incompressible neo-Hookean elastic solid where the extra stress tensor is assumed to be linearly proportional to the $Almansi$ strain tensor, to govern the deformation of the particle. A monolithic finite element solver which uses an Arbitrary Lagrangian-Eulerian moving mesh technique is then used to solve the velocity, pressure and stress field in both the fluid and solid phases simultaneously. The particle is initially elliptical and is aligned perpendicular to the direction of the applied electric field. Elastic deformation is observed as the particle moves. Two cases of zero and finite Reynolds number are examined to delineate the effect of the inertial terms on the deformation of the particle. The stress and pressure distributions on the particle surface are also compared with some analytical solutions.   

Effects of Ion Sterics and Hydrodynamic Slip on Electrophoresis of a Colloidal Particle

The classical theory of a spherical colloids' electrophoretic mobility is founded on the Poisson-Nernst-Planck (PNP) equations and assumes the standard hydrodynamic no-slip boundary condition at the fluid/solid interface. In the (common) limit of thin double-layers, the mobility has long been known to exhibit a maximum at some zeta potential, then decrease and asymptote to a constant value. Dukhin, O'Brien, White and others showed this to result from the importance of excess ionic surface conductivity within the double-layer. The fundamental assumptions that underpin this result are, however, subject to challenge: in recent years, a finite liquid/solid slip has been measured over a variety of surfaces, and the PNP equations predict physically impossible ion concentrations precisely at the high zeta potentials where the mobility maximum occurs. Here, we discuss the dramatic effect that hydrodynamic slip and finite-ion-size steric effects in double-layers have upon the electrophoretic mobility of spherical colloids, and therefore upon the interpretation of electrophoretic mobility measurements.   

Electrokinetic Traveling Waves in Non-Dilute Colloidal Dispersions

The existence of electrokinetically-driven, traveling waves in colloidal dispersions is presented. A non-dilute colloidal dispersion of 2 micron polystyrene microspheres are exposed to an ac electric field. Traveling waves consist of alternating regions of compressed and rarefied particle volume fraction that propagate through the dispersion parallel to the applied field. Colloids under the application of these ac fields have no net displacement, yet the travelling waves propagate at speeds at a tenth of the RMS electrophoretic velocity of individual particles. The collective dynamics of the colloids are described by the one dimensional, inviscid Burgers' equation. The waves originate from the modification of the colloid velocity due to the mobility's dependence on the local volume fraction and the particle electrokinetic polarization dipole interactions. The Burgers' equation analysis is used to predict the wave speed of the traveling waves.   

Aggregation and Coalescence of Emulsion Droplets via Electrohydrodynamic Flows

Electrohydrodynamic (EHD) flows are known to cause rigid colloids to aggregate near electrodes [1]. Here we report that EHD flows also induce immiscible liquid droplets to aggregate and, for sufficiently strong electric fields, to coalesce. We measure the aggregation and coalescence rates of micron-scale olive oil droplets in water, and we interpret the coalescence rates in terms of a balance between EHD flow and repulsive colloidal scale (DLVO) forces. The results have broad implications for industrial processes in which trace amounts of immiscible oils need to be removed from aqueous solutions.\\[4pt] [1] Ristenpart, Aksay \& Saville, J. Fluid Mechanics 575, 83, (2007).   

Electric field induced self assembly of floating rectangular plates

We show that an external electric field normal to a fluid-fluid interface can be used to self assemble rectangular plates floating on the interface and that the lattice spacing of the monolayer thus formed can be varied by changing the electric field intensity. In our experiments, a rectangular plate floats so that the contact line is pinned at the upper edge. Plates experience lateral forces due to capillarity which cause them to cluster. In the presence of an electric field, plates are also subjected to the repulsive electrostatic forces which, together with the attractive capillary forces, determine the equilibrium spacing of the monolayer. The interface profile around the plates is also modified by the electric field.   

Brownian Dynamics modeling of electrophoretic dsDNA-molecule separation using nanofluidic devices

We present a Brownian Dynamics model of electrophoretic separation of short (up to 7 persistence lengths) dsDNA molecules in nanofluidic devices. Our formulation uses the Worm-Like-Chain model with hydrodynamic interactions. Our simulation results are in good agreement with the experimental results of Fu et al. [{\it Phys. Rev. Lett.}, {\bf 97}, 018103, 2006] for realistic values of all physical parameters. We also find good agreement between our simulation results and the theoretical model of Li et al. [{\it Anal. Bioanal. Chem.}, {\bf 394}, 427, 2009] who proposed an asymmetric separation device that operates under the effect of an alternating electric field.