Ehud Yariv

“Force-free” electrophoresis?

When a colloidal particle is exposed to an externally applied electric field, it acquires an electrophoretic velocity, resulting from fluid slip occurring across the Debye screening layer. When the field is uniformly applied, it is usually assumed that the net neutrality of the combined particle-layer system implies that the net electric force acting on it must vanish. This assumption of “force-free” phoretic motion has been employed extensively to describe electrophoresis in both unbounded and bounded fluid domains [J. L. Anderson, Annu. Rev. Fluid Mech. 21, 61 (1989)]. A careful inspection reveals here that this intuitive premise may fail when the fluid domain is bounded, in which case a nonzero electric force (resembling dielectrophoretic forces in nonuniformly applied fields) may actually exist. Such forces (represented via surface integrals of Maxwell stresses) result in particle motion above and beyond the one driven by the phoretic slip mechanism. A positive demonstration for the existence of a suc...

Induced-charge electrophoresis of nonspherical particles

The electrophoretic motion of a conducting particle, driven by an induced-charge mechanism, is analyzed. The dependence of the motion upon particle shape is embodied in two tensorial coefficients that relate the particle translational and rotational velocities to the externally applied electric field. The coefficients are represented as surface integrals of the electric potential over the particle boundary, thereby eliminating the need to solve the flow field. Nonspherical particles may translate and∕or rotate in response to the imposed field, even if their net electric charge vanishes.

AN ASYMPTOTIC DERIVATION OF THE THIN-DEBYE-LAYER LIMIT FOR ELECTROKINETIC PHENOMENA

The thin-Debye-layer model for field-induced electrokinetic processes (e.g., electrophoresis) is driven using a systematic asymptotic methodology. Coxs method for analyzing the Debye-layer equations over curved interfaces (J. Fluid. Mech., 338, 1997) illuminates the subtlety in the prevailing assumption of a locally flat boundary.

Electro-osmotic flow near a surface charge discontinuity

Electro-osmotic flows in the vicinity of surface charge density transitions are studied using a two-dimensional model problem. The analysed configuration consists of an electrolyte solution in contact with a dielectric planar wall, on which the density transition is approximated by a finite jump. The flow field in the semi-infinite fluid domain is driven by an external electric field which is applied parallel to the charged wall, in the direction of the jump. The problem is analysed using both the thin-Debye-layer (TDL) formulation, which does not resolve the fine details of the Debye-layer structure, and an approximate electrokinetic model

Electro-convection about conducting particles

A perfectly conducting spherical particle is suspended within an electrolyte solution and is exposed to a uniformly applied electric field. Using a weak-field approximation, the electro-kinetic flow is analysed for arbitrary Debye-layer thickness, the commonly employed thin-layer model emerging as a special case. We identify a scalar property which quantifies the global strength of the quadrupolar flow structure.

Nonlinear electrophoresis of ideally polarizable particles

An initially charged ideally polarizable spherical particle is placed under a uniformly imposed electric field. The ensuing electrokinetic transport in the thin–Debye-layer limit is characterized by three voltage scales, associated with the respective effects of initial charge, applied field, and ionic thermal motion. The magnitude of these three scales affects the asymmetric zeta-potential distribution along the particle surface, and then also the electrophoretic velocity engendered by the accompanied electro-osmotic slip. An analysis is presented for arbitrary (non-small) zeta-potentials, thus extending the small–zeta-potential prevailing models. The evaluation of the zeta-potential distribution is made non-trivial by its dependence upon the (uniform) value of the particle potential. This value, which is not a priori prescribed, is determined using global charge conservation arguments. Due to the nonlinear Debye-layer capacitance, the electrophoretic mobility of the particle differs from that of a comparable non-polarizable particle possessing the same net electric charge. Specifically, it decreases monotonically with both initial particle charge and applied-field magnitude. Extensions to non-spherical particles are also described.

Electro-osmotic flows over highly polarizable dielectric surfaces

A thin-Debye-layer macroscale model is developed and analyzed for electrokinetic flows about dielectric surfaces, wherein solid polarization modifies the zeta-potential distribution. The harmonic electric potential within the solid is governed by a nonlinear boundary condition, which constitutes a generalization of the linear Robin-type condition of Yossifon et al. [Phys. Fluids 19, 068105 (2007)] to voltages comparable with the thermal scale. The resulting polarization model is demonstrated in the classical context of spherical-particle electrophoresis, where the electrophoretic mobility—now a function of applied-field magnitude and solid permittivity—is evaluated using both eigenfunction series expansions and asymptotic approximations. For strong polarization, the mobility saturates at a field-dependent value which is lower than the comparable Smoluchowski slope. At strongly applied fields, the mobility diminishes at a rate that corresponds to a logarithmic increase of particle velocity with applied-fie...

Slender-body approximations for electro-phoresis and electro-rotation of polarizable particles

Slender-body asymptotic theory is used to evaluate the translational and rotational electrophoretic velocities of initially uncharged polarizable bodies of revolution. These velocities are obtained as asymptotic expansions in the small particle slenderness. Conducting particles which lack fore-aft symmetry translate parallel to the applied field direction, regardless of their orientation relative to it. Both conducting and dielectric particles tend to align with the field. The translational and rotational velocities of dielectric particles are asymptotically smaller than those of comparable conducting particles.

Flow animation by unsteady temperature fields

Simple mass conservation principles show that unsteady temperature fields in thermally expandable fluids are always accompanied by flow, even in the absence of gravity. This mechanism is demonstrated using several model problems, which exhibit its peculiar features. The thermally induced flows become substantial in small-scale systems, suggesting possibilities for microfluidic applications.

Self-propulsion in a viscous fluid: arbitrary surface deformations

The self-propulsion of a generally deformable body at low-Reynolds-number conditions is discussed. The translational and rotational velocities of the body relative to an inertial reference system are presented as surface quadratures using a Lagrangian ‘body-fixed’ shape description. The power dissipated into the fluid is obtained as a quadratic functional of the surface deformation rate. For symmetric strokes, the net displacement obtained by the execution of a single deformation cycle is provided by a functional of the intrinsic swimmer shape and its time derivative.