Dynamics of Electrorheological Suspensions Subjected to Spatially Nonuniform Electric Fields

Abstract

A numerical method based on the distributed Lagrange multiplier method (DLM) is developed for the direct simulation of electrorheological (ER) liquids subjected to spatially nonuniform electric field. The flow inside particle boundaries is constrained to be rigid body motion by the distributed Lagrange multiplier method and the electrostatic forces acting on the particles are obtained using the point-dipole approximation. The numerical scheme is verified by performing a convergence study which shows that the results are independent of mesh and time step sizes. The dynamical behavior of ER suspensions subjected to nonuniform electric field depends on the solids fraction, the ratio of the domain size and particle radius, and four additional dimensionless parameters which respectively determine the importance of inertia, viscous, electrostatic particle-particle interaction and dielectrophoretic forces. For inertia less flows a parameter defined by the ratio of the dielectrophoretic and viscous forces, determines the time duration in which the particles collect near either the local maximums or local minimums of the electric field magnitude, depending on the sign of the real part of the Clausius-Mossotti factor. In a channel subjected to a given nonuniform electric field, when the applied pressure gradient is smaller than a critical value, the flow assists in the collection of particles at the electrodes, but when the pressure gradient is above this critical value the particles are swept away by the flow.

Micro- and nanoparticles self-assembly for virtually defect-free, adjustable monolayers

“…Similarly, the electrostatic interactions among polarized particles, which normally cause the particles to cluster in the direction of the electric field when particles are suspended in a bulk fluid (mutual attraction leading to chain formation), create here repulsive forces instead, thus preventing the particles from clustering. To further explain this, we note that when the line joining the centers of two particles is perpendicular to the electric field, the force acting on them is repulsive and when it is parallel the force is attractive (16)(17)(18)(19)(20)(21)(22)(23). The former orientation, however, is typically unstable, and therefore, particles of an electrorheological suspension cluster into chains aligned with the electric field direction.…”

“…However, the repulsive forces caused by the interparticles electrostatic interactions (Eq. 2) decay relatively faster (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23) with the distance between the particles (these forces decay as r Ϫ4 ). Because the repulsive force decays faster than the attractive capillary force, there is an equilibrium distance at which the two curves intersect and the total lateral force acting on the particles is zero.…”

Magnetically controlled dielectrophoresis of metallic colloids

“…Several experimental and theoretical works demonstrated that the basic theory of DEP and electrorotation [1,13,14] may successfully be applied to predict full trajectories [15] or equilibrium configurations (chaining) [16] of spherical dielectric beads. For particles of arbitrary shapes, analytical multipolar approaches [17] and numerical strategies [18] have already been proposed.…”

Concentrating particles on drop surfaces using external electric fields

“…Using this expression, it is easy to show that the electrostatic interaction force between two particles is attractive and also that it causes the particles to orient such that the line joining their centers is parallel to the electric field direction (except in the degenerate case when the line joining their centers is perpendicular to the electric field, in which case they repel). Similar interactions take place between particles in a nonuniform electric field [27,30,31]. Direct numerical simulations (DNS) conducted using this expression for the interaction force show that two particles subjected to a nonuniform electric field attract each other and orient such that the line joining their centers is parallel to the local electric field direction while they move together toward the location where the electric field strength is locally maximal or minimal, depending on the value of their dielectric constant relative to that of the two fluids [32][33][34].…”

“…If a particle is sufficiently small compared to the length scale over which the nonuniform electric field varies, the point dipole (PD) approach can be used to estimate the DEP force. According to the PD model, which assumes that the gradient of the electric field is constant, the time averaged DEP force acting on a spherical particle in an AC electric field is given by [27][28][29][30] …”