scholarly journals Reconstruction of the electric field of the Helmholtz equation in three dimensions

2017 ◽  
Vol 309 ◽  
pp. 56-78 ◽  
Author(s):  
Nguyen Huy Tuan ◽  
Vo Anh Khoa ◽  
Mach Nguyet Minh ◽  
Thanh Tran
Keyword(s):  
Electric Field ◽  
Helmholtz Equation ◽  
Three Dimensions

Direct Simulation of Electrorheological Suspensions

2001 ◽  
Author(s):  
Aijun Wang ◽  
Pushpendra Singh ◽  
Nadine Aubry
Keyword(s):  
Electric Field ◽  
Stokes Equations ◽  
Hydrodynamic Force ◽  
Particle System ◽  
Electrostatic Force ◽  
Body Motion ◽  
Three Dimensions ◽  
Spherical Particles ◽  
Point Dipole ◽  
Direct Simulation

Abstract A new distributed multiplier/fictitious (DLM) domain method is developed for direct simulation of electrorheological (ER) suspensions subjected to spatially uniform electrical fields. The method is implemented both in two and three dimensions. The fluid-particle system is treated implicitly using the combined weak formulation described in [1,2]. The governing Navier-Stokes equations for the fluid are solved everywhere, including the interior of the particles. The flow inside the particles is forced to be a rigid body motion by a distribution of Lagrange multipliers. The electrostatic force acting on the polarized spherical particles is modeled based on the point-dipole approximation. Using our code we have studied the time evolution of particle-scale structures of ER suspensions in channels subjected to the pressure driven flow. In our study, the flow direction is perpendicular to that of the electric field. Simulations show that when the hydrodynamic force is zero, or very small compared to the electrostatic force, the particles form chains that are aligned approximately parallel to the direction of electric field. But, when the magnitude of hydrodynamic force is comparable to that of the electrostatic force the particle chains orient at an angle with the direction of the electric field. The angle between the particle chain and the direction of the electric field depends on the relative strengths of the hydrodynamic and electrostatic forces.

A 3-D Numerical Modeling of Droplet Actuation via Electrowetting in Microchannels

2007 ◽  
Author(s):  
Alborz Arzpeyma ◽  
Ali Dolatabadi ◽  
Paula Wood-Adams
Keyword(s):  
Contact Angle ◽  
Numerical Modeling ◽  
Liquid Phase ◽  
Electric Field ◽  
Threshold Voltage ◽  
Contact Angle Hysteresis ◽  
Three Dimensions ◽  
Time Step ◽  
Droplet Behavior ◽  
Droplet Morphology

Numerical investigation is performed to study the droplet behavior under electrowetting actuation inside microchannels. Volume of Fluid (VOF) technique is employed to track the interface while the electric field is solved inside the whole domain in each time step simultaneously. The equations are solved in three dimensions for water as the liquid phase. Droplet morphology under the application of an electric field is investigated. Droplet velocity studied under different actuation voltages and compared to the experiments. Contact angle hysteresis and its effects on the threshold voltage are discussed.

A wideband fast multipole method for the Helmholtz equation in three dimensions

2006 ◽  
Vol 216 (1) ◽  
pp. 300-325 ◽  
Author(s):  
Hongwei Cheng ◽  
William Y. Crutchfield ◽  
Zydrunas Gimbutas ◽  
Leslie F. Greengard ◽  
J. Frank Ethridge ◽  
...  
Keyword(s):  
Helmholtz Equation ◽  
Fast Multipole Method ◽  
Three Dimensions ◽  
Fast Multipole ◽  
Multipole Method

Disturbance of a many-dimensional field satisfying the Helmholtz equation due to the presence of a hyperplane boundary

1958 ◽  
Vol 246 (1246) ◽  
pp. 423-428
Keyword(s):  
Boundary Conditions ◽  
Helmholtz Equation ◽  
Laplace Equation ◽  
Three Dimensions ◽  
Special Case ◽  
Disturbance Function

The disturbance function of an n -dimensional field satisfying the Helmholtz equation due to the presence of a hyperplane boundary is expressed in terms of the undisturbed function. The field may contain singularities on both sides of the boundary. In the special case of a field satisfying the Laplace equation in three dimensions the boundary conditions include those in hydrodynamics, heat, magnetism, and electrostatics.

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