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Modeling of Micro- and Nanoscale Electromechanical Systems and Devices
Published in Sergey Edward Lyshevski, Nano- and Micro-Electromechanical Systems, 2018
The electromagnetic force is found applying the Maxwell stress tensor. This concept employs a volume integral to obtain the stored energy, and F=∫υ(ρυE+J×B)dv=1μ∮sTs↔·ds
Electromagnetic Fields in Transformers: Theory and Computations
Published in S.V. Kulkarni, S.A. Khaparde, Transformer Engineering, 2017
Maxwell stress tensor: This is widely used for electromagnetic force computations. The local force distribution in the magnetized bodies (without magnetostriction) can be expressed as [57, 58] () Fv=−12H⋅H∇μ.
Electrodynamic multiple-scattering method for the simulation of optical trapping atop periodic metamaterials
Published in Journal of Modern Optics, 2018
Vassilios Yannopapas, Emmanuel Paspalakis
where denotes the time average, is the normal vector at the surface surrounding the object, and . The components of the Maxwell stress tensor are given by is the Kronecker symbol and are the electric permittivity and magnetic permeability of vacuum, respectively. The field appearing in Equation (10) is the total field outside the sphere, i.e. the sum of the incident and scattered fields: , where and are given by Equations (4) and (6), respectively. By substituting Equations (4) and (6) into Equation (10) and by performing the surface integration analytically we obtain a final formula for the EM force. Explicit relations for the EM force acting on a homogeneous sphere (such as the one considered in the test case below) can be found elsewhere [50,51].
Electroplasticity: A review of mechanisms in electro-mechanical coupling of ductile metals
Published in Mechanics of Advanced Materials and Structures, 2022
Nikolay K. Dimitrov, Yucheng Liu, M. F. Horstemeyer
The Maxwell stress tensor methodology, as described in Appendix A, shows great potential in solving numerous electromagnetic problems (pinch and skin effects, Lorenz law force, nonequilibrium electrostatic fields) using algebraic techniques, similar to those with mechanical stress tensors. To this day, the Maxwell stress tensor has not been implemented in the EP theory of metals.
Electric Field Controlled Heat Transfer Through Silicon and Nano-confined Water
Published in Nanoscale and Microscale Thermophysical Engineering, 2019
One of the major active heat transfer control techniques emerged from the use of an electric field to manipulate the solid and/or liquid domains, and their interface couplings. For example, the major challenge of boiling heat transfer known as the Leidenfrost phenomenon could be resolved by the aid of an electric field [6–8]. The vapor film formed on a surface can be removed by drawing liquid toward the surface with an applied electric field to boost surface wetting. Also known as electrowetting, interface energy between solid and liquid can be actively controlled by an electric field [9]. Electrowetting-on-dielectric (EWOD) is its main application where the electrodes are covered by a dielectric layer acting as a capacitor. Variation of wetting angle as a function of the applied electric field was examined theoretically by the Lippmann–Young equation [10, 11]. Fundamentally, an electromechanical force is applied on the system as the Maxwell stress tensor. In the case of an ionic liquid, the prominent net force develops on the ions, which is the conventional EWOD principal. On the other hand, in the case of a deionized polar liquid, a bulk force can only be formed on its dipoles if there is a non-uniform electric field, as described in dielectrowetting applications using dielectrophoretic forces [12]. Instead, a polar dielectric liquid can be controlled by manipulating its molecular dipole distribution in a uniform electric field. For example, dipolar water molecules tend to orient along the applied electric field direction, and such reorientations and shifts produce a net stretching action [13–16]. Orientation polarization in water dominates the intermolecular forces as a function of the electric field strength that water elongates in the direction of the electric field known as electrostretching [15]. Alteration of dipole distribution results in a change of phase transitions of water [17]. Water molecules start to form crystalline structures, even at room temperature, under an electric field, which is known as electro-freezing [18–20]. The ice-like structures were imaged at room temperature by means of atomic force microscopy [21, 22]. Such structural manipulations were proven to be useful for active thermal conductivity control of both solids [23, 24] and liquids [25].