Body force electric

Assuming that the current in the gas is carried mostly by electrons, the induced electric field uB causes transverse electron motion (electron drift), which, being itself orthogonal to the magnetic field, induces an axial electric field, known as the Hall field, and an axial body force, F, given by... 

Electrokinetics. The first mathematical description of electrophoresis balanced the electrical body force on the charge in the diffuse layer with the viscous forces in the diffuse layer that work against motion (6). Using this force balance, an equation for the velocity, U, of a particle in an electric field... 

It is useful to think of two different kinds of forces, one that acts over the volume of a fluid element and the other that acts on the element s surface. The most common body force is exerted by the effect of gravity. If an element of fluid is less dense than its surroundings (e.g., because it is warmer), then a volumetric force tends to accelerate it upward—hot air rises. Other fields (e.g., electric and magnetic) can exert volumetric body forces on certain fluids (e.g., ionized gases) that are susceptible to such fields. Here we are concerned mostly with the effect of gravity on variable-density flows,... 

The field forces, also known as the body forces, are long-range forces exerted by various fields outside the flow system. Typical field forces in a gas-solid system include the gravitational force, the electric force, and the magnetic force. 

The direction of the electric current varies from one location to another. A uniform magnetic field normal to the channel bottom is applied. By coupling of the electric and the magnetic forces, a Lorentz body force is yielded which is perpendicular to the electric and magnetic fields and directed towards the side walls. The direction of this force also alternates. As a result, the fluid is moved up- and downwards. The net effect is eddy-type convection. 

If the propellant is to be accelerated by electric body forces a primary requirement is that the propellant be a charged particle. While interest has centered on positively charged atomic ions, the use of both negatively and positively charged colloids has been considered. 

In electrophoresis of colloidal particles, the inertial effect is typically much smaller than the viscous effect for the fluid motion so that the fluid flow is governed by the Stokes equations incorporating an electric body force... 

The characterization and control of electrostatic forces are of particular interest. Electrostatic forces depend on the electric charge and potential at the particle surfaces. When subjected to a uniform, unidirectional electric field E. charged colloidal particles accelerate until the electric body force balances the hydrodynamic drag force, so that the particles move at a constant average velocity v. This motion is known as electrophoresis, and v is the electrophoretic velocity. 

Body forces relevant to flame structure may be electrical forces acting on ionized species for flames in strong electric fields we do not discuss influences of electric fields. 

The forces acting on the control volume consist of body forces that act throughout the entire body of the control volume (such as gravity, electric, and magnetic forces) and are proportional to the volume of the body, and surface forces that act on the control surface (such as ihe pressure forces due to hydrostatic pressure and shear stresses due to viscous effects) and are proportional to the surface area. The surface forces appear as the conlrol volume is isolated from it.s surroundings for analysis, and the effect of the detached body is replaced by a force at that location. Note that pres.surc represents the compressive force applied on the fluid element by the surrounding fluid, and i.s always directed to the surface. 

Consider a microchannel filled with an aqueous solution. There is an eleetrieal doubly layer field near the interface of the channel wall and the liquid. If an electric field is applied along the length of the channel, an electrical body force is exerted on the ions in the diffuse layer. In the diffuse layer of the double layer field, the net charge density, pe is not zero. The net transport of ions is the excess counterions. If the solid surface is negatively eharged, the counterions are the positive ions. These excess counterions will move under the influenee of the... 

Particles from a dispersion can be convected to the inner or outer surface of a porous substrate in contact with the dispersion due to fluid flow through the porous support. Also body forces due to centrifugal or electric fields can, in principle, be used to assist the particle transport towards the substrate. When the support is not permeable for the particles in the dispersion, the particle transport results in a more or less dense particle compact. The gravitational force on the particles can also contribute to the particle packing process when the gravitational force is in the same direction as the fluid flow. 

The forces acting on the control volume include surface forces, such as pressure forces, and shear stresses caused by velocity gradients and body forces, such as gravity. We consider only the pressure forces in the analysis that follows the effects of other forces, such as gravity and electric fields, will be discussed in more detail in a later chapter (and from a rather different viewpoint too). Actually, the system as a whole is assumed to be at constant pressure and there is, therefore, no net force acting on the mixture as a whole. 

When an electrical field of intensity E is applied in parallel to a charged flat interface, the excess of counterions in the diffuse layer gives rise to a body force exerted on the liquid. The liquid starts moving with local velocity varying from zero in the plane of shear (x = x ) to some maximal value. 

Work, like energy, can take various forms mechanical, electrical, gravitational, etc. All have in common the fact that they are the product of two factors, an intensity term and a capacity term. For example, the simplest form of mechanical work arises when an object moves a certain distance against an opposing force. Electrical work is done when a body having a certain charge moves through a potential difference. 

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