Body force gravitational

In this section, we first introduce interfadal tension and consider a resting fluid interface, and discuss its interaction with a microchannel wall. We continue with consideration of dynamically moving fluid interfaces that are relevant to multiphase microflows. The diEFerent body forces, gravitational, viscous and inertial effects are... 

The creation terms embody the changes in momentum arising from external forces in accordance with Newton s second law (F = ma). The body forces arise from gravitational, electrostatic, and magnetic fields. The surface forces are the shear and normal forces acting on the fluid diffusion of momentum, as manifested in viscosity, is included in these terms. In practice the vector equation is usually resolved into its Cartesian components and the normal stresses are set equal to the pressures over those surfaces through which fluid is flowing. 

Several additional studies [Winitzer, Sep. ScL, 8(1), 45 (1973) ibid., 8(6), 647 (1973) Maru, Wasan, and Kintner, Chem. Eng. Set., 26, 1615 (1971) and Rapacchietta and Neumann, J. Colloid Inteiface ScL, 59(3), 555 (1977)] which include body forces such as gravitational acceleration and buoyancy have been made. A typical example of a force balance describing suen a system (Fig. 22-39) is summarized in Eq. (22-41). 

Here v is the space- and time-dependent velocity field, p is the density of the fluid, p is the local pressure, v is the kinematic viscosity, and / is some arbitrary body-force acting on each small element of the fluid (gravitation, for example). 

In this balance p is the static pressure, xtj is the stress tensor, and pgt is the gravitational body force. Ft is an external body forces component it can include forces from interaction between phases, centrifugal forces, Coriolis forces, and... 

The results are shown in Fig. 5. We notice that the EOS calculated with the microscopic TBF produces the largest gravitational masses, with the maximum mass of the order of 2.3 M , whereas the phenomenological TBF yields a maximum mass of about 1.8 M . In the latter case, neutron stars are characterized by smaller radii and larger central densities, i.e., the Urbana TBF produce more compact stellar objects. For completeness, we also show a sequence of stellar configurations obtained using only two-body forces. In this case the maximum mass is slightly above 1.6 M , with a radius of 9 km and a central density equal to 9 times the saturation value. 

In the case of hydrostatic pressure arising from gravitational forces, this may be removed by simply neglecting the gravitational body force in the N-S Equation (5). For the thermodynamic pressure, it is less obvious what can be done. However it may be noticed that at equilibrium, the N-P Equation (1) is satisfied and the ion fluxes are zero. It can now be seen that the thermodynamic... 

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. 

Next, we consider the forces that act on the control volume. The body forces are due to gravitation and act on all the mass in the control volume ... 

Free or natural convection occurs when fluid motion is generated predominantly by body forces caused by density variations, under the earth s gravitational field. In the absence of the gravitational field, body forces may be caused by surface tension. The subject material here is focussed on heat transfer with motion produced by buoyancy forces. 

When a fluid moves under natural convection Because of body forces caused by density variations This phenomenon results from the earth s field of gravitation Body forces may also be caused by surface tension. 

Potential energy. Potential energy (P) is energy the system possesses because of the body force exerted on its mass by a gravitational or electromagnetic... 

In these equations, tt is the molecular flux of momentum and g and F are gravitational acceleration and external body forces, respectively. The physical interpretation of the various terms appearing in these equations again follows similar lines the first term is the rate of increase in momentum per unit volume the second term represents... 

The body forces have an effect on all the particles in the body. They are far ranging forces and are caused by force fields. An example is the earth s gravitational field. The acceleration due to gravity g acts on each molecule, so that the force of gravity on a fluid element of mass AM is... 

In the case of gravitational force with kj = gj and fj = QQj, in general it holds that fj = gkj. Other body forces are centrifugal forces or forces created by electromagnetic helds. 

Forces that act on a fluid can be classified as either body forces or surface forces. Body forces are distributed throughout the material, e.g., gravitational, centrifugal, and electromagnetic forces. Surface forces are forces that act on the surface. 

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. 

Eqs. (11) and (12) must be modified if gravitational and centrifugal body forces are involved. 

Not all the terms in these equations have the same importance in determining the flow solution in chemical reactors. The only body force considered in most reactor models, gj (per unit mass), is gravitation which is the same for all chemical species, g. The model equations for momentum and energy can then be simplified. In the momentum equation Pc c = f cS = PS-In the energy equation Xlc=i(jc Sc) = Sc=i jc S = 0- Furthermore, in most multicomponent flows, the energy or heat flux contributions from the interdiffusion processes are in general believed to be small and omitted in most applications, ft-cV jc 0 (e.g., [148], p. 816 [89], p. 198 [11], p. 566). 

---