Generalized drag force

The generalized drag force per unit mixture volume which is acting on the dispersed phases of mean diameter d is commonly formulated as [112, 113, 114, 115, 168, 4, 54, 57, 58, 154, 119, 120] ... 

The net hydrodynamic force, frequently also referred to as the generalized drag force, is usually further divided into numerous contributions like the steady drag, virtual mass, lift, and history forces ... 

We reiterate that for a dispersed flow Fp the macroscopic generalized drag force normally contains numerous contributions, as outlined in chap 5. However, for gas-solid flows the lift force the virtual mass force fy, and the Besset history force components are usually neglected [39]. The conventional generalized drag force given by (5.27) thus reduces to ... 

The interfacial pressure difference effect and the combined interfacial shear and time fraction gradient effect are treated in the same manner as suggested discussing the analogous terms in (3.161). The modified definition of the generalized drag force follows naturally from an analogy to (3.163). 

Generalized drag force per unit mixture volume (N/m )... 

The drag force is exerted in a direction parallel to the fluid velocity. Equation (6-227) defines the drag coefficient. For some sohd bodies, such as aerofoils, a hft force component perpendicular to the liquid velocity is also exerted. For free-falling particles, hft forces are generally not important. However, even spherical particles experience lift forces in shear flows near solid surfaces. 

The term mist generally refers to liquid droplets from submicron size to about 10 /xm. If the diameter exceeds 10 /xm, the aerosol is usually referred to as a spray or simply as droplets. Mists tend to be spherical because of their surface tension and are usually formed by nucleation and the condensation of vapors (6). Larger droplets are formed by bursting of bubbles, by entrainment from surfaces, by spray nozzles, or by splash-type liquid distributors. The large droplets tend to be elongated relative to their direchon of mohon because of the action of drag forces on the drops. 

In the general case, the direction of movement of the particle relative to the fluid may not be parallel with the direction of the external and buoyant forces, and the drag force then creates an angle with the other two. This is known as two-dimensional motion. In this situation, the drag force must be resolved into two components, which complicates the treatment of particle mechanics. This presentation considers only the one-dimensional case in which the lines of action of all forces acting on the particle are collinear. 

Note /3 is, in general, not a constant, rather it must be found from a general expression for the drag force. 

Although CE separations can be reasonable well described by the classical theoretical relationships for electrophoretic migration, slight deviations from the theory occur in the case of many classes of solutes. Thus, it has been reported that the CE separation of oligosaccharides follow the general rule [124], while the description of the separation of DNA in polymer solutions necessitated a new mathematical model. The drag forces were expressed by... 

It will be noted in Fig. 9 that diffusional forces are small compared with other forces for particles smaller than 1000 microns in diameter. Inertial forces can become significant with particles larger than 10 microns. Fluid drag forces can be of the same general order as van der Waal s forces at these assumed high velocity levels. Electrostatic forces can be quite large but only... 

Eq. (2.119). A diffusion equation of the form given in Section IV is recovered if and only if we identify (Fa )f as a hydrodynamic drag force, and (as for the rigid system) assume that it may be described by a generalized Stokes equation of the form given in Eq. (2.74), where U is defined for a stiff system by Eq. (2.106). 

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