Flow velocity gradient

Cross-Flow Velocity Gradient Combined with a Field Action... 

Fig. 5.5. The Saffman force on a particle in a shear flow. The sketch illustrates that this lift force is caused by the pressure distribution developed around the sphere due to particle rotation induced by the shear flow velocity gradient.

When concentration, temperature or flow velocity gradients exist in a gas, the Brownian movement of the molecules tends to reduce these differences. Table 1 shows an inventory of these phenomena and of the corresponding laws. 

The viscosity of gases is such that, if there is a flow velocity gradient between two adjacent filaments, the faster tends to accelerate the slower, and the slower to slow down the faster in other words, there is transport of momentum from regions of high velocity towards those of low velocity, i.e. in the opposite direction to the velocity gradient. The corresponding law is NEWTON s law. 

The first three terms on the right-hand side of Eq. (5.6) account for the diffusion of turbulence dissipation, the mean flow velocity gradient production term, and the homogeneous dissipation term. The last group of terms in Eq. (5.6) describes the effect of interfacial momentum transfer on the production of turbulence dissipation. The time constant is given by the following empirical correlation ... 

One other limitation to elementary equations is that the material being examined is typically assumed to be isotropic, with equal stiffness in all directions. However, molded plastic parts are likely to have at least some orientation, as a result of flow velocity gradients that exist during the melt-processing operation (see Chapter 7). Reinforced plastics and composites do exhibit strong anisotropy, because there is much higher stiffness along the fiber direction than in the transverse direction. 

The subscripts 1, 2, and 3 refer to the flow, velocity gradient, and neutral directions, respectively, and X2 is the vertical distance measured from the fixed plate. Apart from pressure, the forces acting on each element of the liquid are also the same everywhere. 

Flame stretch (FS) A measure of the velocity at which a flame surface changes due to the curvature and flow velocity gradients in front of the flame. 

Normal stress difference Complex fluid Rheometers Rheometry Viscometric flows Velocity gradient Rate of deformation Weissenberg effect Extrudate Die swell Melt fracture Hydrostatic pressure Shear direction Anisotropic... 

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