Inertia and Secondary Flow

The main sources of error in the concentric cylinder type measuring geometry arise from end effects (see above), wall shp, inertia and secondary flows, viscous heating effects and eccentricities due to misahgnment of the geometry [Macosko, 1994],... 

If we used the Stokes equation to calculate the viscosity in a faUing-ball viscometer when the Re molds number is high, the viscosity appears to be too large, and we need to apply a correction to the formula. For small Reynolds numbers up to 2 this is accoimted for by a factor of 1/(1 + Re/16), where Re = lapV/rj. Figure 7 shows the form of the inertia-driven secondary flows developing behind the sphere in this situation which accoimt for the extra energy in the flow that could be misinterpreted as higher viscosity. 

Low viscosity limited by inertia corrections, secondary flow, and loss of sample at edges... 

The propenies of the solid-liquid or liquid-liquid interfaces are also important. often so important that their influence overshadows any other factor. The contribution of hydrodynamic driven phenomena such as slip Row, secondary flow, edge and end effects, viscous heating, and inertia may also play an important role (see Sec. IV). Good experimental and calculation procedures should ensure either that these factors are absent or that the data are corrected to eliminate their contribution. These will be discussed in Sec. IV. In the following sections, the main physicochemical factors that influence rheological behavior and viscosity are discussed. For the sake of clarity, a distinction will be made between the factors that are related to physical propeities such as composition and particle size, and physicochemical aspects, especially inteifacial properties. 

The effects of secondary flow on droplet collision and coalescence mechanisms have not been considered in the literature currently reviewed. The scale of secondary flow is much larger than the Kolmogorov microscale q and it will, therefore, only affect droplets of diameter d > q (those subject to turbulent inertia). Secondary flow will be most prevalent following changes in duct geometry, particularly where there is some form of duct divergence. 

Apart from the microchannel cross-section, the impact of non-straight charmels is crucial, especially for mixing applications, where serpentine channels have been shown to break symmetry and enhance mixing in bubbles [106]. Note that this enhanced mixing is due to chaotic advection in Stokes flow. Dean vortices, i.e. secondary flow patterns due to centrifugal inertia, are typically not a problem in low-inertia (Re< 1) microfluidic applications. 

Divergiiig Flows Diverging streamlines upstream at the contraction are a feature of contraction flows, which are mainly controlled by both elasticity and inertia. When the flow system reaches a critical value of Re, inertial effects cause a reduction in the size of the vortex and are often accompanied hy diverging flow patterns at the interface region between the main stream flow and the secondary stream flow (comer vortices), (see Fig. 1) as indicated by the dashed line at De 240. A comprehensive illustration... 

Inertia also generates secondary flows in the r9 plane. These have been observed for large cone angles (Giesekus, 1963 Hopp-man and Miller, 1963 Walters and Waters, 1968) and modeled theoretically for the Newtonian case (IVnian, 1969, 1972 Fewell and Heliums, 1977 Sdougas et al., 1984). Secondary flow will... 

Several flow irregularities occur in the cone-plate flow of molten polymers, and these limit the use of these fixtures at low shear rates [98]. One of these is secondary flow. It is known that Newtonian fluids exhibit an inertial instability leading to flow recirculation in cone-plate and plate-plate flow, but inertia is not a factor with molten polymers due to their high viscosity. However, for elastic fluids it can be shown that the circular streamlines that are assumed in cone-plate flow can become imstable when Nj is large. This instability leads to a secondary flow that increases with strength as the cone angle or gap is increased [98]. 

These devices are employed for fine powders (40-400 im) and also coarser particles. In the Franken or Vandenhoek inertial separators [13,14] (Fig. 4a) particle-air mixture enters from the top and falls down in the inlet pipe. The air turns abruptly to the outlet pipe inclined by about 45-50° and carries the fine particles. Coarse fraction proceeds straight down because of high inertia towards the discharge pipe. On its way this material undergoes repeated separation in a secondary air flow carrying fines into a curvilinear chamber. Then they exit via the outlet pipe with blades mounted for better air distribution. These classifiers, manufactured by Buell Co., are used for separation of pulverized limestone at cut size of 150 pra with feeds from a few pounds to 600 t/h [15], In the Buell s variant of this device [14] blades have different angles to increase the efficiency. Such devices were used for separation of 15-1000 pm particles. 

Near the top of the silo is an annular ring of a secondary solidified salt. As the temperature of the secondary salt increases, the salt melts, flows into the silo, and floods the silo to a higher level. The melting, heating, and boiling of the secondary salt can provide a significant source of thermal inertia ... 

Thus, with flow velocity decrease in the inertia drip pan and diameter of a drop the drop kinetic energy is diminished, and efficiency drop spreads is reduced. However, the increase in speed of a gas flow carmot be boimdless as in a certain velocity band of gases there is a sharp lowering of efficiency drop spreads owing to origination of secondary ablation the fluids trapped drops. For calculation of a breakdown speed of gases in the inertia drip pans it is possible to use the formula, m/s ... 

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