Vortex viscosity

D. Antisymmetric Stresses, Internal Spin Fields, and Vortex Viscosity in Magnetic Fluids... 

Accompanying the impeded particle rotation is the (kinematical) existence of an internal spin field 12 within the suspension, which is different from one-half the vorticity to = ( )V x v of the suspension. The disparity to — 2 between the latter two fields serves as a reference-frame invariant pseudovector in the constitutive relation T = ((to — 12), which defines the so-called vortex viscosity ( of the suspension. Expressions for (( ) as a function of the volume of suspended spheres are available (Brenner, 1984) over the entire particle concentration range and are derived from the prior calculations of Zuzovsky et ai (1983) for cubic, spatially-periodic suspension models. 

These suspension viscosity concepts are of growing technological importance in rationalizing and quantifying the behavior and properties of so-called magnetic fluids (Rosensweig, 1982, 1985, 1987). In a novel proposal, Brenner (1984) outlined a potentially useful scheme to use the apparently rigid-body rotation of a dipolar suspension to measure its vortex viscosity... 

Ferrofluid suspension viscosity Hydrodynamic-to-magnetic volume fraction Scalar moment of inertia density Vortex viscosity Initial magnetic susceptibility LMM approximation correction... 

Offset constant of the applied magnetic field Ferrofluid/solid interface inside V Gravitational amplification factor of a-phase Goeffrcient in the Muller porosity model Porous medium porosity Bed holdup of a-phase Vortex viscosity Dynamic viscosity... 

Mitsoulis, E., Valchopoulos, J. and Mirza, F. A., 1985. A numerical study of the effect of normal stresses and elongational viscosity on entry vortex growth and extrudate swell. Poly. Eng. Sci. 25, 677 -669. 

Vortex-shedding flow meters typically provide 1% of flow rate accuracy over wide ranges on Hquid, gas, and steam service. Sizes are available from 25 to 200 mm. The advantages of no moving parts and linear digital output have resulted in wide usage in the measurement of steam, water, and other low viscosity Hquids. 

Fig. 4. Typical design elements foi wet deagglomeiation in low viscosity systems (a) a high, ipm lotoi (shown below its normal position within stator) produces turbulence and cavitation as blades pass each other (b) a rotating disk creates a deep vortex to rapidly refresh the surface, and up- and downtumed teeth at the edge cause impact, turbulence, and sometimes cavitation and (c) the clearance of a high rpm rotor can be reduced as the batch...

Special vortex no22le designs which deUver lower flows using a large opening have been used to reduce plugging problems. Also, viscosity-sensitive no22les, where flow is increased as viscosity is increased, are used to control variation in soflds concentrations. 

It is also interesting to note that the angular momentum conservation is assumed in predictions 4 and 9 however, the viscosity increases owing to temperature rise in the burnt gas, and the vortex motion diminishes rapidly behind the flame. The pressure behind the flame is raised up and becomes nearly equal to the ambient pressure. This may explain why the hot, stagnant gas model by Asato et al., line 5a, can considerably predict the results. 

In fluid dynamics the behavior in this system is described by the full set of hydrodynamic equations. This behavior can be characterized by the Reynolds number. Re, which is the ratio of characteristic flow scales to viscosity scales. We recall that the Reynolds number is a measure of the dominating terms in the Navier-Stokes equation and, if the Reynolds number is small, linear terms will dominate if it is large, nonlinear terms will dominate. In this system, the nonlinear term, (u V)u, serves to convert linear momentum into angular momentum. This phenomena is evidenced by the appearance of two counter-rotating vortices or eddies immediately behind the obstacle. Experiments and numerical integration of the Navier-Stokes equations predict the formation of these vortices at the length scale of the obstacle. Further, they predict that the distance between the vortex center and the obstacle is proportional to the Reynolds number. All these have been observed in our 2-dimensional flow system obstructed by a thermal plate at microscopic scales. ... 

Polymer solutions were prepared by dispersing the polymer powder in a saline solution prepared with distilled deionized water. Following complete dispersion in the vortex of the fluid the samples were agitated under mild conditions (< 100 RPM) until the solution was homogeneous. For some solutions the dissolution was so rapid that the agitation step could be eliminated. The polymer viscosities were then measured using a Ubbelohde viscometer. The pH of the polymer solutions was adjusted using dilute acetic acid and sodium hydroxide. Some polymers were supplied as liquids and were subsequently diluted with distilled deionized water to the appropriate concentration. 

On the reverse, how does the presence of particles affect local and global flow features in the vessel such as the vortex structure in the vicinity of the impeller, power consumption, circulation and mixing times, and the spatial distribution of turbulence quantities more specifically colliding particles have an impact on the liquid s turbulence (Ten Cate et al., 2004) while local particle concentrations affect the effective (slurry) viscosity which may be useful in the macroflow simulations ... 

If turbine or marine propeller agitators are used to mix relatively low viscosity liquids in unbaffled tanks, vortexing develops. In this case the liquid level falls in the immediate vicinity of the agitator shaft. Vortexing increases with rotational speed N until eventually the vortex passes through the agitator. As the liquid viscosity increases, the need for baffles to reduce vortexing decreases. 

The specific surface area of an industrial-sized continuous stirred tank reactor (CSTR) can be calculated from the reactor dimensions. However, it is difficult to estimate the effect of the formation of bubbles and of the stirrer-induced vortex at low melt viscosity. The calculation of the characteristic length of diffusion in a high-viscosity finishing reactor with devices for the generation of thin films with respective high specific surface areas is more complex. 

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