Fano flow

Now let us take a look at a recent NMR imaging experiment of Fano flow, in which the local velocities in the tubeless column were mapped out quantitatively and nondestructively [20], For such a set-up, the weight force of the column is balanced by the extensional stress difference azz - axx associated with the vertical velocity gradient (dvz/dz), as... 

P. T. Callaghan, Y. Xia 2004, (Nuclear magnetic resonance imaging and veloc-imetry of Fano flow),/. Phys. Condens. Matter 16, 4177- 1192. 

Fanning number, 59 Fano flow, 632 Faraday-Verdet effect, 299 Fatigue, 832 failure, 469 life, 832 limit, 832 resistance, 832 tester, 832... 

The siphon phenomenon is normally conducted by a tube. Polymer melt can suck the liquid into the tube even if the tube end locates high above the liquid surface, because of a significant viscoelastic effect. Such a flow is also called Fano flow (Fano 1908). Another situation is the pouring of the viscous polymer melt from a cup. Once the flow starts, the polymer melt can be continuously poured out, even if the liquid surface inside the cup becomes lower than the cup edge, as illustrated in Fig. 7.16. So far, a clear theoretical descriptirMi of this phenomenon is still lacking. 

Velocimetry. - An analytic model for the velocity field within a tubeless siphon (Fano flow) was presented. The model was based on a simple differential equation in which extensional, shear and gravitational pressure gradient forces are balanced. The role of surface tension in determining boundary conditions for the flow is considered. The analysis is applied to NMR velocimetry data (Xia and Callaghan, J. Magn. Reson., 2003, 16, 365) on a... 

A variation on fiber spinning is the ductless or tubeless siphon, which is simply fiber spinning in reverse. A nozzle is dipped in a bath of the test fluid, a vacuum applied, and fluid sucked out of the bath. The nozzle is slowly raised, and a free-standing, rising colunm of fluid develops as shown in Figure 1.4. Sometimes the tubeless siphon is called a Fano flow, after the physician who first reported the technique (1908). 

Fig. 4.3.1 (a) Photographs of a tubeless siphon formed by dissolving 0.5%w/v poly (ethylene oxide) powder in tap water, where a Fano column can be seen between the tip of the glass pipette at the top and fluid reservoir at the bottom, (b) Excess fluid can be seen just below the fluid entrance, (c) A large amount of excess fluid eventually flows downwards outside and along the Fano column, which can disturb the vertical location of the column. These figures illustrate the fact that there is an optimum volume flow rate for a particular flow system. 

Fig. 4.3.6 Velocity maps and profiles at differ- mark the NMR foldbacks from the stationary ent heights of the Fano column. The dark ring fluid at the inner surface of the fluid reservoir, surrounding the pipe at z= 1.5 mm (larger In the velocity profiles, the solid curves are the white arrow) is due to a layer of stationary fluid calculated Poiseuille profiles in tube flow, adhering to the pipe exterior following the Velocity images are reprinted from Ref. [20], dipping of the pipe into the reservoir at the with permission from Elsevier, start of the experiment. The small white arrows...

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